diff --git "a/1tE1T4oBgHgl3EQfRwOf/content/tmp_files/load_file.txt" "b/1tE1T4oBgHgl3EQfRwOf/content/tmp_files/load_file.txt" new file mode 100644--- /dev/null +++ "b/1tE1T4oBgHgl3EQfRwOf/content/tmp_files/load_file.txt" @@ -0,0 +1,1566 @@ +filepath=/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf,len=1565 +page_content='Characterizing Quantile-varying Covariate Effects under the Accelerated Failure Time Model Harrison T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Reeder Massachusetts General Hospital Biostatistics Department of Medicine, Harvard Medical School Kyu Ha Lee Departments of Nutrition, Biostatistics, and Epidemiology, Harvard T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Chan School of Public Health Sebastien Haneuse Department of Biostatistics, Harvard T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='H.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Chan School of Public Health Abstract An important task in survival analysis is choosing a structure for the relationship between covariates of interest and the time-to-event outcome.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For example, the accel- erated failure time (AFT) model structures each covariate effect as a constant multi- plicative shift in the outcome distribution across all survival quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Though parsi- monious, this structure cannot detect or capture effects that differ across quantiles of the distribution, a limitation that is analogous to only permitting proportional hazards in the Cox model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' To address this, we propose a general framework for quantile-varying multiplicative effects under the AFT model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Specifically, we embed flexible regression structures within the AFT model, and derive a novel formula for interpretable effects on the quantile scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' A regression standardization scheme based on the g-formula is proposed to enable estimation of both covariate-conditional and marginal effects for an exposure of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We implement a user-friendly Bayesian approach for estimation and quantification of uncertainty, while accounting for left truncation and complex cen- soring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We emphasize the intuitive interpretation of this model through numerical and graphical tools, and illustrate its performance by application to a study of Alzheimer’s disease and dementia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Keywords: Accelerated failure time model;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Bayesian survival analysis;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Left-truncation;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Time- varying coefficients;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Time-varying covariates This is the pre-peer reviewed, “submitted” version of the following article which is published in Biostatistics by Oxford University Press: Reeder HT, Lee KH, Haneuse S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Characterizing quantile-varying covariate effects under the accelerated failure time model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Biostatistics.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' kxac052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 2022 Jan 04.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' doi: 10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1093/biostatistics/kxac052.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' PMID: 36610077.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Arxiv will be updated with the final peer-reviewed “accepted” version of the manuscript after a 24 month embargo period.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 1 arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03057v1 [stat.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='ME] 8 Jan 2023 1 Introduction Modeling the relationship between a time-to-event outcome T and a vector of covariates X requires choosing a structure for the covariate effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The proportional hazards model is by far the most commonly used model, specifying a constant multiplicative effect on the hazard of the outcome, yielding a ‘hazard ratio.’ Though ubiquitous, hazard ratios can be difficult to interpret, and the constant effect across time—that is, the ‘proportionality’ of the hazards—is not always plausible (Hern´an, 2010;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Uno et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2015).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' As an alternative, the accelerated failure time (AFT) model directly describes shifts in the outcome distribution between populations having different characteristics, via multiplicative effects on event time quantiles (Wei, 1992).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Specifically, every survival quantile is multiplied by a constant ‘accel- eration factor,’ equivalent to a horizontal stretching or compressing of the survivor function.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In other words, the times by which 10 percent of events occur, or 90 percent, or 50 percent (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', the median survival time), or any other quantile, are shifted by the same multiplicative (or relative) constant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This common effect across quantiles is the central feature of the AFT model, making it highly interpretable because contrasts of survival quantiles are tangible and often clinically meaningful.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Despite the parsimony of a constant multiplicative effect, in some settings it may be important to allow for more flexible effects across quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For example, consider the study of Alzheimer’s disease (AD) and dementia among older adults.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Prospective cohort studies of incident AD and dementia typically enroll subjects and follow them over decades, often subject to left truncation and sometimes complex censoring.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Age at AD onset among those with a particular risk factor, for example, may skew earlier than among those without the risk factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' However, because AD is a complex disease that can arise over a long time scale, baseline risk factors may not affect the entire distribution uni- formly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This could occur if, for example, a risk factor did not affect the timing of ‘early-onset’ cases, but made ‘late-onset’ cases occur sooner.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Modeling hazard ratios flexibly across time is a well-known and commonly used tool un- der the Cox model, but analogous extensions of the AFT model are not well-studied.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Very recently, a paper by Crowther et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (2022) suggests a frequentist spline-based AFT model and discusses potential for time-varying effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' However, their work considers a less common interpretation of the acceleration factor on the scale of log time, rather than investigating the potential for flexibility on the quantile scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Moreover, their paper does not present any nu- merical results for the use of flexible effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Separately, a recent paper by Pang et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (2021) considers a Frequentist spline-based AFT model using a completely different formulation derived from Prentice and Kalbfleisch (1979), requiring a specialized estimation algorithm and bootstrapping for inference.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' However, these papers do not incorporate left truncation or complex censoring, or consider effects of time-dependent covariates that commonly arise in longitudinal studies, for which the resulting relationship varies both over the trajectory of the covariate, and over the survival quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 2 In this paper, we extend the AFT model to allow flexible acceleration factors that vary across quantiles, while simultaneously accommodating left-truncation, complex censoring, and time-varying covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Our approach builds on a time-varying AFT model first in- troduced in Cox and Oakes (1984) but seemingly largely overlooked in the literature, and a general framework for flexible covariate effect specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We illustrate how AFT regres- sion coefficients specified to vary over time can be inverted into quantile-varying acceleration factors, and we develop a regression standardization scheme based on the g-formula to allow estimation of both covariate-conditional and marginal acceleration factors for an exposure of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We propose a Bayesian estimation approach for this modeling framework using the Stan language, which allows rigorous quantification of uncertainty and increased modeling flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Through this investigation, we also uncover new insights into the use of binary time-varying covariates under the AFT model, and present novel tools for modeling and visualizing such effects.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This further expands the AFT modeling toolkit to cover many ex- tensions commonly used under the Cox model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We motivate these methods with an in-depth analysis of the Religious Orders Study and Memory and Aging Project prospective cohort studies of AD and dementia (Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 2 The Accelerated Failure Time Model The standard AFT model with time-invariant effects can be written as a log-linear model of time: log(T) = X Tβ + ϵ, where ϵ is a random error term and β is a vector of regression coefficients corresponding with covariates X.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We denote the exponentiated error T0 = exp(ϵ), which represents a hy- pothetical random variable drawn from the “baseline distribution” having survivor function S0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' It is straightforward to show that this model structures covariate effects such that the distribution of event times among subjects having covariate pattern x, denoted Tx, is directly shifted from the baseline distribution by the transformation Tx × exp(−x Tβ) ∼ S0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Based on this connection, an equivalent representation of the standard AFT model is given directly via the baseline survivor function S0 as S(t | X) = S0(t × exp(−X Tβ)).