Randomized controlled trials (RCTs) are a cornerstone of comparative
effectiveness because they remove the confounding bias present in observational
studies. However, RCTs are typically much smaller than observational studies
because of financial and ethical considerations. Therefore it is of great
interest to be able to incorporate plentiful observational data into the
analysis of smaller RCTs. Previous estimators developed for this purpose rely
on unrealistic additional assumptions without which the added data can bias the
effect estimate. Recent work proposed an alternative method (prognostic
adjustment) that imposes no additional assumption and increases efficiency in
the analysis of RCTs. The idea is to use the observational data to learn a
prognostic model: a regression of the outcome onto the covariates. The
predictions from this model, generated from the RCT subjects' baseline
variables, are used as a covariate in a linear model. In this work, we extend
this framework to work when conducting inference with nonparametric efficient
estimators in trial analysis. Using simulations, we find that this approach
provides greater power (i.e., smaller standard errors) than without prognostic
adjustment, especially when the trial is small. We also find that the method is
robust to observed or unobserved shifts between the observational and trial
populations and does not introduce bias. Lastly, we showcase this estimator
leveraging real-world historical data on a randomized blood transfusion study
of trauma patients.Comment: 12 pages, 3 figure