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In this paper, we present a practical approach for computing the sandwich variance estimator in 2-stage regression model settings. As a motivating example for 2-stage regression, we consider regression calibration, a popular approach for addressing covariate measurement error. The sandwich variance approach has rarely been applied in regression calibration, despite its requiring less computation time than popular resampling approaches for variance estimation, specifically the bootstrap. This is probably because it requires specialized statistical coding. Here we first outline the steps needed to compute the sandwich variance estimator. We then develop a convenient method of computation in R for sandwich variance estimation, which leverages standard regression model outputs and existing R functions and can be applied in the case of a simple random sample or complex survey design. We use a simulation study to compare the sandwich estimator to a resampling variance approach for both settings. Finally, we further compare these 2 variance estimation approaches in data examples from the Women's Health Initiative (1993–2005) and the Hispanic Community Health Study/Study of Latinos (2008–2011). In our simulations, the sandwich variance estimator typically had good numerical performance, but simple Wald bootstrap confidence intervals were unstable or overcovered in certain settings, particularly when there was high correlation between covariates or large measurement error. [ABSTRACT FROM AUTHOR]

Measurement error is a major issue in self-reported diet that can distort diet-disease relationships. Use of blood concentration biomarkers has the potential to mitigate the subjective bias inherent in self-reporting. As part of the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) baseline visit (2008–2011), self-reported information on diet was collected from all participants (n  = 16,415). The HCHS/SOL also included annual telephone follow-up, as well as a second (2014–2017) and third (2020–2023) clinic visit. Blood concentration biomarkers for carotenoids, tocopherols, retinol, vitamin B12, and folate were measured in a subset of participants (n  = 476) as part of the Study of Latinos: Nutrition and Physical Activity Assessment Study (SOLNAS) (2010–2012). We examined the relationships among biomarker levels, self-reported intake, Hispanic/Latino background (Central American, Cuban, Dominican, Mexican, Puerto Rican, or South American), and other participant characteristics in this diverse cohort. We built regression calibration–based prediction equations for 10 nutritional biomarkers and used a simulation to study the power of detecting a diet-disease association in a multivariable Cox model using a predicted concentration level. Good statistical power was observed for some nutrients with high prediction model R 2 values, but further research is needed to understand how best to realize the potential of these dietary biomarkers. This study provides a comprehensive examination of several nutritional biomarkers within the HCHS/SOL, characterizing their associations with subject characteristics and the influence of the measurement characteristics on the power to detect associations with health outcomes. [ABSTRACT FROM AUTHOR]