BAYESIAN METHODS FOR CLINICAL TRIAL DESIGN: APPROACHES FOR JOINT MODELS

Joint models are increasingly used for the analysis of clinical trials data. However, few methods have been proposed for designing clinical trials using these models. In this dissertation, we propose an approach for sample size determination such that the design has a high power and a well-controlled type I error rate with both defined from a Bayesian perspective. In the first project, we develop a Bayesian clinical trial design focused on evaluating an investigational product’s (IP’s) effect on the time-to-event endpoint using a flexible trajectory joint model. By incorporating the longitudinal trajectory into the hazard model for the time-to-event endpoint, the joint modeling framework allows for nonproportional hazards (e.g., an increasing hazard ratio over time). Inference for the time-to-event endpoint is based on an average of time-varying hazard ratio which can be decomposed according to the IP’s direct effect on the time-to-event endpoint and its indirect effect, mediated through the longitudinal outcome. In the second project, we develop a Bayesian design focused on estimating treatment effect on recurrent event and the terminating event processes with both considered as multiple primary endpoints, using a multi-frailty joint model. Dependence between the recurrent and terminating event processes are accounted for using a shared frailty. Inferences for the multiple primary outcomes are based on posterior model probabilities corresponding to mutually exclusive hypotheses regarding the benefit of IP with respect to the recurrent and terminating event processes. A colorectal cancer clinical trial is designed with to demonstrate that the IP causes a favorable effect on at least one of the two outcomes but no harm on either. In the third project, we develop a Bayesian clinical trial design focused on evaluating the treatment’s effect on a time-to-event endpoint using a promotion time cure rate model. A piecewise linear hazard model for the period after assessment of the longitudinal measure ends is proposed as an alternative to extrapolating the longitudinal trajectory. Inference for the time-to-event endpoint is based on an estimand which combines the treatment’s effect on the probability of cure and its effect on the promotion time distribution, mediated by the longitudinal outcome.Doctor of Philosoph