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

In this paper, we investigate the selection of minimal and efficient covariate adjustment sets for the imputation-based regression calibration method, which corrects for bias due to continuous exposure measurement error. We use directed acyclic graphs to illustrate how subject-matter knowledge aids in selecting these sets. For unbiased measurement error correction, researchers must collect, in both main and validation studies, (I) common causes of both the true exposure and the outcome, and (II) common causes of both measurement error and the outcome. For regression calibration under linear models, at minimum, covariate set (I) must be adjusted for in both the measurement error model (MEM) and the outcome model, while set (II) should be adjusted for in at least the MEM. Adjusting for non-risk factors that are correlates of true exposure or measurement error within the MEM alone improves efficiency. We apply this covariate selection approach to the Health Professionals Follow-up Study, assessing fiber intake's effect on cardiovascular disease. We also highlight potential pitfalls in data-driven MEM building that ignores structural assumptions. Additionally, we extend existing estimators to allow for effect modification. Finally, we caution against using regression calibration to estimate the effect of true nutritional intake through calibrating biomarkers.