Dose Selection Balancing Efficacy and Toxicity Using Bayesian Model Averaging

Successful pharmaceutical drug development requires identifying ranges of doses providing an acceptable efficacy response while not causing unacceptable intolerance or toxicity. This article describes a novel application of Bayesian model averaging (BMA) methodology to the construction of dose ranges with a high probability of clinical acceptability that can be read directly from simple graphical displays. The ranges are based on posterior distributions of efficacy and toxicity outcomes from possibly different unknown functional dose–response relationships and different likelihoods. The approach provides an operationally practical, graphically oriented, model agnostic strategy that is distributionally general, statistically valid, and allows for continuous, binary, or ordinal data. Efficacy and toxicity are considered in two ways: as separate outcomes for which possibly different dose–response functions are fitted along with simultaneous error bounds, and as outcomes generated by ordinal distributions of categories combining efficacy and toxicity nonlinearly. The calculations are carried out with readily available R software and require no additional programming. The performance of the method is evaluated via three simulation studies using efficacy and toxicity outcomes generated from copulas with different association patterns, and with application to a real clinical example. In all cases, the BMA strategy identified consistent ranges of acceptable doses.