Moment estimation method of parameters in additive measurement error model

In nutritional epidemiology, covariates in some studies such as the EPIC are prone to measurement error. Estimation of unknown parameters in most measurement error models for food frequency questionnaire (FFQ) and nutrient biomarkers requires replicated measurements. But, the EPIC-InterAct Study did not collect replicated measurements for FFQ or 24-hour dietary recalls (24HR). The method of correcting measurement error in this case is worth studying.

A moment method is applied to estimate unknown parameters of the proposed error model with correlated errors between biased measurements of FFQ and 24HR. Then, correction factor and reliability ratio of each error-prone nutrient can be obtained correspondingly. Afterwards, regression calibration (RC) under a Cox model is used to correct measurement error of nutrients of interest in the EPIC-InterAct data.

Compared to the naive estimation, estimation results for dietary intakes could be very different when we take measurement error into consideration. Using RC as the correction method, hazard ratios (HR) of vegetable plus fruit, fat and energy for males become 1.01 (95% CI 0.75-1.35), 1.30 (95% CI 1.12-1.51) and 1.16 (95% CI 1.04-1.28), respectively, and HR of energy for females becomes 0.99 (95% CI 0.91-1.08). These HRs are greatly different from those by naive estimation.

Although there is no repeated measurement for FFQ and 24HR, we can still estimate all unknown parameters in our proposed error model under four assumptions and then correct measurement error in nutrients of interest in EPIC-InterAct Study by RC for avoiding some misleading results from naive estimation.