A comparative study of augmented inverse propensity weighted estimators using outcome-adaptive lasso and other penalized regression methods

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.