Issues in Implementing Regression Calibration Analyses

TL;DR

This paper reviews the statistical framework and practical challenges of implementing regression calibration to correct measurement error bias in regression analyses, with examples and recommendations.

Contribution

It provides a comprehensive overview of regression calibration, discusses issues like Berkson error and mediator covariates, and offers practical guidance for application.

Findings

Regression calibration reduces bias from measurement error.

Berkson error can arise in estimated exposures.

Proper calibration and error estimation are crucial for valid results.

Abstract

Regression calibration is a popular approach for correcting biases in estimated regression parameters when exposure variables are measured with error. This approach involves building a calibration equation to estimate the value of the unknown true exposure given the error-prone measurement and other confounding covariates. The estimated, or calibrated, exposure is then substituted for the true exposure in the health outcome regression model. When used properly, regression calibration can greatly reduce the bias induced by exposure measurement error. Here, we first provide an overview of the statistical framework for regression calibration, specifically discussing how a special type of error, called Berkson error, arises in the estimated exposure. We then present practical issues to consider when applying regression calibration, including: (1) how to develop the calibration equation and which covariates to include; (2) valid ways to calculate standard errors (SE) of estimated regression coefficients; and (3) problems arising if one of the covariates in the calibration model is a mediator of the relationship between the exposure and outcome. Throughout the paper, we provide illustrative examples using data from the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) and simulations. We conclude with recommendations for how to perform regression calibration.