Bayesian correction for covariate measurement error: a frequentist evaluation and comparison with regression calibration

TL;DR

This paper compares Bayesian methods and regression calibration for covariate measurement error, highlighting Bayesian advantages and demonstrating its practical feasibility through simulations and real data analysis.

Contribution

It provides a comprehensive overview of Bayesian correction methods, contrasts them with regression calibration, and empirically evaluates their frequentist properties.

Findings

Bayesian approach has statistical advantages over RC.

Bayesian methods are feasible with standard tools.

Bayesian approach performs well in simulations and real data.

Abstract

Bayesian approaches for handling covariate measurement error are well established, and yet arguably are still relatively little used by researchers. For some this is likely due to unfamiliarity or disagreement with the Bayesian inferential paradigm. For others a contributory factor is the inability of standard statistical packages to perform such Bayesian analyses. In this paper we first give an overview of the Bayesian approach to handling covariate measurement error, and contrast it with regression calibration (RC), arguably the most commonly adopted approach. We then argue why the Bayesian approach has a number of statistical advantages compared to RC, and demonstrate that implementing the Bayesian approach is usually quite feasible for the analyst. Next we describe the closely related maximum likelihood and multiple imputation approaches, and explain why we believe the Bayesian approach to generally be preferable. We then empirically compare the frequentist properties of RC and the Bayesian approach through simulation studies. The flexibility of the Bayesian approach to handle both measurement error and missing data is then illustrated through an analysis of data from the Third National Health and Nutrition Examination Survey.