Robust Bayesian monitoring of sequential trials

Abstract

In sequential experiments the sample size is not planned in advance. Data are progressively collected and a stopping rule based on the observed results is defined in order to terminate the study. In a Bayesian framework, it is straightforward to monitor an ongoing experiment looking at the posterior probability that a parameter of interest $$\theta $$ , belongs to a given set. Specifically, in this paper we focus on the context of phase II clinical trials, where $$\theta $$ represents treatment efficacy. The Bayesian stopping rule we adopt involves the posterior probability that $$\theta $$ exceeds a clinically relevant threshold. Moreover, we introduce a robust version of this criterion by replacing the single prior distribution with a class of prior distributions. A simulation study is performed to compare the average sample sizes of the robust sequential approach both with the sample sizes of the non robust approach and of the non sequential approach. An interesting result is that, when the class of prior distributions is sufficiently narrow, the average sample sizes of the robust sequential approach can be smaller than the non sequential sample sizes.