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

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.