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (1) The AFT model admits a direct interpretation of covariate effects as multiplicative shifts of the survival quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For any particular quantile p, define t(p) x and t(p) 0 to be the pth quantile times under x and baseline respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Then p = S(t(p) x | x) = S0(t(p) x × exp(−x Tβ)) = S0(t(p) 0 ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 3 Solving for the pth quantile survival time under x yields t(p) x = S−1(p | x) = S−1 0 (p) exp(x Tβ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The acceleration factor between two arbitrary covariate patterns x and x′ is then defined as the ratio of pth quantiles, t(p) x /t(p) x′ = S−1 0 (p) exp(xTβ) S−1 0 (p) exp((x′)Tβ) = exp((x − x′) Tβ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Under the standard AFT model, the acceleration factor does not depend on the form of S0 or the value of p, and thus characterizes a constant multiplicative covariate effect across the entire distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 AFT model with time-varying components In the standard AFT model (2), the covariate-adjusted survivor function is directly charac- terized by the time shift defined by t × exp(−XTβ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Towards a more flexible AFT model, we replace this time shift with a general increasing function V (t | X), yielding the covariate- adjusted survivor function S(t | X) = S0 (V (t | X)) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (2) This formulation, first discussed by Cox and Oakes (1984) in the context of time-varying covariates, reduces to the standard AFT when V (t | X) = t × exp(−XTβ), while also admit- ting other temporal specifications of the relationship between covariates and the outcome distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In fact, one interpretation of this V function is as a transformation linking the distribution of Tx under covariates x, and the baseline distribution of T0, V (Tx | x) ∼ S0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Under this extended AFT model (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1), the pth quantile survival time for subjects under covariate pattern x is t(p) x = S−1(p | x) = V −1(S−1 0 (p) | x).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Now it may no longer be the case that the ratio of pth quantile survival times between covariate patterns x and x′ is a constant factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Instead, the more general quantile-varying acceleration factor is ξ(p | x, x′, S0) = t(p) x /t(p) x′ = S−1(p | x) S−1(p | x′) = V −1(S−1 0 (p) | x) V −1(S−1 0 (p) | x′), (3) with notation explicitly capturing the additional potential for dependence on p and S0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 4 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 Examples and Interpretation To emphasize both the flexibility and interpretability of this new quantity, Figure 1 shows sample survivor curves and corresponding acceleration factors under simple forms of quantile- varying effect for a single contrast between exposure levels X = 1 and X = 0, with baseline S0(t) = exp(−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For simplicity we will interpret the effects at p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='75 and p = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='25, which represent the time by which 25% and 75% of people experience the event, respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' As a reference point, the blue curve (second row of the legend) in each figure shows a constant acceleration factor of exp(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5) ≈ 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='65, constant across quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The green curve (fourth row of the legend) shows a protective effect that is increasingly pronounced among later-onset cases, with ξ(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='75 | 1, 0) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='25 and ξ(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='25 | 1, 0) = 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In words, the estimated time by which 25% of the exposed die is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='25 times as great as that among the unexposed, but the estimated time by which 75% of the exposed die is 2 times greater than unexposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Conceptually, this form of protective effect corresponds with delayed onset of all cases among the exposed, but specifically a much longer tail of late-onset cases compared to a standard AFT protective effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The orange curve (third row of the legend) shows a more nuanced effect that delays the earliest cases, while also accelerating later onset cases.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Numerically, ξ(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='75 | 1, 0) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='65 and ξ(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='25 | 1, 0) = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='9, meaning the estimated time by which 25% of the exposed die is 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='65 times as great as that among the unexposed, but the estimated time by which 75% of the exposed die is only 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='9 times as great as among the unexposed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Conceptually, this form of effect is a ‘compressing’ of the outcome distribution, with earlier events being delayed and later events being accelerated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This is visible in the relative steepness of the survivor curve, with more than 50% of all events occurring between times 2 and 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Furthermore, this represents an effect with ‘crossing survivor curves’, which despite being common in certain health research domains cannot be modeled by standard proportional hazards or AFT models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In summary, we see that this approach to conceptualizing covariate effects for time-to-event outcomes yields nuanced and interpretable insights beyond what is available from standard proportional hazards or AFT models.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 3 Model Definition The proposed quantile-varying AFT model is purposefully general with respect to the base- line survivor distribution S0 and the time-varying covariate process V .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In this section we outline several choices for specifying these model components, weighing tradeoffs between flexibility, stability, and computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' While this modeling framework in principle admits estimation under both frequentist and Bayesian paradigms, we focus on the latter approach and employ a Markov Chain Monte Carlo (MCMC) estimation routine via the No-U-Turn sampler implemented in the Stan language (Carpenter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 Specification of the covariate process V For ease of exposition, we will consider a d length vector of baseline covariates X, of which an exposure of interest X1 is specified with a flexible regression effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' However, this can easily be expanded to allow multiple such exposures of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The form of the covariate process V dictates the potential shapes the quantile-varying acceleration factor for X1 can take, and requires a balance of flexibility and stability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We focus on spline-based methods, which require a vector of knots τ characterizing a set of J basis functions B1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' , BJ, and corresponding coefficients α = (α1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' , αJ)T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This results in the specification V (t | X) = t × exp � −X Tβ − X1 J � j=1 αjBj(t | τ) � , (4) Note that when α = 0, then this reduces to the standard AFT model, allowing straight- forward model comparison to assess the flexible effect specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Furthermore, letting B′ j(t | τ) = dBj(t | τ)/dt, then the derivative of the covariate process, which is used in likelihood computation, has the simple form v(t | X) = d dtV (t | τ) = V (t | τ) � 1 t − X1 J � j=1 αjB′ j(t | τ) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' One specification inspired by the parametric proportional hazards spline model of Roys- ton and Parmar (2002) and discussed by Crowther et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (2022) is the natural cubic spline basis, which combines cubic polynomial basis functions with a restriction that the ends be- yond the lower and upper boundary knots be linear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Numerically stable forms for each natural cubic spline basis function Bk and B′ k are readily available in statistical software, and the resulting V combines flexibility and stability, with the added advantage of being a smooth function of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' However, the inverse V −1(t | X) used in the quantile-varying acceleration factor (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1) does not have a closed form, and must be computed numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' A computationally simpler alternative is to specify V as a piecewise linear function, which yields a simplified analytical form and closed form inverse.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Define J + 2 knots 0 = τ0 < τ1 < · · < τJ < τJ+1 = ∞, with basis functions defined Bj(t | τ) = t−1(min{t, τj+1} − τj)+ where (z)+ = min{0, z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Then the final specification for V simplifies to V (t | X) = t × exp (−X Tβ) � J � j=1 exp (−X1αj) Bj(t | τ) � , with the straightforward derivative v(t | X) = exp � −XTβ − �J j=1 X1αjI(τj ≤ t < τj+1) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Computation of the inverse is also straightward, and left to Appendix B of the Supplementary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' As above, this reduces to the standard AFT model when α = 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 6 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 Specification of the baseline distribution S0 As with the specification of V , there are numerous possible choices of baseline distribution characterizing S0, both fully parametric and semi-parametric.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Parametric specifications have several advantages in this setting: they are computationally efficient, well-defined across all quantiles, have tractible inverse survivor functions, and can lead to improved efficiency in smaller samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Two such parametric specifications are the log-Normal baseline distribution with survivor function defined by S0(t | µ, σ) = 1 − Φ(log t − µ)/σ2 where Φ(·) is the standard normal distribution function, and the Weibull baseline distribution defined by S0(t | µ, σ) = exp {[t × exp(−µ)]σ}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Let φ = (µ, σ)T denote the collection of parameters corresponding to the baseline distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Nevertheless, an important benefit of the Bayesian paradigm is the well-established liter- ature on semi-parametric AFT survival models with flexible baseline distributions, such as Dirichlet process mixture (DPM) models (Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2017) and Polya tree priors (Hanson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2009).