Bayesian adaptive dose-escalation procedures for binary and continuous responses utilizing a gain function

One of the main aims of early phase clinical trials is to identify a safe dose with an indication of therapeutic benefit to administer to subjects in further studies. Ideally therefore, dose-limiting events (DLEs) and responses indicative of efficacy should be considered in the dose-escalation procedure. Several methods have been suggested for incorporating both DLEs and efficacy responses in early phase dose-escalation trials. In this paper, we describe and evaluate a Bayesian adaptive approach based on one binary response (occurrence of a DLE) and one continuous response (a measure of potential efficacy) per subject. A logistic regression and a linear log-log relationship are used respectively to model the binary DLEs and the continuous efficacy responses. A gain function concerning both the DLEs and efficacy responses is used to determine the dose to administer to the next cohort of subjects. Stopping rules are proposed to enable efficient decision making. Simulation results shows that our approach performs better than taking account of DLE responses alone. To assess the robustness of the approach, scenarios where the efficacy responses of subjects are generated from an Emax model, but modelled by the linear log-log model are also considered. This evaluation shows that the simpler log-log model leads to robust recommendations even under this model showing that it is a useful approximation to the difficulty in estimating Emax model. Additionally, we find comparable performance to alternative approaches using efficacy and safety for dose-finding.