A two-dimensional biased coin design for dual-agent dose-finding trials

Given the limited efficacy observed with single agents, there is growing interest in Phase I clinical trial designs that allow for identification of the maximum tolerated combination of two agents.

Existing parametric designs may suffer from over- or under-parameterization. Thus, we have designed a nonparametric approach that can be easily understood and implemented for combination trials.

We propose a two-stage adaptive biased coin design that extends existing methods for single-agent trials to dual-agent dose-finding trials. The basic idea of our design is to divide the entire trial into two stages and apply the biased coin design, with modification, in each stage.

We compare the operating characteristics of our design to four competing parametric approaches via simulation in several numerical examples. Under all simulation scenarios we have examined, our method performs well in terms of identification of the maximum tolerated combination and allocation of patients relative to the performance of its competitors.

In our design, stopping rule criteria and the distribution of the total sample size among the two stages are context-dependent, and both need careful consideration before adopting our design in practice. Efficacy is not a part of the dose-assignment algorithm, nor used to define the maximum tolerated combination.

Our design inherits the favorable statistical properties of the biased coin design, is competitive with existing designs, and promotes patient safety by limiting patient exposure to toxic combinations whenever possible.