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Re: Effects of standard adjustment approaches on relative and absolute inequalities

In a 2006 comment [1] on the article by Lynch et al.,[2] I pointed out that the authors’ findings of different contributions of risk factors to relative and absolute inequalities in CHD rates were functions of the fact that the authors studied the effects of the elimination of risk factors rather the effects of adjusting for the implications of differing risk profiles in different education groups. In making this point, I noted that “while various approaches to such an adjustment yield somewhat different results,” information available in the Lynch article showed that an adjustment that attributed the risk profile of the highest education group to the lowest education group yielded exactly the same 19% percent reduction of relative and absolute inequalities in CHD. The quoted language was meant merely to suggest that the percentage reductions in the two inequalities effected by one adjustment method might differ from those effected by another method. The intended implication, however, was that under any standard approach to adjustment for risk factors, the percentage reduction of the relative difference between rates would be the same as the percentage reduction of the absolute difference between rates.

In a 2008 comment in a different forum on another article that had made an argument similar to that in Lynch et al.,[3] I pointed out that adjusting for differing risk profiles by attributing the advantaged group’s risk profile to the disadvantaged group and by attributing the disadvantaged group’s risk profile to the advantaged group, while yielding somewhat different results, yield exactly the same percentage reductions in the relative difference between rates that they yield for the absolute difference between rates. There, too, the point was the all standard adjustment techniques yield the same percentage reductions in relative differences between rates that they yield for absolute differences between rates. But the point is not correct.

In a 2008 article in Epidemiology, Singh-Manoux et al.[4] addressed the article by Lynch et al., making points similar to those in my 2006 comment. Singh-Manoux et al. also explained that adjusting for risk factors by attributing the risk profile of the advantaged group to the disadvantaged group yields exactly the same percentage reductions of relative and absolute risk differences. But the authors’ main adjustment approach (which they applied to data from the Whitehall II study) involved attributing the risk profile of the entire population both to the advantaged group and to the disadvantaged group. Such approach yielded similar, but not identical, percentage reductions in relative and absolute differences.

The authors’ point was that standard approaches to adjustment yielded similar percentage reductions in relative and absolute inequalities and that the findings by Lynch et al. of substantially different percentage reductions in relative and absolute inequalities were the consequence of addressing a different question from that addressed by standard approaches to adjustment for risk factors. But the fact is that Singh-Manoux et al. did not find identical reductions in relative and absolute differences.

Thus, whereas adjusting for risk factors either by attributing the advantaged group’s risk profile to the disadvantaged group or by attributing the disadvantaged group’s risk profile to the advantaged group yields exactly the same percentage reduction in a relative between rates as in an absolute differences between rates, adjusting for risk factors by attributing the entire population’s risk profile to both groups apparently does not. Further, while Singh-Manoux et al. seem to read their results as indicating that adjusting for risk factors in such a manner typically will yield similar reductions in relative and absolute differences, that will not necessarily be the case. Singh-Manoux et al. examined a setting where 29,121 person years were analysed for the advantaged group but only 3,387 person years were analyzed for the disadvantaged group. Hence, the risk profile of the entire population that underlay the authors’ adjustment approach was based on a population that was almost entirely (94.7%) comprised of the advantaged group. In such circumstances, adjusting according to the risk profile of the entire population will tend to yield results that are little different from adjusting according to the advantaged group’s profile – both with respect to the size of the reduction generally and with respect to the extent to which the percentage reductions in the relative and absolute differences are similar. Neither of these patterns will necessarily hold when the disadvantaged group comprises a much larger proportion of the entire population than was the case in the Singh-Manoux study.

The fact that adjustment according the risk profile of the entire population can yield different relative and absolute risk reductions would seem to militate against use of that adjustment approach – even though, as I have discussed in reference 5 and many other places, both relative and absolute differences between rates are problematic measures of the size of inequalities because each is affected by the overall prevalence of an outcome. The fact that, whatever the measure of inequality, the relative size of the groups being compared may generally affect the size of an adjustment for differing risk profiles would seem even more strongly to militate against adjusting according to the risk profile of the entire population. Further, an important reason society is interested in learning the contribution of differing risk profiles to health inequalities is to assess the impact of efforts to bring the disadvantaged group’s risk profile into line with the advantaged group’s risk profile. There is no similarly practical purpose in learning the implications of causing the advantaged group’s risk profile to worsen at the same time that the disadvantaged group’s risk profile improves, since no society would undertake to do so.

At any rate, the suggestion in my earlier comments that any standard approach to adjustment for risk factors will yield the same percentage change in the relative difference between rates that it yields for the absolute difference between rates is not correct.

References:

1. Scanlan JP. Understanding social gradients in adverse health outcomes within high and low risk populations. J Epidemiol Community Health May 18, 2006.

2. Lynch J, Davey Smith G, Harper S, Bainbridge K. Explaining the social gradient in coronary heart disease: comparing relative and absolute risk approaches. J Epidemiol Community Health 2006:60:436-441.

