Joint Regression Adjustment for Sequential Randomized Experiments with Pretrained Predictions

In longitudinal randomized experiments on internet platforms, researchers often need to assess the effects of sequential interventions on long-term outcomes. In such experiments, there are two types of potentially useful information for predicting outcomes: within-experiment covariates that evolve with past treatments, and fixed pretrained predictors trained using offline data available before the experiment. However, the former are affected by past treatments, while the latter may not transfer accurately to the current experiment. These difficulties limit the usability of such information. We propose a joint regression adjustment method for estimating average potential outcomes under fixed treatment paths and causal contrasts between these paths. It learns sequential outcome predictions through cross-fitting using time varying covariates within the experiment, then jointly adjusts for these predictions and fixed pretrained predictions. Under general conditions, we establish asymptotic normality and consistent variance estimation for valid Wald inference. Its asymptotic variance is no larger than that of Horvitz–Thompson, Hájek, and AIPW estimators. We characterize the incremental variance reduction from the pretrained predictions and give a necessary and sufficient condition for attaining the semiparametric efficiency bound, which can hold even when the internal predictions are misspecified. We demonstrate the advantages of our method through synthetic experiments and real-data experiments on a Chinese game platform.