Dose Optimization Design for Randomized Phase <scp>II</scp> Trials With Toxicity and Efficacy Endpoints

Several study designs for identifying optimal biological dose (OBD) have been proposed for phase I, II, and I/II clinical trials, considering toxicity and efficacy of anticancer drugs, especially molecular-targeted therapies and immune checkpoint inhibitors. Among these, the multiple-dose randomized phase II trial (MERIT) design selects OBD candidates using hypothesis testing for toxicity and efficacy outcomes. However, it does not consistently control the type I error rate below the significance level, as the null hypothesis is defined only at specific points in a two-dimensional null space. To address this limitation, we developed a design treating toxicity and efficacy as co-primary endpoints, ensuring strict dose-level type I error control across the entire null space. A Bonferroni correction addressed multiplicity in dose selection, providing overall type I error control. Unlike the existing method, the rejection region is determined analytically rather than by simulation, reducing computational costs. The type I error rate of the existing method exceeds the significance level in regions outside points considered in its sample size calculation. By contrast, the proposed method maintains the type I error rate below the significance level across the null space, though conservatively due to the co-primary endpoint framework and Bonferroni adjustment. Required sample sizes of the proposed method tend to be larger than those of the existing one.