Bayes methods in group sequential clinical trials

Bayesian methods for group sequential clinical trials have received increasing at­tention recently. They offer an approach for dealing with many difficult problems and have some practical advantages over frequentist methods. This thesis covers Bayesian methods for group sequential clinical trials comparing two treatments using both the Bayes sequential procedure and the Bayes sequential decision pro­cedure. The main outcome measures for clinical trials are distributed as normal, binomial, and exponential and the proportional hazard model for survival time data. Under the framework of Bayes sequential procedure for group sequential clini­cal trials, the student t prior distribution for the parameter of interest is proposed as a replacement for the normal prior distribution when the sample mean is very distant from the mean of the prior distribution. The framework of Bayes sequen­tial procedure in clinical trials on normal distribution responses with variance unknown is given. Bayes sequential decision theory is applied to group sequential clinical trials. First, Bayes sequential decision procedures with piecewise continuous loss func­tions are used in clinical trials on normal distribution responses. The procedures with loss functions which consider treatment efficacy and patient horizon are then given in clinical trials on binary responses. Approximation methods of Bayes sequential decision procedures are explored in clinical trials with survival time data. Robust Bayes analysis in clinical trials is presented to address the criticism on the subjective prior distribution for parameters of interest.