Phase I/<scp>II</scp> Design for Selecting Subgroup‐Specific Optimal Biological Doses for Prespecified Subgroups

We propose a phase I/II trial design to support dose-finding when the optimal biological dose (OBD) may differ in two prespecified patient subgroups. The proposed design uses a utility function to quantify efficacy-toxicity trade-offs, and a Bayesian model with spike and slab prior distributions for the subgroup effect on toxicity and efficacy to guide dosing and to facilitate identifying either subgroup-specific OBDs or a common OBD depending on the resulting trial data. In a simulation study, we find the proposed design performs nearly as well as a design that ignores subgroups when the dose-toxicity and dose-efficacy relationships are the same in both subgroups, and nearly as well as a design with independent dose-finding within each subgroup when these relationships differ across subgroups. In other words, the proposed adaptive design performs similarly to the design that would be chosen if investigators possessed foreknowledge about whether the dose-toxicity and/or dose-efficacy relationship differs across two prespecified subgroups. Thus, the proposed design may be effective for OBD selection when uncertainty exists about whether the OBD differs in two prespecified subgroups.