A three-part regression calibration to handle excess zeroes, skewness and heteroscedasticity in adjusting for measurement error in dietary intake data

George O. Agogo and Alexander K. Muoka

Journal of Applied Statistics, 2022, vol. 49, issue 4, 884-901

Abstract: Exposure measurement error (ME) biases exposure-outcome associations. Calibration dietary intake data used in the regression calibration (RC) response to adjust for ME are usually right-skewed, heteroscedastic and with excess zeroes. We proposed three-part RC models to handle these distributional complexities simultaneously, while correcting for ME in fish intake. We applied data from the National Health and Nutrition Examination Survey (NHANES), where long-term intake was measured with food frequency questionnaire (FFQ) in the main study and short-term intake with 24-hour recall (24HR) in the calibration study. In the three-part RC models, never consumers were modelled using two approaches: a zero distribution (Three-part RC-het-det), and logistic distribution (Three-part RC-het-prob); heteroscedasticity using an exponential distribution and right-skewness using generalized gamma distribution. The proposed models were compared with two-part RC model that ignores never consumers, and with methods that estimate intakes using FFQ and 24HR. The models were evaluated in a simulation study. With NHANES data, mean increase in the mercury level (in $ \mu \mathrm{g/L} $ μg/L) was 1.20 using FFQ-method, 0.4 using 24HR-method, 1.87 using two-part RC and 2.02 using three-part RC-het-prob method. The three-part RC estimated the association with the least bias in the simulation study.

Date: 2022
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DOI: 10.1080/02664763.2020.1845622

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