IJE Advance Access originally published online on September 2, 2005
International Journal of Epidemiology 2005 34(6):1368-1369; doi:10.1093/ije/dyi186
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Commentary |
Commentary: Over-correction for regression dilution bias? Not for blood pressure vs coronary heart disease
1 Department of Primary Care and Population Sciences, Royal Free and University College Medical School, Royal Free Campus, Rowland Hill Street, London NW3 2PF, UK.
2 University of Oxford, CTSU, Oxford OX2 6HE, UK.
* Corresponding author. E-mail: r.morris{at}pcps.ucl.ac.uk
In 1886 Francis Galton showed that children of tall parents tended to be shorter than their parents on average and that children of short parents tended to be taller than their parents on average, a phenomenon he originally called ‘regression to mediocrity’, but which we now know as ‘regression to the mean’.1 Regression to the mean is well recognized by epidemiologists because of its effect on estimating risk factor–disease associations; unusual or extreme values tend upon re-measurement to be followed by less extreme values, and hence the strength of the associations between these second ‘true’ risk factor levels and disease incidence will be underestimated when ‘baseline’ measures are used in analyses. Several methods have been developed to correct for this ‘regression dilution bias’,2 allowing unbiased estimates of ‘true’ risk associations to be made.
Frost and White3 thoughtfully investigate the effects of methods to correct for regression dilution bias and suggest that overcorrection may occur because of failure to take account of variations in the influence of the risk-exposure throughout the life-course. Using blood pressure data from the Framingham Heart Study, they construct a multiple regression model that relates risk of death from coronary heart disease in the interval 25–30 years after baseline to ‘error free’ levels of the risk factor not only at 25 years, but also at the start of all previous 5 year intervals. They consider implausible the assumption that the risk in a given follow-up period depends only on the underlying level of the risk factor at the start of that period, and introduce a concept of ‘weight halving’. By this they mean that the importance of true levels of the risk factor halves as we travel backwards through successive previous time periods. By varying the duration of this weight halving interval (from ‘exclusively current level prediction’ to ‘exclusively historical level prediction’), they describe the performance of the baseline association and the ‘regression-dilution-corrected’ association at estimating: (i) the ‘crude current’ association; (ii) the ‘history-adjusted’ current association; and (iii) the ‘lifetime level’ association (the difference in risk between two subjects whose level has differed by 1 unit throughout their lives), identifying this last association as the most epidemiologically relevant. Frost and White demonstrate the well-known phenomenon whereby the uncorrected odds ratio underestimates the lifetime odds ratio. This is shown to be true for all weight-halving intervals, and that the magnitude of this bias is greatest when risk is driven predominantly by current error-free blood pressure levels (i.e. a weight-halving interval of 0 or close to 0). Under this scenario, the standard techniques used to correct for regression dilution bias, and in particular the ‘range ratio’ method, leads to estimates that are either unbiased, or nearly unbiased.
Nevertheless the degree of bias produced by standard methods of correction increase when the weight-halving interval increases. Because of this, Frost and White claim that previous studies, and in particular studies of the influence of blood pressure and blood cholesterol on cardiovascular risk, are likely to have ‘over-corrected’ risk estimates. In particular, they suggest that the associations between blood pressure and vascular mortality estimated in the Prospective Studies Collaboration4 will be overestimates if risk in each decade is, at least in part, dependent on error free levels prior to the start of that decade. So how valid is it to assume that the level of cardiovascular risk associated with blood pressure or blood cholesterol during a particular decade depends only on usual levels at the start of that decade? This is difficult to answer purely from epidemiological studies. However, randomized controlled trials of blood pressure and cholesterol lowering treatments demonstrate that risk reductions occur within 1 year of starting treatment,5,6 and that the full epidemiologically expected reductions in risk may be realized within just a few years. Thus, trials appear to support the suggestion that true underlying blood pressure level at the start of an ‘at risk’ period provides the most important determinant of blood pressure-related cardiovascular risk during that period. A similar argument would apply for blood cholesterol.
However, even if cardiovascular risk during a particular decade was, to some degree, dependent on previous blood pressure levels independently of current blood pressure, we suggest that it is also influenced by usual blood pressure levels during that decade. For example, randomized trials suggest that a real change in blood pressure within the first 2 years, say, would have an effect on vascular risk over the following 8 years, and thus influence the overall 10 year risk. The correction methods used in the Prospective Studies Collaboration, for example, consider the ‘usual’ blood pressure at the start of each decade of age at risk,4 not the ‘usual’ blood pressure during that decade. In this sense, such ‘simple correction’ could be regarded as conservative, and the potential bias identified by Frost and White would not be as large as they suggest; indeed it may even be completely abolished.
Through their asbestos–mesothelioma example, Frost and White expose the potential dangers of applying correction techniques without due consideration of both the most relevant measure of association and the relative importance of the risk factor at various points throughout the life-course. Correction for regression dilution bias should only be employed when interest is in the underlying aetiological relationship between the risk of disease and ‘usual’ risk exposure levels at some point in time. If interest centres on how risk is truly accumulated throughout the life-course, the methods described by Frost and White could be fruitfully employed.
 |
References |
|---|
 Top References |
|---|
1 Galton F. Regression towards mediocrity in hereditary stature. J Anthropol Inst 1886;15:246–63.
2 Frost C, Thompson SG. Correcting for regression dilution bias: comparison of methods for a single predictor variable. J Roy Stat Soc A 2000;163:173–89.[CrossRef]
3 Frost C, White IR. The effect of measurement error in risk factors that change over time in cohort studies: do simple methods over-correct for ‘regression dilution’? Int J Epidemiol 2005;34:1359–68.
4 Prospective Studies Collaboration. Age-specific relevance of usual blood pressure to vascular mortality: a meta-analysis of individual data for one million adults in 61 prospective studies. Lancet 2002;360:1903–13.[CrossRef][Web of Science][Medline]
5 Blood Pressure Lowering Treatment Trialists' Collaboration. Effects of different blood-pressure-lowering regimens on major cardiovascular events: results of prospectively-designed overviews of randomised trials. Lancet 2003;362:1527–35.[CrossRef][Web of Science][Medline]
6 Heart Protection Study Collaborative Group. MRC/BHF Heart Protection Study of cholesterol lowering with simvastatin in 20,536 high-risk individuals: a randomised placebo-controlled trial. Lancet 2002;360: 7–22.[CrossRef][Web of Science][Medline]
CiteULike 
Connotea 
Del.icio.us What's this?
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||