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Re: Interpreting departures from expected patterns of relative differences

Dear Editor

Mustard and Etches examined the differences between male and female socioeconomic gradients in mortality, finding that, in absolute terms, the gradient is consistently larger for men, but that in relative terms, the gradients are equal or at least less consistently larger for men.[1] But efforts to evaluate differences in socioeconomic inequality in some outcome for groups with different overall rates of experiencing the outcome need to be undertaken with an appreciation of the way various measures of inequality are affected by the prevalence of an outcome.

First, consider relative differences in mortality. Ordinarily, the rarer an outcome, the greater tends to be the relative difference between rates of experiencing it and the smaller tends to be the relative difference between rates of avoiding it.[2-7]. Thus, one typically finds greater relative socioeconomic (or racial) difference in mortality among groups with lower overall mortality, as, for example, among the young (compared with the old),[6] in relatively healthy countries like Norway and Sweden,[2,6] among British civil servants (compared with the UK population at large),[6] among infants born to better educated mothers (compared with those born to less educated mothers).[4] When such patterns are observed, it is a mistake, without more, to regard greater relative differences in mortality within the group with lower mortality to reflect greater inequality in a meaningful way (particularly when the relative difference in the opposite outcome is smaller in that group).

The notable thing about a comparison of the size of relative socioeconomic differences in mortality among women and those among men is that the observed pattern does not conform to the expectation of a greater relative socioeconomic difference among the group with lower overall mortality (women). Thus, that relative socioeconomic differences in mortality are as large for men as women (and sometimes larger) suggests the existence of a meaningful difference between socioeconomic effects upon men and upon women. That is, the departure from the usual pattern suggests that the risk distributions of higher and lower SES men differ more than the risk distributions of higher and lower SES women – presumably due to the various factors discussed by Mustard and Etches, notwithstanding the inconsistent results of studies exploring the roles of such factors. And the greater socioeconomic difference in the risk distributions of men is sufficient to overcome the tendency for the greater relative difference to be observed among the group with lower mortality. On the other hand, the relative socioeconomic difference in survival rates will likely be lower among women, as would typically be the case simply because mortality is lower among women, and will be so to an enhanced degree because of the greater SES difference in the male than the female risk distribution.

While it is a point more pertinent in the usual circumstances where a factor such a SES causes a greater relative difference among the group with lower base rate rather than in the instant situation where that pattern does not exist, it nevertheless warrants note that there is no reason ever to expect any factor to have the same relative effect within two different populations that have different baseline rates. In fact, it would be illogical to expect such a pattern. In the case of the young compared with the old, for a simple example, there is obviously no more reason to expect a factor like lower SES to cause equivalent relative increases in mortality among the young and the old than there is to expect lower SES to cause equivalent relative decreases in survival rates. And in situations where baseline rates are different, it is mathematically impossible for a factor to cause equivalent relative increases in one outcome and equivalent relative decreases in the other outcome. More concretely, if mortality is 5% percent among high SES young people and 10% among high SES old people and being of low SES increased mortality to the same relative degree among the young and old (say, doubling it in each population, that is, from 5% to 10% among the young and from 10% to 20% among the old), it necessarily would cause different proportionate decreases in survival rates among the two populations (from 95% to 90% among the young, a 5.3% reduction, and from 90% to 80% among the old, a 11.1% reduction. Thus, it makes no sense to have any expectation of similar proportionate effects of some factor or to attribute significance to the fact that proportionate effects differ.

All to say, in the usual case where a factor causes a greater relative difference within a population with a lower base rate, it is a mistake to attach meaning to that greater difference. One may, however, derive meaning from a situation where, as in the context examined by Mustard and Etches, the factor fails to do so or even does the opposite.

Now consider the absolute socioeconomic differences, which the study found to be consistently greater among men than among women. Like relative differences, absolute differences also tend to vary depending on the prevalence of an outcome. Instead of the linear relationship with the prevalence of an outcome exhibited with the relative differences in experiencing or avoiding an outcome, however, the absolute difference exhibits an inverted U-shaped relationship with the prevalence of an outcome. Without exploring the nuances of that relationship, which are explored elsewhere,[2,6,7] with respect to socioeconomic differences in mortality, we should expect the absolute difference to be greater in the population with the higher baseline rate, even when that population shows greater relative socioeconomic in mortality, as for example, where we observe larger socioeconomic absolute differences in mortality among the old than the young notwithstanding the larger relative difference among the young than the old (which, of course, is typically attended by a smaller relative difference in the opposite outcome among the young than the old). In any case, the larger absolute difference in mortality among men than women is what we should expect because of the higher mortality among men regardless of whether there is any meaningful difference in the way socioeconomic status affects men and women.

In sum, one ought not to attach meaning to the consistently greater absolute socioeconomic difference in mortality among men than among women inasmuch as it is exactly what would be expected given the greater mortality of men. One might, however, attach some meaning to the fact that one does not observe a greater relative socioeconomic difference among women than men and more so to the fact that one sometimes observes a larger relative difference among men than women.

References

1. Mustard CA, Etches J. Gender differences in socioeconomic inequality in mortality. J Epidemiol Community Health. 2003;57:974-980.

2. Scanlan JP. Can we actually measure health disparities? Chance 2006:19(2):47-51: http://www.jpscanlan.com/images/Can_We_Actually_Measure_Health_Disparities.pdf

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: http://www.jpscanlan.com/images/Race_and_Mortality.pdf

5. Scanlan JP. Divining difference. Chance. 1994;7(4):38-9,48: http://jpscanlan.com/images/Divining_Difference.pdf

6. Scanlan JP. The misinterpretation of health inequalities in the United Kingdom. Paper presented at: British Society for Population Studies Annual Conference 2006, Southampton, England, Sept. 18-20, 2006: http://www.jpscanlan.com/images/BSPS_2006_Complete_Paper.pdf