A unified framework for fitting Bayesian semiparametric models to arbitrarily censored survival data, including spatially-referenced data

TL;DR

This paper introduces a unified Bayesian framework for fitting semiparametric spatial survival models accommodating various censored data types, with flexible model selection and a novel prior, demonstrated through simulations and real data.

Contribution

It presents a comprehensive Bayesian approach for spatial survival data, including a new prior, efficient computation, and flexible model fitting for multiple censoring types.

Findings

Proportional odds and AFT models often outperform PH models.

The framework effectively handles diverse censoring and spatial data types.

Model selection tools like LPML and DIC are successfully integrated.

Abstract

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.