Table 9.

Other approaches in this systematic review used to assess the impact of measurement error

Reference outlining the method	Classical measurement error model assumed	Requirements of calibration study	Relationship between reference instrument and dietary instrument of interest measure.	Aim of the approach
Simulation Extrapolation (SIMEX) [63]	Yes	External sample with two concentration biomarkers and internal sample with repeat measurements of the FFQ were also used.	Assumes random within-person error for FFQ and that concentration markers are uncorrelated.	To assess the impact of measurement error in nutrient intake as assessed by a FFQ when concentration biomarkers are also available.
Structural equation modelling [64]	Approach can be used with and without assuming a classical measurement error model.	Superior or gold standard reference instrument available with repeat measurements.	Varied the assumptions of the relationship of the reference instrument with the dietary measure.	Aimed to assess the different types of error (either random or systematic), and within or between individuals-that may occur in dietary intake measurements. In addition to demonstrate that the inclusion of biomarker data can allow the estimation of the average magnitude of these errors even if random errors of repeat measures of the reference instrument are correlated.
Moment Reconstruction (MR) [65]	No	Internal sample with gold standard reference instrument available.	Assumes that disease D, true exposure (X), exposure based on dietary instrument of interest (Z) and biomarker (M) are multivariate normal distributed.	As a sensitivity analysis to show that other “substitution methods” have advantages over standard regression calibration when the measurement error is differential (i.e. error is related to disease outcome D).
Imputation (IM) [65]	No	Internal sample with gold standard reference instrument available.	Assumes that disease D, true exposure (X), exposure dietary instrument of interest (Z) and biomarker (M) are multivariate normal distributed.	As a sensitivity analysis to show that other “substitution methods” have advantages over standard regression calibration when the measurement error is differential (i.e. error is related to disease outcome D).