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Here we propose a transformed Bernstein polynomial (TBP) prior for S0 fol- lowing (Zhou and Hanson, 2018), which defines a parametric centering distribution having survivor function S∗ 0(t | φ) (such as the Weibull or log-Normal defined above), then applies a transformation using Bernstein polynomial functions to can flexibly capture a wide array of distributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Formally, define the Beta(a, b) distribution function G(p | a, b) = Γ(a + b) Γ(a)Γ(b)pa−1(1 − p)b−1, 0 ≤ x ≤ 1, and a vector w of length K such that �K k=1 wk = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Then the baseline survivor function is the linear combination S0(t | φ, w) = K � k=1 wkG(S∗ 0(t | φ) | k, K − k + 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Because the domain of G and the range of S∗ 0 are both [0,1], this represents a flexible spline transformation of the centering parametric distribution on the scale of survival quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In particular, if w = (J−1, J−1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' , J−1)T, then S0 = S∗ 0, so the TBP specification contains the centering parametric model, but can also characterize a wide array of survival distribution shapes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' An illustration is provided in Appendix D of the Supplementary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' To complete the Bayesian specification, we place a Dirichlet(θ) prior on w with θ > 0, where larger values of θ correspond to tighter concentration of the elements of w around J−1 and therefore tighter concentration of S0 around S∗ 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This specification offers several advantages over other flexible baseline specifications men- tioned previously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Importantly, each G function can be computed recursively, so overall computation of S0 is efficient.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Moreover, the TBP prior can be straightforwardly sampled using the No-U-Turn algorithm implemented in the Stan language, as described below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' By contrast, many other Bayesian non-parametric specifications such as Polya trees and DPM 7 models require specialized computational methods such as custom MCMC samplers and data augmentation (Hanson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Lee et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The main tradeoff with any flexible form for S0 compared to a fully parametric specification is the increased computational cost, both for the sampler as well as the numerical computation of the inverse function S−1 0 and associated acceleration factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3 Likelihood Another important benefit of the Bayesian approach is the ability to seamlessly handle arbitrary censoring and left truncation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Let (Y l, Y u) the left and right observed endpoints of a censoring interval around a true event time T, such that Y l ≤ T ≤ Y u.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Right-censoring simply corresponds with Y u = ∞.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Define the binary indicator ∆ = I(Y l = Y u) to be a subject observed to experience the event exactly at time Y l.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Finally, let L represent the possible left-truncation time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Along with the baseline covariates X, denote the corresponding observed data for the ith subject Di = {yl i, yu i , δi, li, xi}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' After specifying V and S0, let ψ = (β T, αT, φ T, wT)T denote the full set of parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Then assuming that censoring is non-informative of the outcome, the resulting likelihood contribution for subject i is then Li(ψ | Di) = [f0(V (yl i | xi))v(yl i | xi)]δi[S0(V (yl i | xi)) − S0(V (yu i | xi))](1−δi) S0(V (li | xi)) where f0 is the density function corresponding to the baseline distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' By convention, S0(∞) = 0, so under right-censoring this reduces to the standard censored data likelihood.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 Bayesian Computation and Prior Specification To implement this modeling framework, we propose Bayesian estimation via the No-U-Turn sampler implemented by the Stan language (Carpenter et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In brief, this MCMC algorithm uses gradient information on the log-posterior to generate Markov transitions that efficiently explore the posterior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This choice reflects our goal of developing a practical and accessible methodology, as our implementation can be easily called from R via the rstan package with minimal algorithmic tuning (Stan Development Team, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' To complete our model specification, we consider priors on the parameters β, α, and φ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The No-U-Turn sampler does not require or leverage conjugacy between prior and posterior, so prior distributions can be chosen or adjusted without changing the implementation of the sampler.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In the application below, we adopt flat priors for regression parameters β and α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For the parametric (centering) distribution, we also adopt a flat prior for the log location parameter log µ, and for the scale parameter a σ ∼ Gamma(aσ, bσ) prior.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The TBP prior is defined by a w ∼ Dirichlet(θ) prior for the weights, and we adopt a θ ∼ 8 Gamma(aθ, bθ) hyperprior on θ, regulating the level of flexibility around the parametric centering distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 Model Evaluation and Comparison A conceptual benefit of our proposed modeling framework is that the flexible structures naturally encompass simpler models: the standard AFT model is nested within the flexible effect specification of covariate process V , and a fully parametric baseline is nested within the TBP prior for S0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In this section, we propose a model evaluation metric to inform decisions regarding the necessary level of model complexity, facilitated by the Stan language and the loo package in R (Vehtari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The expected log pointwise predictive density (ELPD) is a metric that evaluates how well a fitted model can predict future out-of-sample data, with larger values indicating better predictive ability.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For n future observations �y1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' , �yn, the ELPD is defined via the posterior predictive density p(�y | D) as ELPD = n � i=1 � log p(�yi | D)d�yi.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' While typically future out-of-sample data is not available, the ELPD can be estimated by leave-one-out cross validation by averaging the log posterior predictive distribution for each observed data point of a model fit excluding that data point.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This quantity can in turn be estimated efficiently from a single Bayesian model fit via Pareto smoothed importance sampling, which we denote � ELPDpsis-loo (Vehtari et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2017), and has been shown to exhibit improved performance relative to other common Bayesian model criteria, such as Deviance Information Criterion (DIC).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6 Computation of Regression Standardized Acceleration Factors Importantly, under the covariate process V defined by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1), the quantile-varying accelera- tion factor (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1) depends on the specified values of all covariates x and x′, not just those that differ.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This conditionality on the values of all covariates may be insightful if interest is in assessing effect heterogeneity in particular subpopulations defined by specific covari- ate patterns.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' However, practical interest is often in assessing the effect of an exposure in a population standardized with respect to the other covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Therefore, in this section we propose a regression standardization approach to estimating the quantile-varying accel- eration factor for a particular covariate of interest, averaged over the distribution of other covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Conceptually, the goal is to first estimate the survivor curves we would observe in the population if everyone was alternately exposed or unexposed, and then back out the quantile-varying acceleration factor that relates the two curves.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 9 For clarity, consider a single binary exposure of interest X, and vector of additional covariates Z.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Then the marginal ratio of interest is ξ(p | X = 1, X′ = 0) = S−1(p | X = 1) S−1(p | X = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Following Rothman et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (2021) and Sj¨olander (2016), define the survivor function for X = x, standardized to the distribution of Z, as SZ(t | x) = EZ[P(T > t | X = x, Z)].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Using standardized survivor functions, we define the standardized quantile-varying acceler- ation factor as ξZ(p | X = 1, X′ = 0) = [SZ]−1(p | X = 1) [SZ]−1(p | X = 0).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' where [SZ]−1(p | X = x) is the function solving SZ(t | X = x) − p = 0 for t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This contrast represents the magnitude of the horizontal shift in the standardized survivor curve SZ between X = 1 and X = 0, at each quantile p.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' To estimate and quantify uncertainty for these contrasts, we develop a novel approach based on the Bayesian g-formula (Keil et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In brief, for each MCMC draw m = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' , M, for each X = x we compute the standardized survivor function S(m) Z (t | X = x) = n−1 n � i=1 S(t | X = x, Z = zi;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' ψ(m)), and then form contrast of interest ξ(m) Z (p | X = 1, X′ = 0) = [S(m) Z ]−1(p | X = 1) [S(m) Z ]−1(p | X = 0) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This may require numerical evaluation of the inverse standardized survivor functions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Esti- mating the posterior mean and credible intervals of ξZ proceeds using the mean and suitable quantiles of ξ(1) Z , .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' , ξ(M) Z .