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 LPML and 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 are available online.

针对三类最常用的半参数模型：比例风险（proportional hazards）、比例优势（proportional odds）与加速失效时间（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统一完备方法。与多数现有方法不同，本方法可同时适配各类删失生存时间数据，涵盖未删失、区间删失、当前状态（current-status）、左删失、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，进而支持时变协变量（time-dependent covariates）模型的构建。本方法可同时处理地理参考（georeferenced，即位置精确观测）与面域观测（areally observed，即位置可通过县等地理单元确定）两类空间位置数据；其内置的形式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，模型选择则可借助LPML与DIC指标完成。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新开发的函数实现拟合，该函数会调用R包spBayesSurv中经过高效编译的C++代码。本文通过模拟实验与真实数据应用场景，对所提方法进行了全面演示。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。本文补充材料可在线获取。