Designs of Early Phase Cancer Trials with Drug Combinations

We discuss several innovative phase I and phase I--II designs for early phase cancer clinical trial with drug combinations focusing on continuous dose levels of both agents. For phase I trials with drug combinations, the main objective is to estimate the maximum tolerated dose (MTD) curve in the two-dimensional Cartesian plane. A parametric model is used to describe the relationship between the doses of the two agents and the probability of dose-limiting toxicity (DLT). Trial design proceeds using cohorts of two patients receiving doses according to univariate escalation with overdose control (EWOC) or continual reassessment method (CRM). At the end of the trial, the MTD is estimated as a function of Bayes estimates of the model parameters. Furthermore, we present the model where a fraction of DLTs can be attributed to one or both agents, and show how the parametric designs can be adapted to account for an unknown fraction of attributable DLTs. We also consider the inclusion of a binary baseline covariate to describe sub-groups with different frailty levels. In phase I--II trials, it may not be possible to evaluate efficacy in a short window of time. In this case, two-stage designs are frequently employed. First, a set of maximum tolerated dose combinations is selected. Next, the selected set is then tested for efficacy, sometimes in a different patient population than that used in the first stage. We discuss binary and time-to-event endpoints to identify dose combinations along the MTD curve with maximum probability of efficacy in the second stage.