Combination therapy of two antitumor agents may provide treatment additivity or synergy. Phase I trials for combination therapy search for the maximum tolerated dose (MTD) for combined agents. The conventional approach is to preselect an escalation path, usually increasing the dose of one agent and then another, and to use the standard 3 + 3 design. However, this procedure may miss the optimum dose combination, prolong the time it takes, and increase the number of patients necessary to reach the MTD. In this study, we present strategies for a comprehensive search for MTD for a two-agent combination therapy. We evaluate algorithms based on two-stage and three-stage design as well as variations in cohort size. A two-dimensional isotonic estimation method for toxicity rate is provided. We use simulation methods to compare 2 + 1 + 3 vs. 3 + 3 cohort sizes. We conclude that the comprehensive search proposed in our study can be more practical and efficient in identifying the MTD in combination-therapy of two agents.

Existing algorithms for identifying the maximum tolerated combination in dose-finding trials of two agents are mostly one-dimensional. Moreover, these algorithms use only the frequency of observed dose-limiting toxicities as the basis for dose escalations and deescalations. In this article, we propose a two-dimensional algorithm that uses not only the frequency but also the source of dose-limiting toxicities to direct dose escalations and deescalations. In addition, when the doses of both agents are escalated simultaneously, a more conservative design replaces a default aggressive design to evaluate the resulting dose combination. Our method aims to increase in-trial patient safety without unnecessary increase in sample size.

A flexible and simple Bayesian decision-theoretic design for dose-finding trials is proposed in this paper. In order to reduce the computational burden, we adopt a working model with conjugate priors, which is flexible to fit all monotonic dose-toxicity curves and produces analytic posterior distributions. We also discuss how to use a proper utility function to reflect the interest of the trial. Patients are allocated based on not only the utility function but also the chosen dose selection rule. The most popular dose selection rule is the one-step-look-ahead (OSLA), which selects the best-so-far dose. A more complicated rule, such as the two-step-look-ahead, is theoretically more efficient than the OSLA only when the required distributional assumptions are met, which is, however, often not the case in practice. We carried out extensive simulation studies to evaluate these two dose selection rules and found that OSLA was often more efficient than two-step-look-ahead under the proposed Bayesian structure. Moreover, our simulation results show that the proposed Bayesian method's performance is superior to several popular Bayesian methods and that the negative impact of prior misspecification can be managed in the design stage.

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A decision-theoretic framework is proposed for designing sequential dose-finding trials with multiple outcomes. The optimal strategy is solvable theoretically via backward induction. However, for dose-finding studies involving k doses, the computational complexity is the same as the bandit problem with k-dependent arms, which is computationally prohibitive. We therefore provide two computationally compromised strategies, which is of practical interest as the computational complexity is greatly reduced: one is closely related to the continual reassessment method (CRM), and the other improves CRM and approximates to the optimal strategy better. In particular, we present the framework for phase I/II trials with multiple outcomes. Applications to a pediatric HIV trial and a cancer chemotherapy trial are given to illustrate the proposed approach. Simulation results for the two trials show that the computationally compromised strategy can perform well and appear to be ethical for allocating patients. The proposed framework can provide better approximation to the optimal strategy if more extensive computing is available.