Causal Selection of Covariates in Regression Calibration for Mismeasured Continuous Exposure

Abstract

Regression calibration has been used to correct for the bias in causal effect due to measurement error in continuous exposures, but no systematic discussion exists on how to determine covariates appropriate in measurement error model (MEM) and outcome model required by the regression calibration method. In this paper, we investigate the methods for the selection of the minimal and most efficient covariate adjustment sets for the two regression calibration methods, one developed by Rosner, Spiegelman and Willet (RSW, 1990) and the other by Carroll, Rupert and Stefanski (CRS, 2004) under a causal inference framework, where directed acyclic graphs (DAGs) are utilized to encode two distinct measurement error processes (MEPs): the "typical" MEP proposed by Hernan and Cole (2009) versus MEP applicable to some environmental exposure proposed by Weisskopft (2017).

Our theoretical and simulation results suggest that for validity, without linear modeling assumptions, regardless of the regression calibration methods and the MEPs, any common causes (1) of exposure and outcome and (2) of measurement error and outcome should be collected in both main and validation studies and adjusted for in both measurement error model (MEM) and outcome model. When covariates in the nature of set (1) are not available in the validation study, we recommend including such confounding variables in the outcome model only to reduce bias. For some environmental exposure MEP, covariates in the nature of (1) (i.e. individual level confounding variables) that are not causes of measurement error do not need to be collected or adjusted for in either model, provided that variables are not effect modifiers. In addition, for this environmental exposure MEP, outcome risk factors that are cause of measurement error but not cause of true exposure only need to be collected in the main study as they do not need to be adjusted in MEM. To increase efficiency, we recommend using CRS estimator where non-risk factors are adjusted for in MEM only, regardless of the MEP. Finally, regression calibration might not produce the causal effect of interest when a covariate or a mismeasured exposure may be a mediator with respect to the true exposure’s effect.