A Unified Framework for Fitting Bayesian Semiparametric Models to Arbitrarily Censored Survival Data, Including Spatially Referenced Data

A comprehensive, unified approach to modeling arbitrarily censored spatial survival data is presented for the three most commonly used semiparametric models: proportional hazards, proportional odds, and accelerated failure time. Unlike many other approaches, all manner of censored survival times are simultaneously accommodated including uncensored, interval censored, current-status, left and right censored, and mixtures of these. Left-truncated data are also accommodated leading to models for time-dependent covariates. Both georeferenced (location exactly observed) and areally observed (location known up to a geographic unit such as a county) spatial locations are handled; formal variable selection makes model selection especially easy. Model fit is assessed with conditional Cox–Snell residual plots, and model choice is carried out via log pseudo marginal likelihood (LPML) and deviance information criterion (DIC). Baseline survival is modeled with a novel transformed Bernstein polynomial prior. All models are fit via a new function which calls efficient compiled C++ in the R package spBayesSurv. The methodology is broadly illustrated with simulations and real data applications. An important finding is that proportional odds and accelerated failure time models often fit significantly better than the commonly used proportional hazards model. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

针对三类最常用的半参数模型（semiparametric models）——比例风险模型（proportional hazards）、比例优势模型（proportional odds）以及加速失效时间模型（accelerated failure time），本文提出了一种用于建模任意删失空间生存数据的全面且统一的方法。与多数现有方法不同，本方法可同时适配所有类型的删失生存时间数据，包括未删失、区间删失、现状删失（current-status）、左删失与右删失数据，以及上述类型的混合数据。同时还可处理左截断数据，从而支持时变协变量（time-dependent covariates）模型的构建。本方法可同时覆盖地理参考（georeferenced，即位置精确观测）与面状观测（areally observed，即位置已知至县级等地理单元）两类空间点位；内置的标准化变量选择流程可大幅简化模型选择工作。模型拟合效果可通过条件Cox-Snell残差图进行评估，模型选择则借助对数伪边际似然（log pseudo marginal likelihood, LPML）与偏差信息准则（deviance information criterion, DIC）完成。基线生存函数采用一种新颖的变换伯恩斯坦多项式先验（transformed Bernstein polynomial prior）进行建模。所有模型均可通过一款全新的函数实现拟合，该函数会调用R包spBayesSurv中经过编译的高效C++代码。本文通过仿真实验与真实数据应用案例，对所提方法进行了全面的演示验证。一项重要研究发现表明，比例优势模型与加速失效时间模型的拟合效果通常显著优于当前常用的比例风险模型。本文的补充材料（包含可复现研究所需材料的标准化说明）可作为在线附录获取。