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 an 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.

翻译：治疗效应异质性（HTE）是精准医学的核心。随机对照试验是估计治疗效应的金标准，但通常对异质性效应的检验效能不足。相比之下，大规模观察性研究具有较高的预测能力，但由于缺乏治疗随机化，往往存在混杂偏倚。我们证明，即使存在潜在混杂，观察性研究仍可通过混杂函数的概念增强试验对HTE的估计能力。混杂函数在给定观测协变量的条件下，总结了未测量混杂因素对观测治疗效应与因果治疗效应之间差异的影响，该函数仅基于观察性研究是不可识别的。通过联合分析试验与观察性数据，我们证明HTE与混杂函数具有可识别性。随后我们推导了HTE与混杂函数的半参数有效评分及融合估计量。我们明确了HTE融合估计量严格优于试验估计量的条件。最后，通过模拟与应用案例对融合估计量进行了演示。