Abstract
We consider the problem of optimizing treatment allocation for statistical efficiency in randomized clinical trials. Optimal allocation has been studied previously for simple treatment effect estimators such as the sample mean difference, which are not fully efficient in the presence of baseline covariates. More efficient estimators can be obtained by incorporating covariate information, and modern machine learning methods make it increasingly feasible to approach full efficiency. Accordingly, we derive the optimal allocation ratio by maximizing the design efficiency of a randomized trial, assuming that an efficient estimator will be used for analysis. We then expand the scope of optimization by considering covariate-dependent randomization (CDR), which has some flavor of an observational study but provides the same level of scientific rigor as a standard randomized trial. We describe treatment effect estimators that are consistent, asymptotically normal, and (nearly) efficient under CDR, and derive the optimal propensity score by maximizing the design efficiency of a CDR trial (under the assumption that an efficient estimator will be used for analysis). Our optimality results translate into optimal designs that improve upon standard practice. Real-world examples and simulation results demonstrate that the proposed designs can produce substantial efficiency improvements in realistic settings.