Title

Bayesian methodology for survival data with competing risks

Date of Completion

January 2011

Keywords

Statistics

Degree

Ph.D.

Abstract

Competing risks data are routinely encountered in various medical applications due to the fact that patients may die from different causes. Recently, several models have been proposed for fitting such survival data. In this research work, the model of Fine and Gray (1999) is extended to develop a new model with subdistribution hazard of the primary cause and conditional hazards of other causes. Various properties of this proposed extended subdistribution model have been examined. An efficient Gibbs sampling algorithm via latent variables is developed to carry out posterior computations. Deviance Information Criterion (DIC) and Logarithm of the Pseudomarginal Likelihood (LPML) are used for model comparison. An extensive simulation study is carried out to examine the performance of DIC and LPML in comparing the cause-specific hazards model, the mixture model, and the extended subdistribution model. The proposed methodology is applied to analyze a real dataset from a prostate cancer study in details. ^ In the survival data analysis, the likelihood may converge to certain finite value with one or more than one parameter estimates diverging to infinity. This monotone likelihood problem can happen a lot in clinical studies, where zero event in certain study arms is one possible situation. Penalized maximum partial likelihood estimation was introduced as an efficient frequentist solution in Heinze and Schemper (2001). The Bayesian solution is yet lacking. In this dissertation, Jeffreys type priors as well as hierarchical priors are proposed for the competing risks model. Simple illustrations applying both types of priors are shown. ^ It is important in survival data analysis to choose a proper time scale in the modeling. Different definitions of time zero lead to different formulations of time scales. Timeon-study scale, age scale, and calendar period scale are compared and discussed. The cause-specific hazards models using different time scales are fitted to a real dataset from a prostate cancer study. ^