We consider causal inference in observational studies with choice-based sampling, in which subject enrollment is stratified on treatment choice. Choice-based sampling has been considered mainly in the econometrics literature, but it can be useful for biomedical studies as well, especially when one of the treatments being compared is uncommon. We propose new methods for estimating the population average treatment effect under choice-based sampling, including doubly robust methods motivated by semiparametric theory. A doubly robust, locally efficient estimator may be obtained by replacing nuisance functions in the efficient influence function with estimates based on parametric models. The use of machine learning methods to estimate nuisance functions leads to estimators that are consistent and asymptotically efficient under broader conditions. The methods are compared in simulation experiments and illustrated in the context of a large observational study in obstetrics. We also make suggestions on how to choose the target proportion of treated subjects and the sample size in designing a choice-based observational study.

中文翻译：

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使用基于选择的抽样估计观察性研究中的人群平均治疗效果

我们在使用基于选择的抽样的观察性研究中考虑因果推断，其中受试者入组按治疗选择分层。基于选择的抽样主要在计量经济学文献中得到考虑，但它也可用于生物医学研究，特别是当比较的治疗方法之一不常见时。我们提出了在基于选择的抽样下估计总体平均治疗效果的新方法，包括由半参数理论推动的双重稳健方法。通过用基于参数模型的估计替换有效影响函数中的干扰函数，可以获得双重稳健、局部有效的估计。使用机器学习方法来估计滋扰函数会导致估计量在更广泛的条件下是一致且渐近有效的。这些方法在模拟实验中进行了比较，并在产科的大型观察研究的背景下进行了说明。我们还就如何在设计基于选择的观察性研究中选择治疗对象的目标比例和样本量提出建议。