Modified Goldilocks Design with strict type I error control in confirmatory clinical trials

Goldilocks Design (GD) utilizes predictive probability to adaptively select a trial’s sample size based on accumulating data. In order to control type I error at a desired level for a subset of the null space, extensive simulations at the study design stage are required to choose critical values, which is a challenge for this type of Bayesian adaptive design to be used for confirmatory trials. In this article, we propose a Modified Goldilocks Design (MGD) where type I error is analytically controlled over the entire null space. We do so by applying the conditional invariance principle and a combination test approach on $p$-values that are obtained from independent cohorts of subjects. Simulation studies show that despite analytic control of type I error rate, the proposed MGD has similar power when compared with the original GD. We further apply it to an example trial with time-to-event endpoint in oncology.