Propensity Score Adapted Covariate Selection for Causal Inference

TL;DR

This paper introduces a novel covariate selection method for causal inference that leverages propensity scores to effectively exclude irrelevant variables and improve estimation accuracy in observational studies.

Contribution

It proposes a propensity score adapted variable selection procedure that requires only propensity score consistency and does not need correct outcome model specification.

Findings

Successfully excludes instrumental variables and spurious covariates.

Demonstrates oracle properties under linear association conditions.

Outperforms other methods in simulations, especially under model misspecification.

Abstract

In this paper, we propose a propensity score adapted variable selection procedure to select covariates for inclusion in propensity score models, in order to eliminate confounding bias and improve statistical efficiency in observational studies. Our variable selection approach is specially designed for causal inference, it only requires the propensity scores to be $\sqrt{n}$-consistently estimated through a parametric model and need not correct specification of potential outcome models. By using estimated propensity scores as inverse probability treatment weights in performing an adaptive lasso on the outcome, it successfully excludes instrumental variables, and includes confounders and outcome predictors. We show its oracle properties under the "linear association" conditions. We also perform some numerical simulations to illustrate our propensity score adapted covariate selection procedure and evaluate its performance under model misspecification. Comparison to other covariate selection methods is made using artificial data as well, through which we find that it is more powerful in excluding instrumental variables and spurious covariates.