1 Department of Social Medicine, University of Bristol, Bristol BS8 2PR, UK. E-mail: d.j.gunnell{at}bristol.ac.uk
2 Faculty of Health and Social Care Sciences, St. George's Hospital Medical School, Cranmer Terrace, London SW17 0RE, UK
3 Department of Public Health, University of Liverpool, Liverpool, UK
4 MRC Social and Public Health Sciences Unit, University of Glasgow, 4 Lilybank Gardens, Glasgow G12 8RZ, UK
5 Department of Social Science and Medicine, Imperial College of Science, Technology and Medicine, Charing Cross, St Dunstans Road, London W6 8RP, UK
6 Department of Social Medicine, University of Bristol, Bristol BS8 2PR, UK. E-mail: d.j.gunnell{at}bristol.ac.uk
In a paper published four years ago in this journal1 we included an assessment of factors influencing the accuracy of self-reported anthropometry in the elderly. The analysis was based on 257 surviving members of the Boyd Orr Cohort aged 5678 years with both self-reported (questionnaire) and measured values recorded for their weight, height, and leg length.
As well as comparing self-report and measured values using Bland-Altman plots2 we also carried out a multivariable linear regression analysis to investigate factors associated with the difference between self-reported and measured anthropometry (misreporting). The factors examined in these models were age, gender, social class, and other anthropometric values. We also investigated the extent to which mis-reporting was associated with the magnitude of the measured values of stature or weight. For example, we were interested in whether overweight individuals reported their weight less accurately and were more prone to under-reporting. To assess systematic error, the difference between reported and measured anthropometry was used as the dependent variable. To assess random error the difference was again used, but the sign of the difference was removedso large negative errors were given the same weight as large positive errors and factors associated with inaccuracy, rather than systematic error, can be assessed.
It has been pointed out to us that due to the phenomenon known as mathematical coupling (MC), findings from these analyses may have been incorrect. In the presence of measurement error, the difference between two measures on the same subject will be correlated with the true value of that measure, even in the absence of any true association.2,3 This phenomenon is more familiarly known as regression to the mean (RTM, for a description see Kirkwood and Sterne4), although MC can occur without RTM. Our findings that an individual's height, leg length, weight, and body mass index (BMI) were associated with the probability of them misreporting their values for these measures may therefore have been biased.
To investigate how this phenomenon may have influenced our conclusions we have conducted new analyses. To make negligible the effects of MC we included a term for the mean of the self-report and measured anthropometric values in the model rather than the measured value alone. Such an approach makes use of the special circumstances whereby the effects of MC are negligible under the null hypothesis of no association between difference and mean.
The findings from this analysis are presented in the Table below. Factors are listed if they are associated (P < 0.10) with the difference between self-report and measured values.
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As illustrated by this re-analysis and letter's published in this edition of the journal, a better understanding of approaches for taking account of MC is required.
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References |
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2 Bland JM, Altman DG. Comparing methods of measurement: why plotting difference against standard method is misleading. Lancet 1995; 346:108587.[CrossRef][ISI][Medline]
3 Oldham PD. A note on the analysis of repeated measures of the same subjects. J Chron Dis 1962; 15:96977.[CrossRef][ISI][Medline]
4 Kirkwood BR, Sterne JAC. Essential Medical Statistics. 2nd Edn. Oxford: Blackwell Science Ltd, 2003, pp. 44446.