Bayesian optimal interval design with multiple toxicity constraints

Most phase I dose-finding trials are conducted based on a single binary toxicity outcome to investigate the safety of new drugs. In many situations, however, it is important to distinguish between various toxicity types and different toxicity grades. By minimizing the maximum joint probability of incorrect decisions, we extend the Bayesian optimal interval (BOIN) design to control multiple toxicity outcomes at prespecified levels. The developed multiple-toxicity BOIN design can handle equally important, unequally important as well as nested toxicity outcomes. Interestingly, we find that the optimal interval boundaries with non-nested toxicity outcomes under the proposed method coincide with those under the standard single-toxicity BOIN design by treating the multiple toxicity outcomes marginally. We establish several desirable properties for the proposed interval design. We additionally extend our design to address trials with combined drugs. The finite-sample performance of the proposed methods is assessed according to extensive simulation studies and is compared with those of existing methods. Simulation results reveal that, our methods are as accurate and efficient as the more complicated model-based methods, but are more robust and much easier to implement.