Adjusting for non-confounding covariates in case-control association studies

TL;DR

This paper clarifies when covariate adjustment in case-control studies improves power, showing that the constrained maximum likelihood method often outperforms traditional logistic regression, especially depending on disease prevalence.

Contribution

It provides a theoretical comparison of covariate adjustment and the constrained maximum likelihood method in case-control studies, highlighting conditions for optimal performance.

Findings

Covariate adjustment benefits depend on disease prevalence.

Constrained maximum likelihood estimator is asymptotically most powerful.

Theoretical insights clarify when to adjust for covariates.

Abstract

There is a considerable literature in case-control logistic regression on whether or not non-confounding covariates should be adjusted for. However, only limited and ad hoc theoretical results are available on this important topic. A constrained maximum likelihood method was recently proposed, which appears to be generally more powerful than logistic regression methods with or without adjusting for non-confounding covariates. This note provides a theoretical clarification for the case-control logistic regression with and without covariate adjustment and the constrained maximum likelihood method on their relative performances in terms of asymptotic relative efficiencies. We show that the benefit of covariate adjustment in the case-control logistic regression depends on the disease prevalence. We also show that the constrained maximum likelihood estimator gives an asymptotically uniformly most powerful test.