BMJ No 7106 Volume 315
Letters Saturday 23 August 1997
Intersalt data
Epidemiological studies should be designed to reduce correction needed for measurement error to a minimum
Editor,George Davey Smith and Andrew N Phillips's critique(1) of the most recent Intersalt paper,(2) and the response of the Intersalt investigators in their commentary,(1) raises an important issue. Measurement error can bias estimates of effect in epidemiology, and some correction is needed to remove the bias. The correction made, however, needs careful justification. The main problem relates to the error structure of the two variables one is attempting to associate and the degree of correlation between these measurement errors. The critical issue is the quantitative effect due to correlation between measurement errors.
In the Intersalt study the outcome, blood pressure, is measured at the same time as urinary sodium excretion. Both measures are taken to represent the long term average value for that individual. Both will be measured with considerable error. Correlation between the two errors may not be negligible, due, for example, to parallel seasonal effects. For the interpopulation association, no problem should arise. For the intrapopulation association, however, the correction for measurement error will depend on the between error correlation.
The Intersalt authors assume the correlation to be zero, and because urinary sodium has a large measurement error the correction they make is large. For systolic blood pressure, 1.6 mm Hg/100 µmol sodium intake/day is 'corrected' to 4.3 mm Hg/100 µmol/day. This value is considered to be consistent with the between population regression coefficient of 7.1. (These values refer to the estimates adjusted for age and sex, over all age groups. Similar consideration would apply to the multivariate estimate.) If the two errors are correlated, however, the correction is overdone. Approximately, for values of the correlation of 0.1, 0.3, and 0.5 the proper corrected values should be 4.0, 3.5, and 2.9 respectively. If one considers a correlation of 0.5-for example, with parallel seasonal effects - to be credible then the agreement claimed by the Intersalt investigators between regression coefficients based on within and between population comparisons is substantially overstated. If one believes a value of 0.1 to be the largest likely to occur then the Intersalt conclusion is approximately correct. Given the dearth of information on what the correct value is likely to be, the large correction made in the Intersalt study seems to be inadequately justified. More generally,
 | corrections for measurement error are not free of assumption | |
| when the correction is large the assumptions must be clearly stated and evidence presented in their support, perhaps with a sensitivity analysis | |
| large corrections presented without such supporting evidence are unsound. |
Statistical complexity should not be used to conceal inadequacies of the data. Generating accurate quantitative data on the variance-covariance structure of measurement error is difficult. The clear message is that epidemiological studies should be designed to reduce to a minimum the correction needed for measurement error. This can be achieved by improving the measurement instruments, taking repeat measures, and choosing study populations to maximise the between individual variance. None of these are achieved by simply increasing the study size.
N E Day Director
MRC Biostatistics Unit,
Institute of Public Health,
Cambridge
CB2 2SR
References
1 Davey Smith G, Phillips A N. Inflation in epidemiology: 'The proof and measurement of association between two things' revisited. [With commentary by A R Dyer et al.] BMJ 1996;312:1659-64.
2 Elliott P, Stamler J, Nichols R, Dyer A R, Stamler R, Kesteloot H, et al for the Intersalt Cooperative Research Group. Intersalt revisited: further analyses of 24 hour sodium excretion and blood pressure within and across populations. BMJ 1996;312:1249-53.
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