In this paper, we identify the criteria for the selection of the minimal and most efficient covariate adjustment sets for the regression calibration method developed by Carroll, Rupert and Stefanski (CRS, 1992), used to correct bias due to continuous exposure measurement error. We utilize directed acyclic graphs to illustrate how subject matter knowledge can aid in the selection of such adjustment sets. Valid measurement error correction requires the collection of data on any (1) common causes of true exposure and outcome and (2) common causes of measurement error and outcome, in both the main study and validation study. For the CRS regression calibration method to be valid, researchers need to minimally adjust for covariate set (1) in both the measurement error model (MEM) and the outcome model and adjust for covariate set (2) at least in the MEM. In practice, we recommend including the minimal covariate adjustment set in both the MEM and the outcome model. In contrast with the regression calibration method developed by Rosner, Spiegelman and Willet, it is valid and more efficient to adjust for correlates of the true exposure or of measurement error that are not risk factors in the MEM only under CRS method. We applied the proposed covariate selection approach to the Health Professional Follow-up Study, examining the effect of fiber intake on cardiovascular incidence. In this study, we demonstrated potential issues with a data-driven approach to building the MEM that is agnostic to the structural assumptions. We extend the originally proposed estimators to settings where effect modification by a covariate is allowed. Finally, we caution against the use of the regression calibration method to calibrate the true nutrition intake using biomarkers.

翻译：在本文中，我们明确了针对Carroll、Rupert和Stefanski（CRS，1992）提出的回归校准方法，用于校正连续暴露测量误差导致的偏差时，选择和最小化及最有效协变量调整集的标准。我们利用有向无环图说明如何借助学科知识来辅助这类调整集的选择。有效的测量误差校正需要在主研究和验证研究中收集以下数据：（1）真实暴露与结局的共同原因；（2）测量误差与结局的共同原因。为使CRS回归校准方法有效，研究人员需要在测量误差模型（MEM）和结局模型中至少调整协变量集（1），并在MEM中至少调整协变量集（2）。实践中，我们建议在MEM和结局模型中均纳入最小协变量调整集。与Rosner、Spiegelman和Willet提出的回归校准方法相比，在CRS方法下，仅调整MEM中非风险因素的真实暴露或测量误差的相关变量是有效且更高效的。我们将所提出的协变量选择方法应用于健康专业人员随访研究，探讨纤维摄入对心血管发病率的影响。在该研究中，我们展示了忽略结构假设的数据驱动方法构建MEM时可能存在的问题。我们将最初提出的估计量推广至允许协变量调节效应的场景。最后，我们提醒不要使用回归校准方法通过生物标志物校准真实营养摄入量。