Integration of external predictions for efficient estimation of the risk ratio
We consider the augmentation of randomized experiments or trials with data from observational studies for the purpose of improving statistical precision. In particular, we focus on the Hybrid Augmented Inverse Probability Weighting estimator, designed to integrate predictions from several foundation models while preserving valid statistical inference. In this article, we extend the Augmented Inverse Probability Weighting framework to the estimation of the risk ratio, the quotient of the absolute risk of an exposed to an unexposed group. Our approach allows one to use information from black-box foundation models trained on external and possibly unstructured data, yielding an estimator of the risk ratio whose asymptotic variance is never larger than the one of the default estimator based on experimental data alone.