A zero-augmented generalized gamma regression calibration to adjust for covariate measurement error: A case of an episodically consumed dietary intake

Measurement error in exposure variables is a serious impediment in epidemiological studies that relate exposures to health outcomes. In nutritional studies, interest could be in the association between long-term dietary intake and disease occurrence. Long-term intake is usually assessed with food frequency questionnaire (FFQ), which is prone to recall bias. Measurement error in FFQ-reported intakes leads to bias in parameter estimate that quantifies the association. To adjust for bias in the association, a calibration study is required to obtain unbiased intake measurements using a short-term instrument such as 24-hour recall (24HR). The 24HR intakes are used as response in regression calibration to adjust for bias in the association. For foods not consumed daily, 24HR-reported intakes are usually characterized by excess zeroes, right skewness, and heteroscedasticity posing serious challenge in regression calibration modeling. We proposed a zero-augmented calibration model to adjust for measurement error in reported intake, while handling excess zeroes, skewness, and heteroscedasticity simultaneously without transforming 24HR intake values. We compared the proposed calibration method with the standard method and with methods that ignore measurement error by estimating long-term intake with 24HR and FFQ-reported intakes. The comparison was done in real and simulated datasets. With the 24HR, the mean increase in mercury level per ounce fish intake was about 0.4; with the FFQ intake, the increase was about 1.2. With both calibration methods, the mean increase was about 2.0. Similar trend was observed in the simulation study. In conclusion, the proposed calibration method performs at least as good as the standard method.