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Two commonly used methods for improving precision and power in clinical trials are stratified randomization and covariate adjustment. However, many trials do not fully capitalize on the combined precision gains from these two methods, which can lead to wasted resources in terms of sample size and trial duration. We derive consistency and asymptotic normality of model-robust estimators that combine these two methods, and show that these estimators can lead to substantial gains in precision and power. Our theorems cover a class of estimators that handle continuous, binary, and time-to-event outcomes; missing outcomes under the missing at random assumption are handled as well. For each estimator, we give a formula for a consistent variance estimator that is model-robust and that fully captures variance reductions from stratified randomization and covariate adjustment. Also, we give the first proof (to the best of our knowledge) of consistency and asymptotic normality of the Kaplan–Meier estimator under stratified randomization, and we derive its asymptotic variance. The above results also hold for the biased-coin covariate-adaptive design. We demonstrate our results using data from three trials of substance use disorder treatments, where the variance reduction due to stratified randomization and covariate adjustment ranges from 1% to 36%.  Supplementary materials  for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Model-Robust Inference for Clinical Trials that Improve Precision by Stratified Randomization and Covariate Adjustment