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Estimating causal effects from randomized experiments is central to clinicalresearch. Reducing the statistical uncertainty in these analyses is animportant objective for statisticians. Registries, prior trials, and healthrecords constitute a growing compendium of historical data on patients understandard-of-care that may be exploitable to this end. However, most methods forhistorical borrowing achieve reductions in variance by sacrificing stricttype-I error rate control. Here, we propose a use of historical data thatexploits linear covariate adjustment to improve the efficiency of trialanalyses without incurring bias. Specifically, we train a prognostic model onthe historical data, then estimate the treatment effect using a linearregression while adjusting for the trial subjects' predicted outcomes (theirprognostic scores). We prove that, under certain conditions, this prognosticcovariate adjustment procedure attains the minimum variance possible among alarge class of estimators. When those conditions are not met, prognosticcovariate adjustment is still more efficient than raw covariate adjustment andthe gain in efficiency is proportional to a measure of the predictive accuracyof the prognostic model above and beyond the linear relationship with the rawcovariates. We demonstrate the approach using simulations and a reanalysis ofan Alzheimer's Disease clinical trial and observe meaningful reductions inmean-squared error and the estimated variance. Lastly, we provide a simplifiedformula for asymptotic variance that enables power calculations that accountfor these gains. Sample size reductions between 10% and 30% are attainable whenusing prognostic models that explain a clinically realistic percentage of theoutcome variance.

Increasing the efficiency of randomized trial estimates via linear adjustment for a prognostic score