Survival Analysis

Abstract

Inference for event time data is one of the most traditional applications of nonparametric Bayesian inference. For survival data, especially in biomedical applications, it is natural to focus on inference for detailed features of the survival function rather than only summaries like mean and variance. We extensively discuss semi-and nonparametric Bayesian methods for survival regression. Inference for such data has been traditionally dominated by the proportional hazards model. We review in detail nonparametric Bayesian alternatives which we introduce as natural generalizations of a parametric accelerated failure time model. We conclude with a discussion of three case studies. Distribution Estimation for Event TimesA special case of density estimation arises in survival analysis as density estimation with event time data, usually involving censoring. Survival analysis is a very traditional application of BNP in the early literature. Any of the earlier discussed models for density estimation can be used for event time data, including DP, DP mixtures, PT, etc. In the following example we use a mixture of finite PTs (MPT) and a DP prior to estimate an event time distribution. Figure 6.1a shows the estimated survival curve EfS.t/ j datag, together with pointwise approximate 80 % CIs. The model is fit via the MCMC algorithm described in Hanson (2006a). Alternatively, we fit a DP model, F DP.M; F ? /. The centering distribution F ? is fixed as an exponential model with m.l.e. rate and the DP mass parameter is M D 1. Figure 6.1b shows the estimated survival curves under the DP prior.Software note: R code for the fit under the DP prior is available at this chapter's software page on-line.Besides the PT and DP models, many other priors for baseline hazard, cumulative hazard, or survival functions have been successfully employed over the last 20