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The heterogeneity of treatment effect lies at the heart of precisionmedicine. Randomized controlled trials are gold-standard for treatment effectestimation but are typically underpowered for heterogeneous effects. Whilelarge observational studies have high predictive power but are often confoundeddue to lack of randomization of treatment. We show that the observationalstudy, even subject to hidden confounding, may empower trials in estimating theheterogeneity of treatment effect using the notion of confounding function. Theconfounding function summarizes the impact of unmeasured confounders on thedifference in the potential outcomes between the treated and untreated groupsaccounting for the observed covariates, which is unidentifiable based only onthe observational study. Coupling the randomized trial and observational study,we show that the heterogeneity of treatment effect and confounding function arenonparametrically identifiable. We then derive the semiparametric efficientscores and the rate-doubly robust integrative estimators of the heterogeneityof treatment effect and confounding function under parametric structuralmodels. We clarify the conditions under which the integrative estimator of theheterogeneity of treatment effect is strictly more efficient than the trialestimator. We illustrate the integrative estimators via simulation and anapplication.

Improved Inference for Heterogeneous Treatment Effects Using Real-World Data Subject to Hidden Confounding