Semiparametric Bayesian Analysis of Survival Data

Abstract

Abstract This review article investigates the potential of Bayes methods for the analysis of survival data using semiparametric models based on either the hazard or the intensity function. The nonparametric part of every model is assumed to be a realization of a stochastic process. The parametric part, which may include a regression parameter or a parameter quantifying the heterogeneity of a population, is assumed to have a prior distribution with possibly unknown hyperparameters. Careful applications of some recently popular computational tools, including sampling-based algorithms, are used to find posterior estimates of several quantities of interest even when dealing with complex models and unusual data structures. The methodologies developed herein are motivated and aimed at analyzing some common types of survival data from different medical studies; here we focus on univariate survival data in the presence of fixed and time-dependent covariates, multiple event-time data for repeated nonfatal events, and multivariate survival data (subjects are related; e.g., families or litters), each patient with interval-censored infection time and interval-censored disease occurrence time in tandem [e.g., patients with acquired immunodeficiency syndrome (AIDS) and other infectious diseases with long incubation times]. Bayesian exploratory data analysis (EDA) methods and diagnostics for model selection and model assessment are considered for each case. Special attention is given to tests of the parametric modeling assumptions and to censoring.