Bayesian dose finding in oncology for drug combinations by copula regression

Treating patients with a combination of agents is becoming commonplace in cancer clinical trials, with biochemical synergism often the primary focus. In a typical drug combination trial, the toxicity profile of each individual drug has already been thoroughly studied in single-agent trials, which naturally offers rich prior information. We propose a Bayesian adaptive design for dose finding that is based on a copula-type model to account for the synergistic effect of two or more drugs in combination. To search for the maximum tolerated dose combination, we continuously update the posterior estimates for the toxicity probabilities of the combined doses. By reordering the dose toxicities in the two-dimensional probability space, we adaptively assign each new cohort of patients to the most appropriate dose. Dose escalation, de-escalation or staying at the same doses is determined by comparing the posterior estimates of the probabilities of toxicity of combined doses and the prespecified toxicity target. We conduct extensive simulation studies to examine the operating characteristics of the design and illustrate the proposed method under various practical scenarios.