In propensity score analysis, the frequently used regression adjustment involves regressing the outcome on the estimated propensity score and treatment indicator. This approach can be highly efficient when model assumptions are valid, but can lead to biased results when the assumptions are violated. We extend the simple regression adjustment to a varying coefficient regression model that allows for nonlinear association between outcome and propensity score. We discuss its connection with some propensity score matching and weighting methods, and show that the proposed analytical framework can shed light on the intrinsic connection among some mainstream propensity score approaches (stratification, regression, kernel matching, and inverse probability weighting) and handle commonly used causal estimands. We derive analytic point and variance estimators that properly take into account the sampling variability in the estimated propensity score. Extensive simulations show that the proposed approach possesses desired finite sample properties and demonstrates competitive performance in comparison with other methods estimating the same causal estimand. The proposed methodology is illustrated with a study on right heart catheterization.

中文翻译：

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倾向得分分析的灵活回归方法及其与匹配和加权的关系。

在倾向得分分析中，经常使用的回归调整涉及对估计的倾向得分和治疗指标的结果进行回归。当模型假设有效时，这种方法可能非常有效，但当假设被违反时，可能会导致结果有偏差。我们将简单回归调整扩展到允许结果和倾向得分之间的非线性关联的可变系数回归模型。我们讨论了它与一些倾向得分匹配和加权方法的联系，并表明所提出的分析框架可以阐明一些主流倾向得分方法（分层、回归、核匹配和逆概率加权）之间的内在联系，并处理常用的因果估计。我们推导出分析点和方差估计量，这些估计量适当地考虑了估计倾向得分中的抽样变异性。广泛的模拟表明，所提出的方法具有所需的有限样本属性，并且与估计相同因果估计的其他方法相比具有竞争力。所提出的方法通过一项关于右心导管插入术的研究来说明。