Average Adjusted Association: Efficient Estimation with High Dimensional Confounders

TL;DR

This paper introduces the Average Adjusted Association (AAA), a new summary measure for binary outcome associations adjusted for confounders, along with efficient estimators using double/debiased machine learning applicable across sampling scenarios.

Contribution

It proposes the AAA as a novel summary measure and develops efficient DML estimators for it, addressing limitations in summarizing associations with confounders.

Findings

Demonstrates the practicality of the estimators with real data

Shows effectiveness of the estimators through simulations

Applicable across various sampling scenarios

Abstract

The log odds ratio is a well-established metric for evaluating the association between binary outcome and exposure variables. Despite its widespread use, there has been limited discussion on how to summarize the log odds ratio as a function of confounders through averaging. To address this issue, we propose the Average Adjusted Association (AAA), which is a summary measure of association in a heterogeneous population, adjusted for observed confounders. To facilitate the use of it, we also develop efficient double/debiased machine learning (DML) estimators of the AAA. Our DML estimators use two equivalent forms of the efficient influence function, and are applicable in various sampling scenarios, including random sampling, outcome-based sampling, and exposure-based sampling. Through real data and simulations, we demonstrate the practicality and effectiveness of our proposed estimators in measuring the AAA.