Noor et al.[1] examined the way that increases in the availability of insecticide-treated bed nets affected socioeconomic inequalities in the use of such nets over a three year period and found that each year the inequality decreased. It is clear enough that by the third year, when the rates were 66.3% for the most poor and 66.6% for the least poor, any inequality was negligible, and that would be so regardless of how one measured inequality. But an appraisal of changing inequality from the first year to the second year would raise important measurement issues, which the data highlighted in the Noor abstract nicely illustrate.

In the first year, the usage rates were 2.9% for the most poor and 15.6% for the least poor; in the second year, the rates were 17.5% for the most poor and 37.9% for the least poor. Comparing the situation of the most and least poor, those who measure inequality in terms of relative differences in favorable outcomes (which is probably most common method) would find a substantial decrease in inequality. The ratio of the usage rate of the least deprived to the most deprived decreased from 5.4 to 2.2.

Those who measure inequality in terms of relative differences in adverse outcomes (as the U.S. National Center for Health Statistics would do) would find a substantial increase in inequality. The ratio of the rate of non-usage of the most poor group to that of the least poor group increased from 1.15 to 1.33 (a doubling of the relative difference).

Those who measure inequality in terms of absolute differences between rates (which include many healthcare researchers and the U.S. Centers for Disease Control and Prevention) would have found a substantial increase in inequality. The difference between rates rose from 12.7 percentage points to 20.4 percentage points. And I note that it was just such a pattern that has led to a perception in the United States that improvements in healthcare as a result of pay-for-performance programs will tend to increase healthcare inequalities.[2]

Each of the measures, however, increased in the direction of that, for reasons related to the shapes of underlying distributions of factors associated with the likelihood of experiencing an outcome, commonly occurs in the circumstances. That is, as an outcome increases in overall prevalence, relative differences in experiencing it tend to decrease, while relative differences in failing to experience it tend to increase. When outcome rates for groups being compared are below 50% and the rates increase to no greater than 50%, absolute differences tend to increase.[3-5]

The authors measured disparities in terms of concentration indexes, which complicates a direct comparison with measures just discussed. But in general, concentration indexes tend to behave like relative differences. Thus, those who measure the concentration of the favorable outcome, as the authors did, will tend to find that increases in the prevalence of an outcome reduces inequality. But those who measure the concentration of the adverse outcome will tend to find that increases in the prevalence of the favorable outcome increases inequality.[6]

How then might one reasonably appraise whether inequality changed between the first and second year? The only apparent method would be to derive from each pair of rates the difference between means of the underlying hypothesized distributions.[7,8] Using that method, we observe that the difference decreased from .885 standard deviations in the first year to .626 standard deviations in the second year. Further, consistent with the virtual elimination of the inequality, however measured, in the third years, the difference between hypothesized means for that year would be only .008 standard deviations.

References:

1. Noor AM, Amin AA, Akhwale WS, Snow RW (2007) Increasing Coverage and Decreasing Inequity in Insecticide-Treated Bed Net Use among Rural Kenyan Children. PLoS Med 4(8): e255. doi:10.1371/journal.pmed.0040255

2. Pay for Performance sub-page of Measuring Health Disparities page of jpscanlan.com: http://www.jpscanlan.com/...

3 Scanlan’s Rule page of jpscanlan.com: http://jpscanlan.com/scan...

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

5. Scanlan JP (2000) Race and mortality. Society 37(2):19-35: http://www.jpscanlan.com/...

6. Concentration Index sub-page of Measuring Health Disparities page of jpscanlan.com: http://www.jpscanlan.com/...

7. Solutions sub-page of Measuring Health Disparities page of jpscanlan.com: http://www.jpscanlan.com/...

8. Scanlan JP. Measuring Health Inequalities by an Approach Unaffected by the Overall Prevalence of the Outcomes at Issue, presented at the Royal Statistical Society Conference 2009, Edinburgh, Scotland, Sept. 7-11, 2009: http://www.jpscanlan.com/...