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 4 Application: Cohort Study of Incident AD and De- mentia Motivating the proposed AFT model is the study of adverse cognitive outcomes among older adults, for which long timescales and complex disease etiology naturally lend themselves to consideration of flexible covariate effects on the quantile scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In this section we investigate 10 risk factors for AD and dementia in older adults using data collected by the Religious Orders Study and Memory and Aging Project (ROSMAP) prospective cohort studies ongoing since 1994 and 1997 respectively (Bennett et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Our analysis focuses on flexible estima- tion of the association of the genetic marker APOE-ϵ4 with the timing of AD or dementia onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Previous analyses of similar cohorts have simply compared incidence rates within age categories to examine whether this marker had differential effects through time (Kukull et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2002).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' So, estimating a quantile-varying acceleration factor for APOE-ϵ4 is of clinical relevance, while also accounting for other risk factors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 2694 subjects were enrolled without AD or dementia between ages 65 and 86, and followed until withdrawal or death.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Subjects underwent cognitive screening annually to diagnose onset of AD or dementia, and death status was monitored continuously.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Table 1 summarizes a set of baseline binary risk factors collected on the subjects: marital status at baseline, sex, education level, race/ethnicity, and presence of the APOE-ϵ4 genetic variant.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The final analysis dataset includes 2335 subjects with complete baseline information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The outcome is defined by the time of diagnosis of AD or dementia, with death treated as a censoring mechanism, yielding a cause-specific analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Because we only include subjects with age at least 65, the time scale of analysis is “years since age 65.” Importantly, our analysis accounts for the presence of left truncation (or “delayed entry”) by subjects who enroll after age 65.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Though this framework admits interval censoring, given the short visit intervals relative to the timescale, for this analysis we defined the timing of AD onset at the midpoint of the corresponding visit interval.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We compare the fits of standard AFT models with those having piecewise and spline forms for V , under Weibull and log-Normal baseline specifications as well as a TBP prior baseline with K = 5, centering around the Weibull distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We set 4 break points for the piecewise linear effect at 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 year intervals across the follow up period, and for the spline effect we set 2 internal knots at quantiles on the log scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The difference between these specifications is due to the spline being naturally more flexible, allowing it to smooth across knots with irregular spacing, while the piecewise linear model requires break points that span the entire timespan in order to achieve flexibility.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For the scale parameter we set the prior σ ∼ Gamma(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05), having prior median 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='46 and 95% central mass between 6e-5 and 38.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Finally, we fit a standard Frequentist Cox proportional hazards model for comparison.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For the TBP concentration parameter we set a hyperprior of θ ∼ Gamma(1, 1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For each model we ran three chains each for 2000 adaptation iterations and 10000 samples, totalling 30000 samples.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' After sampling, all potential scale reduction factors were below 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01 and trace plots indicated good mixing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Table 3 reports the estimates of regression parameters across all AFT specifications, as well as frequentist results from a Cox proportional hazards model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For the AFT models, positive estimates of β correspond with delayed onset of AD or dementia, as do negative estimates for the Cox model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The coefficients estimated for white race/ethnicity, marital 11 status, female sex, and education are stable across all model specifications.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Interpreting the Weibull AFT with constant effect of APOE-ϵ4, for example, indicates that being married is associated with a exp(0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='09) = 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='09 times greater median time to onset of AD or dementia, with 95% credible interval of (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02,1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='19).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Flexible effect coefficients of APOE-ϵ4 cannot be directly interpreted on the quantile scale, therefore we present graphical tools below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The top panel of Table 2 compares estimates of ELPD model criterion for each AFT model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In each case, the spline and piecewise-linear effect specifications outperformed the standard AFT specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The log-Normal models uniformly underperformed, while the Weibull and TBP models performed comparably.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' To graphically assess the effect of APOE-ϵ4 we report the TBP model, and present results for other specifications in Appendix A of the Supplementary Materials.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Results were qualitatively similar for all baseline distributions, with the largest differences in acceleration factor only occurring in the lowest quantiles extrapolated beyond the observed data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Figure 2 shows the estimated survivor functions and corresponding quantile-varying ac- celeration factors for the APOE-ϵ4 genetic variant, after regression standardization over the distribution of the other baseline covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' These figures confirm other findings that APOE-ϵ4 is associated with earlier onset of AD and dementia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' However, quantile-varying effects also indicate that the acceleration is strongest among the earliest cases and subse- quently diminishes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Both piecewise and spline models estimate that the time by which the first 10% of those living with APOE-ϵ4 develop AD or dementia is earlier than those with- out the variant by a factor of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' the median times by which people develop AD or dementia differ by a factor of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='75, and the times by which 75% develop AD or dementia differ by a factor of about 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='85.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Due to censoring of those with advanced age, the acceleration factor at lower quantiles reflects parametric extrapolation beyond the observed distribution, represented in the figure by grey shading.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Nevertheless, this finding has clear clinical significance, indicating the particular need to monitor for early onset AD at younger ages among those with APOE-ϵ4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 5 Effects of Time-varying Covariates on the Quantile Scale In this section, we extend the proposed AFT model to incorporate binary time-varying covari- ates, and provide intuition and graphical tools for effectively interpreting and communicating corresponding effects on the quantile scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' To focus on intuition, consider a single time-varying covariate denoted X1(t) with con- stant regression effect β1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In particular, let X1(t) be a binary-valued step function, such as an indicator for whether a non-terminal event has occurred by time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Formally, define X1(t) = I(t > tX), where tX is the time at which X1 changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' To simplify notation, consider 12 a single additional covariate time-invariant covariate X2, though inclusion of multiple addi- tional covariates is straightforward.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Embedding these covariates directly in the structure for V given by (3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1) and setting α = 0 to denote a constant effect yields V (t | X(t)) = t × exp (−X1(t)β1 − X2β2) = exp (−X2β2) [min{t, tX} + (t − tX)+ exp (−β1)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (5) With complete derivation given in Appendix C of the Supplementary Materials, the accel- eration factor at quantile p between two subjects depends on each person’s value of X2, the change time tX for X1, and the baseline distribution S0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In particular, for those with X2 = x2, the acceleration factor at quantile p for experiencing X1 at tX versus not experiencing X1 is tX S−1 0 (p) exp(x2β2) + exp(β1) � 1 − tX S−1 0 (p) exp(x2β2) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (6) This is a weighted average between 1 and exp(β1), with weight inversely proportional to the duration from tX to the pth quantile survival time in the comparison group, S−1 0 (p) exp(x2β2).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Intuitively, before tX there is no difference between the individuals, so the acceleration factor is 1, and then after tX the effect of X1 starts accumulating, and the acceleration factor gradually shifts towards exp(β1), becoming more pronounced as p extends towards 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' This dynamic is illustrated by example in Figure 3 below.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Finally, a flexible effect for X1(t) can also be specified by adapting the form of (5), yielding V (t | X(t)) = e−X2β2 � min{t, tX} + (t − tX)+ exp � −β1 − K � k=1 αkBk(t − tX | τ) �� .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Following Haneuse et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (2008), this specification characterizes flexibility in the effect of X1 over the time scale t − tX denoting time since the non-terminal event, rather than on the overall time scale of t, enabling evaluation of the temporal effect of X1 on its own timescale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Practically, this means that basis functions and knots τ must be specified on the corresponding time scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 Effect of Incident AD and Dementia on Mortality To illustrate the use of the AFT framework with a time-varying binary covariate, we per- form a secondary analysis of the cohort study to evaluate the association between onset of AD/dementia and subsequent time to death.