• David Wormser, Ian R White, Simon G Thompson, and Angela M Wood.
• Department of Public Health and Primary Care, University of Cambridge, Cambridge, UK. david.wormser@phpc.cam.ac.uk
• Int J Epidemiol. 2013 Jun 1;42(3):849-59.

BackgroundWithin-person variability in measured values of a risk factor can bias its association with disease. We investigated the extent of regression dilution bias in calculated variables and its implications for comparing the aetiological associations of risk factors.MethodsUsing a numerical illustration and repeats from 42,300 individuals (12 cohorts), we estimated regression dilution ratios (RDRs) in calculated risk factors [body-mass index (BMI), waist-to-hip ratio (WHR), and waist-to-height ratio (WHtR)] and in their components (height, weight, waist circumference, and hip circumference), assuming the long-term average exposure to be of interest. Error-corrected hazard ratios (HRs) for risk of coronary heart disease (CHD) were compared across adiposity measures per standard-deviation (SD) change in: (i) baseline and (ii) error-corrected levels.ResultsRDRs in calculated risk factors depend strongly on the RDRs, correlation, and comparative distributions of the components of these risk factors. For measures of adiposity, the RDR was lower for WHR [RDR: 0.72 (95% confidence interval 0.65-0.80)] than for either of its components [waist circumference: 0.87 (0.85-0.90); hip circumference: 0.90 (0.86-0.93) or for BMI: 0.96 (0.93-0.98) and WHtR: 0.87 (0.85-0.90)], predominantly because of the stronger correlation and more similar distributions observed between waist circumference and hip circumference than between height and weight or between waist circumference and height. Error-corrected HRs for BMI, waist circumference, WHR, and WHtR, were respectively 1.24, 1.30, 1.44, and 1.32 per SD change in baseline levels of these variables, and 1.24, 1.27, 1.35, and 1.30 per SD change in error-corrected levels.ConclusionsThe extent of within-person variability relative to between-person variability in calculated risk factors can be considerably larger (or smaller) than in its components. Aetiological associations of risk factors should be compared through the use of error-corrected HRs per SD change in error-corrected levels of these risk factors.

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