Confounder selection may be efficiently conducted using penalized regression methods when causal effects are estimated from observational data with many variables. An outcome-adaptive lasso was proposed to build a model for the propensity score that can be employed in conjunction with other variable selection methods for the outcome model to apply the augmented inverse propensity weighted (AIPW) estimator. However, researchers may not know which method is optimal to use for outcome model when applying the AIPW estimator with the outcome-adaptive lasso. This study provided hints on readily implementable penalized regression methods that should be adopted for the outcome model as a counterpart of the outcome-adaptive lasso. We evaluated the bias and variance of the AIPW estimators using the propensity score (PS) model and an outcome model based on penalized regression methods under various conditions by analyzing a clinical trial example and numerical experiments; the estimates and standard errors of the AIPW estimators were almost identical in an example with over 5000 participants. The AIPW estimators using penalized regression methods with the oracle property performed well in terms of bias and variance in numerical experiments with smaller sample sizes. Meanwhile, the bias of the AIPW estimator using the ordinary lasso for the PS and outcome models was considerably larger.

翻译：当从包含众多变量的观测数据中估计因果效应时，惩罚回归方法可用于高效地进行混杂因素筛选。结果自适应LASSO被提出用于构建倾向得分模型，该模型可与结果模型的其他变量选择方法结合使用，以应用增广逆概率加权（AIPW）估计量。然而，研究者在将AIPW估计量与结果自适应LASSO结合使用时，可能不清楚哪种方法对结果模型最优。本研究为结果模型作为结果自适应LASSO的对应部分应采用的易实现惩罚回归方法提供了启示。我们通过分析临床试验实例和数值实验，在不同条件下评估了基于惩罚回归方法的倾向得分（PS）模型和结果模型的AIPW估计量的偏差和方差；在超过5000名参与者的实例中，AIPW估计量的估计值和标准误差几乎相同。在样本量较小的数值实验中，采用具有神谕性质的惩罚回归方法的AIPW估计量在偏差和方差方面表现良好。与此同时，对PS和结果模型使用普通LASSO的AIPW估计量的偏差则明显更大。