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We fit models specifying onset of AD/dementia as a binary time-varying covariate, adjusting for the same time-invariant baseline covariates as in the above analysis (including a constant effect for APOE-ϵ4).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For the piecewise linear effect, we set break points at 1, 2, 3, 5, and 10 years after time of AD onset, and for the spline effect we set 2 internal knots at observed quantiles of time from 13 AD onset to death on the log scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Other settings and the sampling setup were as above, though for computation of the acceleration surface described below, we thinned the samples by a factor of 10 to facilitate computation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 in Appendix A of the Supplementary Materials reports estimated model parameters varying baseline survival distribution and effect specification, along with frequentist results from an extended Cox proportional hazards model with AD/dementia onset as a time-varying covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' As before, the coefficients estimated for all baseline covariates are stable across specifications for the flexible effect.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The lefthand panels of Figure 3 show estimated regression standardized survivor curves comparing those without AD/dementia onset, and and those with onset at age 70 and 85, respectively, under the TBP prior baseline specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In each case, the curves are identical up until the time of onset, and then once AD/dementia onset occurs mortality increases substantially.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The plots indicate similarity between models fit with piecewise and spline effects of AD/dementia onset relative to a constant effect, though the flexible models indicate a small delay in the mortality increase from the time of AD/dementia onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The corresponding acceleration factors are given on the righthand panels of Figure 3, illustrating the trajectory derived in (5), where no association exists before the quantile of AD/dementia onset, followed by an increasingly pronounced association after AD/dementia onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Selecting and plotting acceleration factors for a few AD/dementia onset times of interest may be sufficient in some settings, but fully communicating the results requires visualizing the quantile-varying effect across the entire range of the time-varying covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Figure 4 reports this acceleration factor surface as a contour plot, with the time of AD/dementia onset on the y-axis, the survival quantile on the x-axis, and the color representing the magnitude of the acceleration factor.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The two acceleration factor plots in Figure 3 correspond with cross-sections of this surface, by drawing horizontal lines at times 5 and 20 on the y-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' More generally, looking horizontally across this plot shows the quantile varying acceleration factor corresponding with different times of AD/dementia onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' However, this plot can also be read vertically, to show how the acceleration factor for a particular quantile changes depending on the timing of the time-varying covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' For example, drawing a vertical line from 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 on the x-axis shows the acceleration factor for median survival, varying across times of AD/dementia onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Therefore, this single plot allows us to read off complex regression effects both as a function of the survival quantile, as well as of the timing of the time-varying covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 6 Discussion The AFT model’s specification of multiplicative covariate effects on the quantile scale pro- vides an interpretable and attractive alternative to the standard proportional hazards model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Our proposed extensions to the AFT model enabling quantile-varying acceleration factors, and admitting binary time-varying covariates represent important additions to the standard 14 toolbox for survival analysis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Just as the Cox proportional hazards model benefits from straightforward incorporation of time-varying hazard ratios, the ability to add flexibility to the AFT model regression effects expands the scope of scientific inquiry.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Motivated by the study of AD in older adults, we found that the association of the APOE-ϵ4 gene with AD onset varied substantially across quantiles, with earlier-onset cases accelerated the most and later-onset cases the least.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Moreover, the ability to model, summarize, and communicate the effects of binary time- varying covariates creates new opportunities to capture nuanced associations between lon- gitudinal health trajectories.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Our proposed visualization of these effects as a surface across both the covariate timescale and the survival quantiles is particularly valuable, as previous work to incorporate time-varying covariates into AFT models has not focused on commu- nication of effects of time-varying components on the quantile scale (Hanson et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2009;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Zhou and Hanson, 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In our application, this approach illustrated that the associa- tion between AD/dementia onset and subsequent mortality varies substantially both across survival quantiles, and depending on the time of AD/dementia onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Estimation within the Bayesian paradigm also contributes important benefits for our proposed methodology.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' In particular, the Bayesian paradigm enables flexible estimation of the baseline distribution using the TBP prior, and allows for seamless uncertainty quan- tification even after regression standardization (Keil et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' To our knowledge, ours is the first implementation of the TBP prior in Stan, and software in R is available at https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='com/harrisonreeder/aftquantile.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Finally, this work complements the related literature on censored quantile regression (Portnoy, 2003;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Reich and Smith, 2013).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Censored quantile regression specifies an additive model for the effects of covariates on the quantile scale, while our model specifies multiplica- tive effects on the quantile scale.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The biological plausibility or clinical relevance of additive versus multiplicative changes to the survival quantiles depends on the application, so our proposed methodology yields a valuable alternative to available quantile-based methods.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Funding This project was supported by the Eunice Kennedy Shriver National Institute of Child Health and Human Development [grant number F31HD102159 to HTR].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The National In- stitutes on Aging supported the Religious Orders Study [grant numbers P30AG010161 and R01AG015819] and the Rush Memory and Aging Project [grant number R01AG017917].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 15 Acknowledgments We thank the study participants and staff of the Rush Alzheimer’s Disease Center.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' ROSMAP resources can be requested at https://www.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='radc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='rush.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='edu.' metadata={'source': 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regression for censored data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Bio- metrics, 69(3):651–660.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Rothman, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', Lash, T.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', VanderWeele, T.' metadata={'source': 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in Medicine, 21(15):2175–2197.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Sj¨olander, A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Regression standardization with the R package stdReg.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' European Journal of Epidemiology, 31(6):563–574.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Stan Development Team (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' RStan: 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=', and Gabry, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (2017).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Statistics and Computing, 27(5):1413–1432.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Wei, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' J.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' A unified framework for fitting bayesian semiparametric models to arbitrarily censored survival data, including spatially referenced data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Journal of the American Statistical Association, 113(522):571–581.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 17 0 2 4 6 8 10 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='75 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='00 Time (t) Survivor Function V(t) t t × exp(−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5X) t × exp((−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 + 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6I(t > 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5))X) (t1−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5X − 1) (1 − 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5X) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='75 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 Survival Quantile (p) Acceleration Factor Figure 1: Sample survivor curves (left panel) and corresponding, possibly quantile-varying, acceleration factors (right panel).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Baseline survivor function shown is S0(t) = exp(−0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Table 1: Baseline covariates by observed AD/dementia and death outcome status.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' All covariates are binary, with 1 indicating the presence of the status and 0 indicating absence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Censored prior AD/dementia Death AD/dementia to AD/dementia and censored without diagnosis Total (%) or death (%) prior to death (%) AD/dementia (%) and death (%) Total 2335 (100%) 750 (100%) 123 (100%) 891 (100%) 571 (100%) White Race/Ethnicity 2178 (93.