that involve stratified randomization, which is commonly used. It is

important to understand the large sample properties of estimators that

adjust for stratum variables (those used in the randomization

procedure) and additional baseline variables, since this can lead to

substantial gains in precision and power. Surprisingly, to the best

of our knowledge, this is an open problem. It was only recently that a

simpler problem was solved by Bugni et al. (2018) for the case with no

additional baseline variables, continuous outcomes, the analysis of

covariance (ANCOVA) estimator, and no missing data. We generalize

their results in three directions. First, in addition to continuous

outcomes, we handle binary and time-to-event outcomes; this broadens

the applicability of the results. Second, we allow adjustment for an

additional, preplanned set of baseline variables, which can improve

precision. Third, we handle missing outcomes under the missing at

random assumption. We prove that a wide class of estimators is

asymptotically normally distributed under stratified randomization and

has equal or smaller asymptotic variance than under simple

randomization. For each estimator in this class, we give a consistent

variance estimator. This is important in order to fully capitalize on

the combined precision gains from stratified randomization and

adjustment for additional baseline variables. The above results also

hold for the biased-coin covariate-adaptive design. We demonstrate our

results using completed trial data sets of treatments for substance

use disorder, where adjustment for additional baseline variables

brings substantial variance reduction.

]]>We compare TMLE versus MMRM by analyzing data from a completed Alzheimer's disease trial data set and by simulation studies. The simulations involved different missing data distributions, where loss to followup at a given visit could depend on baseline variables, treatment assignment, and the outcome measured at previous visits. The TMLE generally has improved robustness in our simulated settings, i.e., less bias and mean squared error, and better confidence interval coverage probability. The robustness is due to the TMLE correctly modeling the dropout distribution. We illustrate the tradeoffs between these estimators and give recommendations for how to use these estimators in practice.

]]>]]>