Using joint utilities of the times to response and toxicity to adaptively optimize schedule-dose regimes

A Bayesian two-stage phase I-II design is proposed for optimizing administration schedule and dose of an experimental agent based on the times to response and toxicity in the case where schedules are non-nested and qualitatively different. Sequentially adaptive decisions are based on the joint utility of the two event times. A utility function is constructed by partitioning the two-dimensional positive real quadrant of possible event time pairs into rectangles, eliciting a numerical utility for each rectangle, and fitting a smooth parametric function to the elicited values. We assume that each event time follows a gamma distribution with shape and scale parameters both modeled as functions of schedule and dose. A copula is assumed to obtain a bivariate distribution. To ensure an ethical trial, adaptive safety and efficacy acceptability conditions are imposed on the (schedule, dose) regimes. In stage 1 of the design, patients are randomized fairly among schedules and, within each schedule, a dose is chosen using a hybrid algorithm that either maximizes posterior mean utility or randomizes among acceptable doses. In stage 2, fair randomization among schedules is replaced by the hybrid algorithm. A modified version of this algorithm is used for nested schedules. Extensions of the model and utility function to accommodate death or discontinuation of follow up are described. The method is illustrated by an autologous stem cell transplantation trial in multiple myeloma, including a simulation study.