Parametric dose standardization for optimizing two-agent combinations in a phase I–II trial with ordinal outcomes

A Bayesian model and design are described for a phase I–II trial to optimize jointly the doses of a targeted agent and a chemotherapy agent for solid tumours. A challenge in designing the trial was that both the efficacy and the toxicity outcomes were defined as four-level ordinal variables. To reflect possibly complex joint effects of the two doses on each of the two outcomes, for each marginal distribution a generalized continuation ratio model was assumed, with each agent's dose parametrically standardized in the linear term. A copula was assumed to obtain a bivariate distribution. Elicited outcome probabilities were used to construct a prior, with variances calibrated to obtain small prior effective sample size. Elicited numerical utilities of the 16 elementary outcomes were used to compute posterior mean utilities as criteria for selecting dose pairs, with adaptive randomization to reduce the risk of becoming stuck at a suboptimal pair. A simulation study showed that parametric dose standardization with additive dose effects provides a robust reliable model for dose pair optimization in this setting, and it compares favourably with designs based on alternative models that include dose–dose interaction terms. The model and method proposed are applicable generally to other clinical trial settings with similar dose and outcome structures.