3. Scanlan JP. Study shows different adjustment approaches rather than different relative and absolute perspectives. Journal Review May 1, 2008 (responding to Khang YH, Lynch JW, Jung-Choi K, Cho HJ. Explaining age-specific inequalities in mortality from all causes, cardiovascular disease and ischaemic heart disease among South Korean public servants: relative and absolute perspectives. Heart 2008;94:75- 82):http://journalreview.org/v2/articles/view/17591645.html

4. Singh-Manoux A, Nabi H, Shipley M, et al. The role of conventional risk factors in explaining social inequalities in coronary heart disease – the relative and absolute approaches. Epidemiology 2008;19:599-605

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Re: Understanding social gradients in adverse outcomes within high and low risk populations

Dear Editor,

In seeking to resolve the seeming paradox whereby risk factors have been found to account for a very high proportion of coronary heart disease (CHD) but only a small part of the social gradient in CHD, Lynch et al. present the CHD rates among groups with different levels of education both for a population at large and for the part of that population without any risk factors.1 Comparing the large difference between absolute educational inequalities in CHD in the two populations with the small difference between relative educational inequalities in CHD in the two populations, the authors conclude that the proportion of educational inequalities in CHD accounted for by risk factors turns on whether one examines absolute or relative inequalities.

Yet, while the CHD rates of advantaged and disadvantaged groups in a population without risk factors do reflect what the rates for such groups would be in the entire population if there were no risk factors at all, that is a different thing from what the rates of disadvantaged and advantaged groups would be if disadvantaged groups had the same risk distributions as advantaged groups. It is the difference between the latter rates that standard adjustments for risk factors generally seek to show, and it is on the basis of such adjustments that one appraises the role of risk factors in explaining differences among groups. Lynch et al. describe their illustration as artificial because it would not be possible to eliminate all risk factors. But in fact the illustration is simply something different from the standard examination of the consequences of different risk profiles among different groups. And, while various approaches to such an adjustment yield somewhat different results, the information in Table 2 of the study allows one to calculate that, if the lowest education group had the same risk profile as the highest educated group, the CHD rate for the lowest education group in the entire population would be reduced from 194 per thousand to 177.4 per thousand. With a rate of 106 per thousand for the highest education group, this means that the excess absolute risk would be reduced from 88 per thousand to 71.4 per thousand, and the excess relative risk would be reduced from .830 to .674 – the same 19% percent reduction for each measure.

The authors are correct, however, in their view that reducing risk factors has much greater impact in terms of reducing absolute inequalities in CHD rates than in reducing relative inequalities, and their concern that the reduction pattern they observe might be peculiar to the studied population is unwarranted. For what they have identified is the near inevitable consequence or reductions in risk factors with regard to relative and absolute differences between the rates at which advantaged and disadvantaged groups experience some adverse outcome.

By and large, the rarer an outcome, the greater the relative difference in experiencing it (though the smaller the relative difference in avoiding it).2,3,4,5. Because populations with few or no risk factors generally have low rates of adverse outcomes, such populations will tend to show large relative socioeconomic differences in experiencing those outcomes. The size of such differences typically will be comparable to or greater than the size of such differences within high risk populations, even when the socioeconomic variation among measures like average income and average education are smaller in the low risk population than in the high risk population. Depending on the differing distributions of advantaged and disadvantaged groups across risk levels, the relative socioeconomic difference in experiencing an adverse outcome within the low risk population can be larger or smaller than the relative difference in the population at large, though infrequently will it be dramatically smaller. A good example may be found in studies of differences between black and white infant mortality rates in the United States broken down by education of mother. One study showed that relative racial differences were greater among infants of mothers with higher education (where overall rates were low) than among infants of mothers with lower education (where overall rates were higher).6 Another study showed relative racial differences solely among college-educated mothers (where overall rates were low) that were very close to those among the population at large (where overall rates were higher) and that may have in fact been larger than the relative racial differences among infants born to mothers with less education (where overall rates were higher than among the population at large).4,7. While in those settings education reflects the differing risk levels and race is the factor distinguishing the demographic groups being compared, the pattern will be the same when something like smoking is the risk factor and education is the factor distinguishing the demographic groups.

In any event, there is little reason to expect relative socioeconomic differences in experiencing adverse health outcomes to be substantially smaller within a low risk population than in the population at large. On the other hand, low risk populations, having low rates of experiencing adverse outcomes, tend to show much smaller absolute differences between rates of advantaged and disadvantaged groups than in the population at large. For, even when the relative differences are large, such differences translate into small absolute differences.

While the focus of Lynch et al. is on the reduction of risks among the disadvantaged, the consequences they show are simply the usual result of reducing risk factors, and, correspondingly, adverse outcomes, throughout society. For example, by and large, as mortality declines, relative differences in mortality rates tend to increase while absolute differences tend to decline.2-5. Whether these changes are more than or less than the standard consequences of declining mortality, and hence may reflect some true change in the relative situation of disadvantaged groups with respect to the outcome, must be evaluated with an understanding of those consequences.

References

1. Lynch J, Davey Smith G, Harper S, Bainbridge K. Explaining the social gradient in coronary heart disease: comparing relative and absolute risk approaches. J Epidemiol Community Health 2006:60:436-441.

2. Scanlan JP. Can we actually measure health disparities? Chance. 2006:19(2): ____. In press.

3. Scanlan JP. Measuring health disparities. J Public Health Manag Pract 2006;12(3):294 [Lttr] (http://www.nursingcenter.com/library/JournalArticle.asp?Article_ID=641470).

4. Scanlan JP. Race and Mortality. Society. 2000;37(2):19-35.

5. Scanlan JP. Divining difference. Chance. 1994;7(4):38-9, 48.

6. Singh GK, Yu SM. Infant mortality in the United States: trends, differentials and projections, 1950 through 2010. Am J Public Health. 1995;85:957-64.