Optimal Stopping for Clinical Trials with Economic Costs: A Simulation-Based Approach

We consider the problem of designing an early stopping clinical trial investigating the efficacy of a medical intervention against the available standard of care. The standard approach is to determine a stopping rule minimizing the expected number of patients required, subject to error rate constraints, not considering costs explicitly depending on the magnitude of the treatment effect. In this paper we formulate an optimal stopping problem for clinical trials with instantaneous continuous response, the objective being minimizing an overall risk comprising loss functions accounting for costs involving the treatment effect that might model ethical and economic costs. To solve the optimization problem we propose a feasible directions simulation-based algorithm requiring new stochastic gradient estimators which we derive using Smoothed Perturbation Analysis. We conduct simulation experiments to test the effectiveness of the simulation optimization algorithm and to obtain insights on the effects of the various risk factors on the optimal solution.