Multiply robust inference of average treatment effects by high-dimensional empirical likelihood

In this paper, we develop a multiply robust inference procedure for the average treatment effect (ATE) for data with high-dimensional covariates. We consider the case where it is difficult to correctly specify a single parametric model for the propensity scores (PS). We propose a novel high-dimensional empirical likelihood weighting method under soft covariate balancing constraints to combine multiple working PS models. An extended set of calibration functions is used, and a regularized augmented outcome regression (OR) is developed to correct the bias due to non-exact covariate balancing. Those two approaches provide a new way to construct the Neyman orthogonal score of the ATE. The proposed confidence interval for the ATE achieves asymptotically valid nominal coverage under high-dimensional covariates if any of the PS models, their linear combination, or the OR model is correctly specified. The proposed method is extended to generalized linear models for the outcome variable and data with unknown clusters. Specifically, we consider estimating the ATE for data with unknown clusters, where multiple working PS models can be fitted based on the estimated clusters. We demonstrate the advantages of the proposed approach over existing doubly robust inference methods under high-dimensional covariates via simulation studies. We analyze the right heart catheterization dataset, collected in two study phases across five medical centers, to demonstrate the effectiveness of the proposed method.