  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.
