All covariates are not created equal in regression calibration: a review of methods on using biomarkers to calibrate...

Regression calibration is a widely used method for correcting bias in regression coefficient estimates caused by measurement error in continuous exposures. In nutritional epidemiology, recent studies often use nutrient-derived biomarkers to calibrate true dietary intakes, which are typically assessed through small feeding studies or weighed dietary records. However, biomarkers may themselves lie on the causal pathway between intake and outcome, violating the surrogacy assumption that underpins the validity of regression calibration. We evaluate regression calibration-based methods that have been applied or proposed for calibrating dietary intake using biomarkers, focusing on their validity and relative efficiency. Our assessment combines analytic bias quantification, simulation studies, and a real-data application. Two approaches are generally valid when using mediators to calibrate the true exposure: (1) the expanded calibration method, which recovers the total effect via the product method from mediation analysis, and (2) the two-stage calibration method. In simulations reflecting realistic scenarios, the expanded calibration method demonstrated superior efficiency for a continuous outcome. Finally, we show that estimating the effect of dietary intake using a calibrated biomarker is valid when the mean biomarker calibration model contains a linear term in true intake with coefficient one, possibly along with additional covariates.