  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 three completed,
phase 3, randomized trial data sets of treatments for substance use disorder,
where the variance reduction due to stratified randomization and covariate
adjustment ranges from 1% to 36%.
