Bayesian nonparametric survival analysis

Abstract

This thesis makes contributions to the Bayesian nonparametric approach for survival and bioassay problems. It contains creative work towards a simple and practical Bayesian analysis for right-censored failure time data using smoothed prior, and for binary and doubly-censored data using the Dirichlet process prior.

One-sample survival analysis under a smoothed prior is fully studied. The posterior computations are realized via the Gibbs sampler, and illustrated by unmerical examples. Bayesian inference under non-informative priors is addressed and compared with existing results. A compromised version of Bayesian nonparametric approach is proposed which retreats from the infinite-dimensional priors and considers a more practical treatment using data-dependent priors. Links to some well-known results such as Cox's partial likelihood for proportional hazards regression and Hill's rule for prediction are established. Fiducial inference for failure time data is also discussed, which is numerically equivalent to the Bayesian approach under a non-informative and data-dependent prior.

A new auxiliary variables technique is proposed which has substantially simplified the Bayesian bioassay under a Dirichlet process prior, and application is illustrated in cancer risk assessment. The problem of combining many assays is discussed in the empirical Bayes framework, and more complicated types of data such as doubly-censored data are also considered.