Causal Selection of Covariates in Regression Calibration for Mismeasured Continuous Exposure

Regression calibration as developed by Rosner, Spiegelman, and Willett is used to adjust the bias in effect estimates due to measurement error in continuous exposures. The method involves two models: a measurement error model relating the mismeasured exposure to the true (or gold-standard) exposure and an outcome model relating the mismeasured exposure to the outcome. However, no comprehensive guidance exists for determining which covariates should be included in each model. In this article, we investigate the selection of the minimal and most efficient covariate adjustment sets under a causal inference framework. We show that to address the measurement error, researchers must adjust for, in both measurement error and outcome models, any common causes (1) of true exposure and the outcome and (2) of measurement error and the outcome. We also show that adjusting for so-called prognostic variables that are independent of true exposure and measurement error in the outcome model, may increase efficiency, while adjusting for any covariates that are associated only with true exposure generally results in efficiency loss in realistic settings. We apply the proposed covariate selection approach to the Health Professional Follow-up Study dataset to study the effect of fiber intake on cardiovascular disease. Finally, we extend the originally proposed estimators to a nonparametric setting where effect modification by covariates is allowed.