BOP2-TE: Bayesian optimal phase 2 design for jointly monitoring efficacy and toxicity with application to dose optimization.

We propose a Bayesian optimal phase 2 design for jointly monitoring efficacy and toxicity, referred to as BOP2-TE, to improve the operating characteristics of the BOP2 design proposed by Zhou. BOP2-TE utilizes a Dirichlet-multinomial model to jointly model the distribution of toxicity and efficacy endpoints, making go/no-go decisions based on the posterior probability of toxicity and futility. In comparison to the original BOP2 and other existing designs, BOP2-TE offers the advantage of providing rigorous type I error control in cases where the treatment is toxic and futile, effective but toxic, or safe but futile, while optimizing power when the treatment is effective and safe. As a result, BOP2-TE enhances trial safety and efficacy. We also explore the incorporation of BOP2-TE into multiple-dose randomized trials for dose optimization, and consider a seamless design that integrates phase I dose finding with phase II randomized dose optimization. BOP2-TE is user-friendly, as its decision boundary can be determined prior to the trial's onset. Simulations demonstrate that BOP2-TE possesses desirable operating characteristics. We have developed a user-friendly web application as part of the BOP2 app, which is freely available at https://www.trialdesign.org.