AbstractsMathematics

In clinical trials, subgroup analysis refers to the experimental design and statistical analysisto investigate the efficacy of a new drug in patient groups defined by baseline characteristicssuch as age and gender. While it has become a standard to report subgroup efficacy in aclinical trial, many statistical issues such as multiplicity and lack of power have not beenwell addressed.In this dissertation, we first review the Bayesian approach to subgroup analysis proposedin [18]. We extend this framework using an additive model to allow multiple covariates.Two stepwise algorithms are then proposed for Bayesian model selection. In this Bayesiansetting, multiplicity is controlled by choosing prior distributions for the inclusion parametersin the zero-enrich polya urn scheme, and the thresholds for posterior probability ratios in thestepwise procedure. A special case with two covariates each at two levels are fully discussedand studied using simulations. We also extend the additive model by allowing three-wayinteraction term that represents covariate interaction on subgroup efficacy. We apply theproposed additive model to a read data example from a clincial trial study.