Optimizing doses for multiple indications is challenging. The pooled approach of finding a single optimal biological dose (OBD) for all indications ignores that dose-response or dose-toxicity curves may differ between indications, resulting in varying OBDs. Conversely, indication-specific dose optimization often requires a large sample size. To address this challenge, we propose a Randomized two-stage basket trial design that Optimizes doses in Multiple Indications (ROMI). In stage 1, for each indication, response and toxicity are evaluated for a high dose, which may be a previously obtained MTD, with a rule that stops accrual to indications where the high dose is unsafe or ineffective. Indications not terminated proceed to stage 2, where patients are randomized between the high dose and a specified lower dose. A latent-cluster Bayesian hierarchical model is employed to borrow information between indications, while considering the potential heterogeneity of OBD across indications. Indication-specific utilities are used to quantify response-toxicity trade-offs. At the end of stage 2, for each indication with at least one acceptable dose, the dose with highest posterior mean utility is selected as optimal. Two versions of ROMI are presented, one using only stage 2 data for dose optimization and the other optimizing doses using data from both stages. Simulations show that both versions have desirable operating characteristics compared to designs that either ignore indications or optimize dose independently for each indication.

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