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Although randomized controlled trials (RCTs) are a cornerstone of comparativeeffectiveness, they typically have much smaller sample size than observationalstudies because of financial and ethical considerations. Therefore there isinterest in using plentiful historical data (either observational data or priortrials) to reduce trial sizes. Previous estimators developed for this purposerely on unrealistic assumptions, without which the added data can bias thetreatment effect estimate. Recent work proposed an alternative method(prognostic covariate adjustment) that imposes no additional assumptions andincreases efficiency in trial analyses. The idea is to use historical data tolearn a prognostic model: a regression of the outcome onto the covariates. Thepredictions from this model, generated from the RCT subjects' baselinevariables, are then used as a covariate in a linear regression analysis of thetrial data. In this work, we extend prognostic adjustment to trial analyseswith nonparametric efficient estimators, which are more powerful than linearregression. We provide theory that explains why prognostic adjustment improvessmall-sample point estimation and inference without any possibility of bias.Simulations corroborate the theory: efficient estimators using prognosticadjustment compared to without provides greater power (i.e., smaller standarderrors) when the trial is small. Population shifts between historical and trialdata attenuate benefits but do not introduce bias. We showcase our estimatorusing clinical trial data provided by Novo Nordisk A/S that evaluates insulintherapy for individuals with type II diabetes.

Prognostic Adjustment with Efficient Estimators to Unbiasedly Leverage Historical Data in Randomized Trials