James P. Scanlan, Attorney at Law

CONCENTRATION INDEX

(Dec. 9, 2009; rev. Jan. 2, 2010)

The Concentration Index is an increasingly popular measure of health disparities, as are certain other summary measures of disparities, such as the Relative Index of Inequality.  These measures purport to take into account both the sizes of disparities between particular population groups and the proportion each group makes up of the total population.

Even if these summary measures were based on sound approaches to appraising differences between individual groups, there are issues as to whether they effectively take into account the size of the groups being compared.  For they are in significant part functions of the sizes of differences (however measured) between groups at the extremes, and those differences will typically be affected by the proportion each group makes up of the total population.  That is, a difference between the top and bottom 10 percent of the population will generally be greater than the difference between the top and bottom 20 percent of the populations.  There is also a question whether it is useful to confound issues concerning the size of disparities between groups with issues concerning the sizes of the groups. 

The subject of this item, however, concerns the way that the concentration index is a flawed measured of health disparities because it is a function of relative differences between rates and hence subject to the same factors that undermine relative differences as effective measures of differences in the well-being of two groups – specifically, that relative differences tend to be affected by the overall prevalence of an outcome, or, more specifically, that the rarer an outcome, the greater tends to be the relative difference in experiencing it and the smaller tends to be the relative difference in avoiding – as discussed the Measuring Health Disparities page (MHD) and Scanlan’s Rule page (SR) of this site and the hundred or so references that those pages make available.

A crucial requirement of any measure of health disparities is that it is unaffected by the overall prevalence of an outcome – that is, that it remains the same when there occurs a simple change in overall prevalence akin to that effected by the lowering a cutoff on a test.  The concentration index  does not satisfy that requirement. 

Table A below replicates five key columns of Table 1 of the 2006 British Society for Population Studies presentation.  That table, which can be accessed in its entirety by the indicated link, showed the implications as to various measures of differences between failure rates or pass rates of the lowering of a cutoff on a test where two groups with normal distributions have mean scores that differ by half a standard deviation, and it underlies many graphic illustrations of those implications.  The final two columns added to the abbreviated version of the table below show the concentration index scores both for failing and for passing the test at each cutoff where each group comprises one half of the population. 

It will be noted that, as with the relative differences in failing and passing a test, the concentration indexes for the two outcomes change in opposite directions as a cutoff is lowered and the adverse outcome becomes less common and the favorable outcome becomes more common.  The key point, however, is that the concentration index change at all simply when there occurs a change in overall prevalence.  Such fact demonstrates that the concentration index cannot identify changes in inequalities that are other than the statistically-driven consequences of changes in overall prevalence.

The formula for calculating the concentration index is that discussed on page 67 of the National Cancer Institute document Methods for Measuring Cancer Disparities Using Data Relevant to Health People 2010 Cancer-Related Objectives (by Sam Harper and John Lynch).  Table B below replicates the document’s methodology with regard to changes in educational differences in mammography rates between 1900 and 2002, the document calculated for its Table A1 (at 68) in terms of rates of failure to receive mammography (in accordance with the recommendation of the National Center for Health Statistics recommendation that all disparities be measured in terms of relative differences in adverse outcomes, which recommendation I criticize in a number of places, including Section E.4 of MHD and Section A .6 of SR).  This occurred during a period of substantial increases in mammography rates.

Table B below compares in concentration index for failure to receive mammography with the concentration index for receipt of mammography.

It will be observed that the concentration index for absence of a mammography decreased very slightly while the concentration index for receipt of mammography decreased substantially.  A decrease in  the relative difference in an adverse outcome (or even the absence of an increase) when an adverse outcome is declining would tend to signal a meaningful decrease in the disparity.  And when the relative difference in a declining outcome decreases somewhat, the relative difference in the opposite outcome will tend to decrease substantially.  Of course, as indicated at the outset, as the matter is influenced by changes in the size of the groups being compared, it is difficult to interpret these patterns.

Table C shows that, according to the approach described on the Solutions sub-page or MHD, the disparity between the lowest and highest education group decreased a fair amount, which accords with the pattern also shown whereby the relative difference in the adverse outcomes and the favorable outcomes both decreased.   This illustration, however, is a digression from the subject of this item, which involves the reason that the concentration index is a fundamentally flawed measure of health disparities.

Finally, it warrants note that there is also an absolute concentration index.  Inasmuch as absolute differences are the same regardless of whether one examines the favorable or the adverse outcome, the absolute concentration index presumably would be unaffected by which rate one examines.  But, as with the absolute difference itself, the measure remains problematic as a measure of health disparities because it is affected by the overall prevalence of an outcome.[i]