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3%) 687 (91.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6%) 100 (81.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3%) 849 (95.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3%) 542 (94.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='9%) Male Sex 648 (27.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8%) 147 (19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6%) 24 (19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5%) 316 (35.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5%) 161 (28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2%) Married at Study Entry 462 (19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8%) 216 (28.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8%) 29 (23.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6%) 145 (16.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3%) 72 (12.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6%) 15+ Years of Education 1621 (69.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4%) 532 (70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='9%) 80 (65%) 609 (68.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4%) 400 (70.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1%) APOE-ϵ4 Genetic Variant 575 (24.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6%) 156 (20.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8%) 53 (43.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1%) 173 (19.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4%) 193 (33.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8%) 18 Table 2: Estimated expected log predictive density (ELPD), multiplied by -2 to replicate scale of information criteria.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Smaller values indicate better model fit.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' AFT Model log-Normal Weibull TBP (Weibull Centered) AD/Dementia Onset (Death as a Censoring Mechanism) Constant 5862.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 5806.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3 5804.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 Piecewise Linear 5841.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 5788.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 5786.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 Restricted Cubic Spline 5814.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='9 5780.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='9 5781.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 Death (AD/Dementia as a Time-Varying Covariate) Constant 9997.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 9666.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='7 9628.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 Piecewise Linear 9919.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 9636.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='7 9600.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 Restricted Cubic Spline 9884.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 9600.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='9 9564.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='9 19 Table 3: Regression estimates for time to onset of AD or dementia in the absence of death.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' AFT results are posterior medians and 95% credible intervals for regression parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Cox model results are log-hazard ratio estimates and 95% confidence intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' AFT Model Cox PH log-Normal Weibull TBP (Weibull Centered) White Race/Ethnicity, β1 Constant 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='28 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='57, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='18 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='31) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='19) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='19) Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='18 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='17) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07 (-0.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='16) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='17) Male Sex, β2 Constant 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='06 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='11, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='23) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='13, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05) Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='12, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04) Restricted Cubic Spline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='11, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='19) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='19) Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='13 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04, 0.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='13 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='22) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='09 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='16) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='16) ≥15 Years of Education, β4 Constant 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='26, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='16) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='09) Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07 (0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='15) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='09) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08) Restricted Cubic Spline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='06 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='14) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='42 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='51, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='34) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='28 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='35, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='22) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='28 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='35, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='21) Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='79 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='95, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='62) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='75 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='92, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='55) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='76 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='93, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='52) Restricted Cubic Spline 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='54 (-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='98, -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='95) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='38 (-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08, -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='23) 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='34 (-3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='09, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='92) APOE-ϵ4 Genetic Variant, α1 Constant Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='86 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='49, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='23) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='78 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='35, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='20) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='78 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='28, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='23) Restricted Cubic Spline 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='51 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='12, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='85) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='51 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='77, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='5 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='61, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03) APOE-ϵ4 Genetic Variant, α2 Constant Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='52 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='23, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='80) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='74 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='39, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='06) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='79 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='41, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='14) Restricted Cubic Spline 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='83 (2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='73, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='47) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='63 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='45, 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='76) 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='52 (0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 Quantile (p) Acceleration Factor Constant Piecewise Linear Spline Figure 2: Under a Weibull-centered TBP baseline specification: (left panel) regression stan- dardized survivor function estimates for onset of AD or dementia without death, averaged over other covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Regression standardized estimate from Cox proportional hazards model shown for comparison;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (right panel) regression standardized quantile-varying accel- eration factor estimates for onset of AD or dementia without death, averaged over other covariates.' metadata={'source': 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+page_content='55] Figure 4: Under a Weibull-centered TBP baseline specification, contour plots of regression standardized acceleration factor surface estimates for death following onset of AD/dementia, standardized to other covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Time of AD/dementia onset is shown on y-axis, and sub- sequent survival quantile is shown on x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Color indicates acceleration factor at the given survival quantile, comparing those with AD/dementia onset at the specified time and those without AD/dementia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Horizontal cross-sections illustrate quantile-varying accelera- tion factor for AD/dementia onset at a particular time, while vertical cross-sections illustrate acceleration factor at a particular quantile across times of AD/dementia onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (Left panel) constant effect specification;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (center panel) piecewise linear effect specification;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (right panel) spline effect specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 23 Appendix Introduction In this appendix we present additional details and results beyond what could be presented in the main manuscript.