Improving transportability of regression calibration under the main/external validation study design

In epidemiology, exposures are usually subject to measurement error (ME). Regression calibration with a validation study is widely employed as an analysis method to correct for ME in the main study (MS) due to its broad applicability and simple implementation. However, relying on an external validation study (EVS) carries the risk of introducing bias into the analysis. Specifically, if the parameters of the regression calibration model estimated from the EVS are not transportable to the MS, the subsequent estimator of the parameter will be biased. In this work, we improve the regression calibration method for linear regression models using an external validation study. Unlike the standard approach, our method ensures that the regression calibration model is transportable by estimating the parameters in the ME generating process using the external validation study and obtaining the remaining parameter values in the regression calibration model directly from the MS. This guarantees that parameter values in the regression calibration model will be applicable to the MS. We derived the theoretical properties of our method. The simulation results show that our method effectively reduces bias and maintains nominal confidence interval coverage. We applied this method to data from the Health Professionals Follow-Up Study and the Men's Lifestyle Validation Study to assess the effects of dietary intake on body weight.