Title: Robust trial augmentation using external data

Abstract: Randomized trials often have sample sizes that are too small to produce precise estimates of treatment effects. One approach for improving trial efficiency is to incorporate external data from previously completed trials or observational studies into the estimation process. When the external data are aligned with the trial data and statistical models for nuisance functions are correctly specified, using the external data can yield consistent estimates and enhance efficiency. 

Some degree of misalignment or misspecification, however, is usually expected and can threaten trial validity. We develop a class of estimators that exploit randomization to ensure consistency and asymptotic normality, even when the external data are misaligned with the trial. We also propose a procedure that uses members of this class to construct a combined estimator that is consistent and asymptotically normal and can leverage external data even when that data are misaligned with the trial, or when models for nuisance functions are mis-specified or have slow convergence rates. 

We show that the efficiency of the combined estimator is no lower than that of each of its component estimators (including the efficient trial-only estimator, if it is used as a component for the combined estimator). Our methods allow investigators to use external data to improve the trial's efficiency without concern for misalignment between the external data and the trial. We examine the finite-sample behavior of the proposed methods in simulation studies and apply them to analyze data from a trial comparing coronary artery bypass grafting surgery plus medical therapy versus medical therapy alone for patients with chronic coronary artery disease.