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Regression calibration as developed by Rosner, Spiegelman and Willet is usedto correct the bias in effect estimates due to measurement error in continuousexposures. The method involves two models: a measurement error model (MEM)relating the mismeasured exposure to the true exposure and an outcome modelrelating the mismeasured exposure to outcome. However, no comprehensiveguidance exists for determining which covariates should be included in eachmodel. In this paper, we investigate the selection of the minimal and mostefficient covariate adjustment sets under a causal inference framework. We showthat in order to correct for the measurement error, researchers must adjustfor, in both MEM and outcome model, any common causes (1) of true exposure andthe outcome and (2) of measurement error and the outcome. When such variable(s)are only available in the main study, researchers should still adjust for themin the outcome model to reduce bias, provided that these covariates are at mostweakly associated with measurement error. We also show that adjusting for socalled prognostic variables that are independent of true exposure andmeasurement error in outcome model, may increase efficiency, while adjustingfor any covariates that are associated only with true exposure generallyresults in efficiency loss in realistic settings. We apply the proposedcovariate selection approach to the Health Professional Follow-up Study datasetto study the effect of fiber intake on cardiovascular disease. Finally, weextend the originally proposed estimators to a non-parametric setting whereeffect modification by covariates is allowed.

Causal Selection of Covariates in Regression Calibration for Mismeasured Continuous Exposure