Methods/Statistics
All Covariates Are NOT Created Equal in Regression Calibration: Severe Bias in Causal Effect May Be Induced by Using Biomarkers to Calibrate True Nutrient Intake Wenze Tang* Wenze Tang Zihan Qian Molin Wang
Regression calibration is a popular tool used to correct the bias induced by measurement error in continuous exposures. When estimating the causal effect of nutrient intakes on health outcomes, recent studies frequently used nutrient-derived biomarkers, also known as proxies, to calibrate true nutrient intakes, which are typically measured within small feeding studies. For example, a recent study used serum carbohydrate to calibrate true carbohydrate intake and found that higher carbohydrate density (i.e. percentage of energy intake from carbohydrate) was protective of a range of chronic disease outcomes, largely contradicting other sources of evidence. One explanation for such finding may be that using biomarkers to calibrate true nutrient intake can be subject to severe bias, as the biomarkers themselves may be mediating the causal effect of interest, resulting in a violation of the surrogacy assumption, a critical condition required for the validity of the regression calibration method. In this study, we demonstrate, both theoretically and through simulation studies, that the regression calibration estimators cannot be used to identify the total or the controlled direct effect when a proxy of the true exposure such as biomarker is a mediator between the true exposure and outcome. This is proved by quantifying the bias induced when the regression calibration method is inappropriately applied to such mediation settings under simple linear models. Assuming no exposure-proxy interaction, the bias becomes greater when the effect of the proxy on the outcome is greater, or when the correlation between the true exposure and the proxy is close to zero or one. We additionally quantified the bias when an exposure-proxy interaction is present. Finally, we conducted Monte Carlo simulations under a variety of scenarios to investigate the magnitude of finite sample bias for both continuous and binary outcomes.