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Many estimators of the average effect of a treatment on an outcome requireestimation of the propensity score, the outcome regression, or both. It isoften beneficial to utilize flexible techniques such as semiparametricregression or machine learning to estimate these quantities. However, optimalestimation of these regressions does not necessarily lead to optimal estimationof the average treatment effect, particularly in settings with stronginstrumental variables. A recent proposal addressed these issues via theoutcome-adaptive lasso, a penalized regression technique for estimating thepropensity score that seeks to minimize the impact of instrumental variables ontreatment effect estimators. However, a notable limitation of this approach isthat its application is restricted to parametric models. We propose a moreflexible alternative that we call the outcome highly adaptive lasso. We discusslarge sample theory for this estimator and propose closed form confidenceintervals based on the proposed estimator. We show via simulation that ourmethod offers benefits over several popular approaches.

Robust inference on the average treatment effect using the outcome highly adaptive lasso