Optimal Treatment Allocations Accounting for Population Differences

The treatment allocation mechanism in a randomized clinical trial can be optimized by maximizing the nonparametric efficiency bound for a specific measure of treatment effect. Optimal treatment allocations which may or may not depend on baseline covariates have been derived for a variety of effect measures focusing on the trial population, the patient population represented by the trial participants. Frequently, clinical trial data are used to estimate treatment effects in a target population that is related to but different from the trial population. This article provides optimal treatment allocations that account for the impact of such population differences. We consider three cases with different data configurations: transportation, generalization, and post-stratification. Our results indicate that, for general effect measures, optimal treatment allocations may depend on the covariate distribution in the target population but not on the configuration of data or information that describes the target covariate distribution. For estimating average treatment effects, there is a unique covariate-dependent allocation that achieves maximal efficiency regardless of the target covariate distribution and the associated data configuration.