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' To distinguish the two documents, alpha-numeric labels are used in this document while numeric labels are used in the main paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Section A provides additional results from the data application.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Section B provides derivation of the form of V −1 when V is specified as a piecewise linear function of time.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Section C provides derivation of the form of the acceleration factor associated with a binary time-varying covariate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Section D provides additional detail on the transformed Bernstein polynomial (TBP) prior specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 24 A Additional Data Application Results A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 AD/Dementia Onset In this section we report additional regression-standardized survival curves and acceleration factors for the onset of AD or dementia by APOE-ϵ4 genetic variant status, for alternative specifications for the baseline distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' We note that the most substantial difference be- tween specifications occurs in the lowest quantiles, which represent parametric extrapolation beyond the observed data quantiles.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 0 10 20 30 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 1.' metadata={'source': 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Acceleration Factor Constant Piecewise Linear Spline Figure A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1: Under a Weibull baseline specification: (left panel) regression standardized survivor function estimates for onset of AD or dementia without death, averaged over other covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Regression standardized estimate from Cox proportional hazards model shown for comparison;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (right panel) regression standardized quantile-varying acceleration factor estimates for onset of AD or dementia without death, averaged over other covariates.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 Time to AD/Dementia without Death, Years from Age 65 Survivor Function No APOE-e4 PH, Constant AFT, Constant AFT, Piecewise Linear AFT, Spline APOE-e4 PH, Constant AFT, Constant AFT, Piecewise Linear AFT, Spline 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 Quantile (p) Acceleration Factor Constant Piecewise Linear Spline Figure A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2: Under a log-Normal baseline specification: (left panel) regression standardized survivor function estimates for onset of AD or dementia without death, averaged over other covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Regression standardized estimate from Cox proportional hazards model shown for comparison;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (right panel) regression standardized quantile-varying acceleration factor estimates for onset of AD or dementia without death, averaged over other covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 95% credible intervals represented with dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Grey shaded region represents area of parametric extrapolation beyond quantiles observed in both groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 26 A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 Mortality following AD/Dementia Onset Below we report regression parameter estimates, and additional regression-standardized sur- vival curves and acceleration factors for mortality by AD/dementia status, across alternative specifications for the baseline distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 0 10 20 30 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 Survivor Function AD/Dementia Onset Constant Piecewise Linear Spline No AD/Dementia Onset Constant Piecewise Linear Spline 0 10 20 30 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 Time to Death, Years from Age 65 Survivor Function AD/Dementia Onset Constant Piecewise Linear Spline No AD/Dementia Onset Constant Piecewise Linear Spline 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 Survival Quantile (p) Acceleration Factor Constant Piecewise Linear Spline 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 Survival Quantile (p) Acceleration Factor Constant Piecewise Linear Spline Figure A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3: Under a Weibull baseline specification: (left panel) regression standardized sur- vivor function estimates for mortality following onset of AD or dementia, averaged over other covariates;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (Right panel) regression standardized survivor function estimates for mortality following onset of AD or dementia, averaged over other covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 95% credible intervals represented with dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Grey shaded region represents area of parametric extrapola- tion beyond quantiles observed in both groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 27 0 10 20 30 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 Survivor Function AD/Dementia Onset Constant Piecewise Linear Spline No AD/Dementia Onset Constant Piecewise Linear Spline 0 10 20 30 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 Time to Death, Years from Age 65 Survivor Function AD/Dementia Onset Constant Piecewise Linear Spline No AD/Dementia Onset Constant Piecewise Linear Spline 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 Survival Quantile (p) Acceleration Factor Constant Piecewise Linear Spline 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 Survival Quantile (p) Acceleration Factor Constant Piecewise Linear Spline Figure A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4: Under a log-Normal baseline specification: (left panel) regression standard- ized survivor function estimates for mortality following onset of AD or dementia, averaged over other covariates;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (Right panel) regression standardized survivor function estimates for mortality following onset of AD or dementia, averaged over other covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 95% credible intervals represented with dashed lines.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Grey shaded region represents area of parametric extrapolation beyond quantiles observed in both groups.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 28 0 10 20 30 40 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='00 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='25 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='50 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='75 1.' metadata={'source': 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following onset of AD/dementia, standard- ized to other covariates.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Time of AD/dementia onset is shown on y-axis, and subsequent survival quantile is shown on x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Color indicates acceleration factor at the given survival quantile, comparing those with AD/dementia onset at the specified time and those without AD/dementia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Horizontal cross-sections illustrate quantile-varying acceleration factor for AD/dementia onset at a particular time, while vertical cross-sections illustrate acceleration factor at a particular quantile across times of AD/dementia onset.' metadata={'source': 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is shown on x-axis.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Color indicates acceleration factor at the given survival quantile, comparing those with AD/dementia onset at the specified time and those without AD/dementia.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Horizontal cross-sections illustrate quantile-varying acceleration factor for AD/dementia onset at a particular time, while vertical cross-sections illustrate acceleration factor at a particular quantile across times of AD/dementia onset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (Left panel) constant effect specification;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (center panel) piecewise linear effect specification;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' (right panel) spline effect specification.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 30 Table A.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1: Regression estimates for time to death.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' AFT results are posterior medians and 95% credible intervals for regression parameters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Cox model results are log-hazard ratio estimates and 95% confidence intervals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' AFT Model Cox PH log-Normal Weibull TBP (Weibull Centered) White Race/Ethnicity, β1 Constant 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='17 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='41) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='17, 0.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='16, 0) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='15, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01) Restricted Cubic Spline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='12) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='14 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='17, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='11) Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='27 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='33, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='21) 0.' metadata={'source': 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metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='33, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='21) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='16 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='13) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='14 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='18, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='11) Married at Study Entry, β3 Constant 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='16 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='12 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='19) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04 (0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08) Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='12 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='19) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04 (0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08) Restricted Cubic Spline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='12 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='19) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04 (0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08) ≥15 Years of Education, β4 Constant 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='21, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='13) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='06) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05) Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='09 