A Targeted Approach to Confounder Selection for High-Dimensional Data

TL;DR

This paper introduces a flexible, machine learning-based method for selecting confounders in high-dimensional causal inference, extending existing techniques to handle various variable types and providing valid confidence intervals.

Contribution

It extends the high-dimensional Propensity Score method to non-binary variables and develops a TMLE approach for robust confounder selection with asymptotic guarantees.

Findings

Effective confounder ranking for diverse variable types

Asymptotic normality of the proposed estimator

Validated with simulated and real data

Abstract

We consider the problem of selecting confounders for adjustment from a potentially large set of covariates, when estimating a causal effect. Recently, the high-dimensional Propensity Score (hdPS) method was developed for this task; hdPS ranks potential confounders by estimating an importance score for each variable and selects the top few variables. However, this ranking procedure is limited: it requires all variables to be binary. We propose an extension of the hdPS to general types of response and confounder variables. We further develop a group importance score, allowing us to rank groups of potential confounders. The main challenge is that our parameter requires either the propensity score or response model; both vulnerable to model misspecification. We propose a targeted maximum likelihood estimator (TMLE) which allows the use of nonparametric, machine learning tools for fitting these intermediate models. We establish asymptotic normality of our estimator, which consequently allows constructing confidence intervals. We complement our work with numerical studies on simulated and real data.