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Table 2 Classical Measurement error model

From: Systematic review of statistical approaches to quantify, or correct for, measurement error in a continuous exposure in nutritional epidemiology

The classical measurement error model assumes additive error that is unrelated to the targeted consumption, unrelated to other study subject characteristics, and independent of the corresponding measurement error in the dietary instrument of interest [103]. It is important that nutritional epidemiologists are aware of what sort of impact measurement error can have on diet-disease associations derived from even generally well conducted large-scale epidemiological studies. If there is a linear relationship between a single dietary exposure and the disease of interest, as in a logistic regression model, and this is also the case for a Cox regression or linear regression model, then the effect of classical measurement error is to attenuate the diet-disease association [37, 47]. This means that diet-disease associations such as log odds ratio, log hazard ratios or linear regression coefficients will be biased towards the null and a further consequence of classical measurement error in linear models is a loss of power to detect diet-disease associations. Classical measurement error in a multivariable exposure situation can bias the diet-disease associations in any direction, even in a linear regression model [47]. Other types of error that depend on the ‘true’ exposure (i.e. systematic error) or that depends on the outcome (i.e. differential error), may result in biases either away or towards the null in an unpredictable manner. [42, 47]