Empirical Likelihood-Based Estimation and Inference in Randomized Controlled Trials with High-Dimensional Covariates

TL;DR

This paper introduces a novel empirical likelihood-based method for treatment effect estimation in high-dimensional randomized trials, leveraging penalized regression and machine learning to improve efficiency and inference accuracy.

Contribution

It develops a data-adaptive empirical likelihood approach that handles high-dimensional covariates, achieving asymptotic normality and efficiency with multiple machine learning models.

Findings

Estimator is more efficient than existing methods with random forests.

Method recovers true variance of treatment effect estimator.

Outperforms existing methods on real datasets.

Abstract

In this paper, we propose a data-adaptive empirical likelihood-based approach for treatment effect estimation and inference, which overcomes the obstacle of the traditional empirical likelihood-based approaches in the high-dimensional setting by adopting penalized regression and machine learning methods to model the covariate-outcome relationship. In particular, we show that our procedure successfully recovers the true variance of Zhang's treatment effect estimator (Zhang, 2018) by utilizing a data-splitting technique. Our proposed estimator is proved to be asymptotically normal and semiparametric efficient under mild regularity conditions. Simulation studies indicate that our estimator is more efficient than the estimator proposed by Wager et al. (2016) when random forests are employed to model the covariate-outcome relationship. Moreover, when multiple machine learning models are imposed, our estimator is at least as efficient as any regular estimator with a single machine learning model. We compare our method to existing ones using the ACTG175 data and the GSE118657 data, and confirm the outstanding performance of our approach.