Comparing Survival Data For Two Therapies: Nonhierarchical and Hierarchical Bayesian Approaches
The problem of comparing two therapies with survival data is considered from a Bayesian point of view. Survival times on each therapy are assumed to have an exponential distribution. The posterior distribution of the log hazard ratio of the experimental therapy to the standard therapy is the basis of inference. Two models are proposed in this dissertation. The first assumes center homogeneity and the second uses a Bayesian hierarchical model for heterogeneity of therapy effects among different centers in a multicenter trial. Center heterogeneity in a multicenter trial is explored in terms of the posterior distributions of the first and second stage parameters as well as the predictive distributions of survival time on each therapy at every center. Posterior distributions of parameters in the first model are derived by doing numerical integration on univariate functions. Posterior distributions of parameters in the second model are derived by using a sampling based algorithm, calld algorithm, called Gibbs sampling. Sensitivity of results to the prior belief is examined by doing the analysis on some different prior distributions. In the first model, stress is given to the prior variance of the log hazard ratio. In the second model, stress is given to the prior belief of the center heterogeneity. Two clinical trials are analyzed in this dissertation as examples. One is a phase III clinical trial conducted by Cancer and Leukemia Group B to test two therapies for treatment of patients with stage III non-small cell lung cancer. The other is a NIMH-PRB Collaborative Study of Long-Term Maintance Drug Therapy in Recurrent Affective Illness.