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='15) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='06) Restricted Cubic Spline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='09 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='15) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03 (0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='06) APOE-ϵ4 Genetic Variant, β5 Constant 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='11, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='13) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='06 (0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='11) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05) 0 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04) Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='06 (0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='12) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05) 0 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04) Restricted Cubic Spline 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='06 (0, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='12) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05) 0 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='04) AD/Dementia Onset, β6 Constant 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='14 (1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02, 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='26) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='06 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='16, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='97) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='73 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='81, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='65) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='68 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='76, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='61) Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='14 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='42, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='17) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='02 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='3, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='29) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='27, 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='32) Restricted Cubic Spline 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='59 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='90, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='35) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='63 (0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='95, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='38) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='68 (1, 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='42) AD/Dementia Onset, α1 Constant Piecewise Linear 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='95 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='29, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='63) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='86 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='21, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='53) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='84 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='18, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='53) Restricted Cubic Spline 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='77 (-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='25, -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='33) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='60 (-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08, -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='17) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='57 (-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='05, -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='14) AD/Dementia Onset, α2 Constant Piecewise Linear 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='15 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='49, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='82) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='90 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='25, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='57) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='86 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='21, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='54) Restricted Cubic Spline 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07 (-6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='56, -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='73) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='40 (-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='86, -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='10) 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='43 (-5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='87, -3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='11) AD/Dementia Onset, α3 Constant Piecewise Linear 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='15 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='49, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='82) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='65 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='99, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='33) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='62 (-0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='96, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='31) Restricted Cubic Spline 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='78 (-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='18, -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='41) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='45, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='75) 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='08 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='44, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='74) AD/Dementia Onset, α4 Constant Piecewise Linear 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='68 (-2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='11, -1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='26) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='71 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='10, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='32) 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='74 (-1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='15, -0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='34) Restricted Cubic Spline 31 B Derivation of V −1(t | X) under Piecewise Linearity Under piecewise linear specification of V (t | X), define J + 2 knots 0 = τ0 < τ1 < · · · < τJ < τJ+1 = ∞, with piecewise linear basis functions defined Bj(t | τ) = t−1(min{t, τj+1} − τj)+ where (z)+ = min{0, z}.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Assuming a flexible effect for X1, the resulting specification becomes V (t | X) = t × exp (−X Tβ) � J � j=1 exp (−X1αj) Bj(t | τ) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The inverse function V −1 can be derived by inspection, noting that the inverse of an increas- ing piecewise linear function is also an increasing piecewise linear function, with changepoints shifted according to the values of X, β, and α.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Specifically, define τ ∗ such that τ ∗ 0 = τ0 = 0, τ ∗ 1 = τ1 × exp(−XTβ), and for j > 1, τ ∗ j = τ ∗ 1 + j � l=2 exp(−X Tβ − X1αl−1)(τl − τl−1).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The lines on each interval of V −1 have the inverse slope of the line in the corresponding interval of V , so the final inverse function is succinctly written V −1(t | X) = t × exp (X Tβ) � J � j=1 exp (X1αj) Bj(t | τ ∗) � .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' C Derivation of Acceleration Factor for a Binary Time- Varying Covariate Let X1(t) be a binary-valued step function, such as an indicator for whether a non-terminal event has occurred by time t.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Formally, define X1(t) = I(t > tX), where tX is the time at which X1 changes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Consider a single additional covariate time-invariant covariate X2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Notating t∗ X = tX exp(−X2β2), the inverse function for V as defined in (5) is derived following Appendix B as V −1(t | X(t)) = exp (X2β2) [min{t, t∗ X} + (t − t∗ X)+ exp (β1)] .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' The resulting acceleration factor at quantile p between a person with X2 = x2 who experi- ences the non-terminal event at time tX, and a person with X2 = x′ 2 who experiences the non-terminal event at time t′ X, is ξ(p | tX, t′ X, x2, x′ 2, S0) = e(x2−x′ 2)β2 min{S−1 0 (p), tXe−x2β2} + eβ1(S−1 0 (p) − tXe−x2β2)+ min{S−1 0 (p), t′ Xe−x′ 2β2} + eβ1(S−1 0 (p) − t′ Xe−x′ 2β2)+ .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Finally, note that when a general flexible effect for X1(t) is specified, in general no closed form exists, but acceleration factors can still be computed numerically.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 32 D Transformed Bernstein Polynomial Prior To illustrate the flexibility of the transformed Bernstein polynomial prior, Figure D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1 shows the basis functions when K = 5, G(p | k, K − k + 1) = Γ(K + 1) Γ(k)Γ(K − k + 1)pk−1(1 − p)K−k.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Moreover, Figure D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 shows a sample of different shapes that the resulting baseline survivor function S0(t | φ, w) = �K k=1 wkG(S∗ 0(t | φ) | k, K − k + 1) can take, for selected weight vectors w and setting S∗ 0(t) = exp(−t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 p G(p) Figure D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='1: Basis functions G for j = 1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' , 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 33 0 1 2 3 4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='6 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='8 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='0 t S0(t) 1 2 3 4 1 2 3 4 w1 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='41 w2 0.' metadata={'source': 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'/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01 w4 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='23 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='03 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='18 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='15 w5 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='64 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='01 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='07 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='41 Figure D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content='2: Sample survivor functions corresponding to varying transformed bernstein poly- nomial prior weight vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' Bold black line shows centering distribution S∗ 0(t) = exp(−t).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'} +page_content=' 34' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/1tE1T4oBgHgl3EQfRwOf/content/2301.03057v1.pdf'}