Abstract When estimating the average causal effect in observational studies, researchers have to tackle both self-selection of treatment and outcome modeling. This is difficult because the parametric form of the outcome model is often unknown and there exists a large number of covariates. In this work, we present a semiparametric strategy for estimating the average causal effect by regressing on the propensity score. Furthermore, we show that regression error terms usually depend on the propensity score as well, which could cause heteroscedastic variances, and thus construct a refined estimator to improve the estimation efficiency. Both estimators are shown to be consistent and asymptotically normally distributed, with the latter one having a smaller asymptotic variance. The simulation studies indicate that our methods compare favorably with many competing estimators. Our methods are easy to implement and avoid hazardous impact due to extreme weights as often seen in weighting estimators. They can also be extended to handle subgroup effects with known structure. We apply the proposed methods to data from the Ohio Medicaid Assessment Survey 2012, estimating the effect of having health insurance on self-reported health status for a population with subsidized insurance plan choices under the Affordable Care Act.

中文翻译：

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使用基于倾向得分的样条对平均因果效应进行半参数估计

摘要 在估计观察性研究中的平均因果效应时，研究人员必须同时处理治疗的自我选择和结果建模。这很困难，因为结果模型的参数形式通常是未知的，并且存在大量协变量。在这项工作中，我们提出了一种半参数策略，通过回归倾向得分来估计平均因果效应。此外，我们表明回归误差项通常也取决于倾向得分，这可能会导致异方差方差，从而构建一个改进的估计量以提高估计效率。两个估计量都显示为一致且渐近正态分布，后者具有较小的渐近方差。模拟研究表明，我们的方法与许多竞争估计器相比具有优势。我们的方法易于实施，并且避免了由于权重估计器中常见的极端权重而造成的危险影响。它们也可以扩展到处理已知结构的子群效应。我们将提议的方法应用于 2012 年俄亥俄州医疗补助评估调查的数据，估计健康保险对根据“平价医疗法案”选择补贴保险计划的人群的自我报告健康状况的影响。