Flexible link continual reassessment methods for trivariate binary outcome phase I/II Trials

Even though the primary goal of a Phase I clinical trial is to determine the dosing schedule of a new treatment subject to toxicity or other safety concerns, treatment efficacy often remains an important secondary consideration. In such settings, the trial may collect both information on final efficacy as well as a surrogate efficacy marker that is obtained more easily, quickly, or both. Extended versions of Bayesian continual reassessment methods (CRMs) offer an attractive approach for a principled combination of all three sources of information, but the precise shape of the dose-response curve may be difficult to specify, especially with the small sample sizes typical of early phase studies. In this article, we propose flexible semi- and nonparametric link functions for a trivariate binary outcome CRM that allows for differential weighting of the outcomes, or even within outcome (say, higher penalties for over- rather than undershooting toxicity). Illustrating in the context of a non-Hodgkin lymphoma trial, we show via simulation that our flexible link methods can outperform standard parametric CRM approaches in terms of both the probability of correct dose selection and the proportion of patients treated at that dose.