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Table 6 De-attenuated Correlation

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

When two measures are correlated, measurement error can lower the correlation coefficient below the level it would have reached if the measures had been free from measurement error. A de-attenuated correlation coefficient can be computed to correct for attenuation due to within-person variation if repeat measurements are available on the reference method. If for example, the dietary instrument was a FFQ and the reference instrument were multiple food diaries the de-attenuated correlation (ρ), under the assumption of a classical measurement error model, could be obtained by the formula:
ρ = r √[1 + (wpv/bpv)*n]
Where r is the observed correlation; wpv is the within-person variance of the reference method; bpv is the between-person variance of the reference method; and n is the number of repeat measurements of the reference method [18]. Often variation due to daily energy intake is removed by adjusting for total energy using the residual method [106] prior to accounting for within-person variation in order to produce energy-adjusted de-attenuated correlations.