Bayesian Inference of survival data with gamma process priors

Date of Completion

January 2011






Cox's (1972) Proportional Hazards (PH) model is one of the most popular models for fitting survival data with covariates. This model assumes that the hazard functions are proportional over time. In practice, however, this assumption is often not valid. For this reason several extensions to nonproportional hazards models have been discussed in the literature. Here we have studied the Generalized Odds Rate Hazards (GORH) model. To estimate the parameters in the PH model Cox proposed the partial likelihood approach. Bayesian method of estimation was introduced by Kalbfleisch (1978) when the cumulative baseline hazard function is assumed to be a stochastic process and in particular a Gamma Process with independent increments. In this study we develop an efficient Bayesian method of estimation for the GORH model under the same setting. Several sets of latent variables have been introduced to facilitate the posterior computation. Conditional Predictive Ordinate has been developed for the PH and GORH models to assess model fit. An innovative simulation algorithm via direct forward sampling and Gibbs sampling is developed to generate tied failure times for simulation studies. We proposed a novel Bayesian method to handle the extensive ties in the datasets and compared it to the existing Breslow (1974) method. The Bayesian Deviance Information Criterion (DIC) has also been derived for model comparison. We have further extended our proposed method to the GORH model and the posterior computation has been discussed. ^