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Two commonly used methods for improving precision and power in clinicaltrials are stratified randomization and covariate adjustment. However, manytrials do not fully capitalize on the combined precision gains from these twomethods, which can lead to wasted resources in terms of sample size and trialduration. We derive consistency and asymptotic normality of model-robustestimators that combine these two methods, and show that these estimators canlead to substantial gains in precision and power. Our theorems cover a class ofestimators that handle continuous, binary, and time-to-event outcomes; missingoutcomes under the missing at random assumption are handled as well. For eachestimator, we give a formula for a consistent variance estimator that ismodel-robust and that fully captures variance reductions from stratifiedrandomization and covariate adjustment. Also, we give the first proof (to thebest of our knowledge) of consistency and asymptotic normality of theKaplan-Meier estimator under stratified randomization, and we derive itsasymptotic variance. The above results also hold for the biased-coincovariate-adaptive design. We demonstrate our results using three completed,phase 3, randomized trial data sets of treatments for substance use disorder,where the variance reduction due to stratified randomization and covariateadjustment ranges from 1% to 36%.

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