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

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.