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In this paper, we identify the criteria for the selection of the minimal andmost efficient covariate adjustment sets for the regression calibration methoddeveloped by Carroll, Rupert and Stefanski (CRS, 1992), used to correct biasdue to continuous exposure measurement error. We utilize directed acyclicgraphs to illustrate how subject matter knowledge can aid in the selection ofsuch adjustment sets. Valid measurement error correction requires thecollection of data on any (1) common causes of true exposure and outcome and(2) common causes of measurement error and outcome, in both the main study andvalidation study. For the CRS regression calibration method to be valid,researchers need to minimally adjust for covariate set (1) in both themeasurement error model (MEM) and the outcome model and adjust for covariateset (2) at least in the MEM. In practice, we recommend including the minimalcovariate adjustment set in both the MEM and the outcome model. In contrastwith the regression calibration method developed by Rosner, Spiegelman andWillet, it is valid and more efficient to adjust for correlates of the trueexposure or of measurement error that are not risk factors in the MEM onlyunder CRS method. We applied the proposed covariate selection approach to theHealth Professional Follow-up Study, examining the effect of fiber intake oncardiovascular incidence. In this study, we demonstrated potential issues witha data-driven approach to building the MEM that is agnostic to the structuralassumptions. We extend the originally proposed estimators to settings whereeffect modification by a covariate is allowed. Finally, we caution against theuse of the regression calibration method to calibrate the true nutrition intakeusing biomarkers.

Causal Covariate Selection for the Imputation-based Regression Calibration Method for Exposure Measurement Error Bias Correction