  One approach for increasing the efficiency of randomized trials is the use of
"external controls" -- individuals who received the control treatment in the
trial during routine practice or in prior experimental studies. Existing
external control methods, however, can have substantial bias if the populations
underlying the trial and the external control data are not exchangeable. Here,
we characterize a randomization-aware class of treatment effect estimators in
the population underlying the trial that remain consistent and asymptotically
normal when using external control data, even when exchangeability does not
hold. We consider two members of this class of estimators: the well-known
augmented inverse probability weighting trial-only estimator, which is the
efficient estimator when only trial data are used; and a more efficient member
of the class when exchangeability holds and external control data are
available, which we refer to as the optimized randomization-aware estimator. To
achieve robust integration of external control data in trial analyses, we then
propose a combined estimator based on the efficient trial-only estimator and
the optimized randomization-aware estimator. We show that the combined
estimator is consistent and no less efficient than the most efficient of the
two component estimators, whether the exchangeability assumption holds or not.
We examine the estimators' performance in simulations and we illustrate their
use with data from two trials of paliperidone extended-release for
schizophrenia.
