On the Use of Regression Calibration in a Complex Sampling Design With Application to the Hispanic Community Health...

Regression calibration is the most widely used method to adjust regression parameter estimates for covariate measurement error. Yet its application in the context of a complex sampling design, for which the common bootstrap variance estimator can be less straightforward, has been less studied. We propose 2 variance estimators for a multistage probability-based sampling design, a parametric and a resampling-based multiple imputation approach, where a latent mean exposure needed for regression calibration is the target of imputation. This work was motivated by the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) data from 2008 to 2011, for which relationships between several outcomes and diet, an error-prone self-reported exposure, are of interest. We assessed the relative performance of these variance estimation strategies in an extensive simulation study built on the HCHS/SOL data. We further illustrate the proposed estimators with an analysis of the cross-sectional association of dietary sodium intake with hypertension-related outcomes in a subsample of the HCHS/SOL cohort. We have provided guidelines for the application of regression models with regression-calibrated exposures. Practical considerations for implementation of these 2 variance estimators in the setting of a large multicenter study are also discussed. Code to replicate the presented results is available online.