Design and monitoring of clinical trials with an interim analysis and a negative binomial endpoint

There are very rich publications devoted to group sequential design, adaptive design and trial monitoring for continuous, binary and time to event endpoints. Many authors also discuss fixed design, blinded sample size re-estimation design and group sequential design for studies with a negative binomial outcome. Nonetheless, literature is sparse in adaptive design for a trial with a negative binomial endpoint. The features of such an endpoint in a flexible trial design setting remains inadequately understood. In this research, we seek to bridge this knowledge gap by offering a thorough examination of utilizing data components from a two-stage adaptive design for unblinded conditional power calculation and corresponding sample size re-estimation. We also provide expression for calculating the probability of meeting the futility criterion to determine the appropriate timing for the interim analysis. To evaluate the performance of the design, we conduct simulations to assess its operation characteristics. Finally, we provide a helpful and illustrative example to demonstrate the practical applications of the methods.