Table 8 Regression calibration based methods that do not assume a classical measurement error model

Person-specific bias adjusted regression calibration (PSBRC) [52]

Superior or gold standard reference instrument available.

An estimate of the person-specific bias in the reference measure and its correlation with systematic error in the FFQ is required.

To be used as sensitivity analysis in order to assess the impact of varying pre-specified ratios of the variance of the person-specific biases in a reference instrument and FFQ and the correlation between these biases.

Flawed reference instrument adjusted regression calibration (FRIRC) [50]

Internal or external sample with superior or gold standard reference instrument available.

Extension of PSBRC where the model assumes for both the FFQ and the dietary report reference instrument, group-specific biases related to true intake and correlated person-specific biases can be estimated.

To be used as a sensitivity analysis in order to assess the impact of additional complexity of both group and person-specific biases.

Biomarker and alloyed gold standard regression calibration (BAGSRC) [51]

Internal or external sample with superior or gold standard reference instrument available

Model assumes that there is a correlation between the “alloyed gold standard” and the level of exposure using dietary instrument of interest.

If a third method of exposure assessment (biomarker) is available and it is reasonable to assume that the errors in this method are uncorrelated with the errors in the other two exposure assessment methods.

Estimate the bias in the standard regression calibration due to the correlation between alloyed gold standard and the level of exposure using dietary instrument of interest.

Derive estimates of the correlation between the errors in alloyed gold standard and exposure assessment using biomarker data.

Auxiliary Information regression calibration (AIRC) [53, 54]

Internal or external sample with superior or gold standard reference instrument available (if a biomarker –then replicates)

The models account for correlated errors in the FFQ and the 24-h diet recall and random within-person variation in the biomarkers.

To be used as a sensitivity analysis in order to assess the impact of correlated subject-specific error on correction factor.

Episodically consumed foods regression calibration (ECFRC) [59]

External sample with superior or gold standard reference instrument available

Model assumed that a food is reported on the 24HR as consumed on a certain day if and only if it was consumed on that day. Also that the 24HR is unbiased for true usual intake on consumption days.

To predict an individual’s usual intake of an episodically consumed food and relating it to a health outcome.

Never and episodic consumers (NEC) model [88]

A subset of the population has repeat measurements of dietary instrument of interest.

Assumes that food record measurements are subject only to random within-person variability. The observed food record measurements are unbiased estimates of “true intake”. Nonzero food records measurements to be normally distributed on a transformed scale.

To predict an individual’s usual intake of an episodically consumed food whilst incorporating never consumers and relating it to a health outcome.