Confounding control is crucial and yet challenging for causal inference based on observational studies. Under the typical unconfoundness assumption, augmented inverse probability weighting (AIPW) has been popular for estimating the average causal effect (ACE) due to its double robustness in the sense it relies on either the propensity score model or the outcome mean model to be correctly specified. To ensure the key assumption holds, the effort is often made to collect a sufficiently rich set of pretreatment variables, rendering variable selection imperative. It is well known that variable selection for the propensity score targeted for accurate prediction may produce a variable ACE estimator by including the instrument variables. Thus, many recent works recommend selecting all outcome predictors for both confounding control and efficient estimation. This article shows that the AIPW estimator with variable selection targeted for efficient estimation may lose the desirable double robustness property. Instead, we propose controlling the propensity score model for any covariate that is a predictor of either the treatment or the outcome or both, which preserves the double robustness of the AIPW estimator. Using this principle, we propose a two-stage procedure with penalization for variable selection and the AIPW estimator for estimation. We show the proposed procedure benefits from the desirable double robustness property. We evaluate the finite-sample performance of the AIPW estimator with various variable selection criteria through simulation and an application.
翻译:在典型的不完全假设下,增加反向概率加权(AIPW)对于估计平均因果关系(ACE)十分受欢迎,因为其具有双重稳健性,因为它依赖于倾向性评分模型或结果中的平均模型,以便正确指定。为了确保关键假设,我们往往努力收集足够丰富的预处理变量,使选择变得必要。众所周知,精确预测目标偏差得分的变量选择可能会产生可变的ACE估测器,包括工具变量。因此,许多最近的工作都建议选择所有结果预测器,以调合控制和高效估算。这篇文章表明,具有不同选择的、旨在有效估算的备选性评分模型可能会失去可取的双重稳健性属性。相反,我们提议对预测待遇或结果或两者的任何共变差性评分模式加以控制,从而保持AIP公司的双倍稳健性估测值。我们建议,利用这一原则,对A节性估标准进行两次阶段性评。我们提议,通过一个可变性估程序,从A节性估A节率和A节率性估算结果。