Data fusion methods for the heterogeneity of treatment effect and confounding function

The heterogeneity of treatment effect (HTE) lies at the heart of precision medicine. Randomized controlled trials are gold-standard for treatment effect estimation but are typically underpowered for heterogeneous effects. In contrast, large observational studies have high predictive power but are often confounded due to the lack of randomization of treatment. We show that the observational study, even subject to hidden confounding, may be used to empower trials in estimating the HTE using the notion of confounding function. The confounding function summarizes the impact of unmeasured confounders on the difference between the observed treatment effect and the causal treatment effect, given the observed covariates, which is unidentifiable based only on the observational study. Coupling the trial and observational study, we show that the HTE and confounding function are identifiable. We then derive the semiparametric efficient scores and the integrative estimators of the HTE and confounding function. We clarify the conditions under which the integrative estimator of the HTE is strictly more efficient than the trial estimator. Finally, we illustrate the integrative estimators via simulation and an application.