Signature
I_DU = sum_(j=1)^J [u_j * Delta_j]
| Inputs | Definition | Unit |
|---|---|---|
u_j | Judgement on cause j: 1 if the cause is judged an illegitimate, unfair source of difference, 0 if it is judged legitimate | indicator |
Delta_j | Part of the standardised gap attributed to cause j by the decomposition | the unit of the gap, for example percentage points |
I_DU | Inequity in the gap under direct unfairness: the sum of the explained parts whose causes are judged illegitimate | the unit of the gap, for example percentage points |
|---|
Function
Health inequity measurement function under stated fairness judgements
Maps the age-specific rates of ill health in social groups, a standard population, and a decomposition of the standardised gap between groups into parts attributed to named causes, to estimates of health inequity: the part of a measured difference judged avoidable and unfair. Differences due to factors classed as legitimate, such as age, are first removed by direct standardisation. The inequity is then the part of the remaining gap whose causes are classed as illegitimate, with the unexplained remainder treated as acceptable under direct unfairness or as unfair under the fairness gap. The size of a gap is measured with the gaps, slope and relative indices and concentration index on the Health Inequality page (HE-FN-HINQ-001), and indirect standardisation of health care use for need is on the Horizontal Equity page (HE-FM-HEQ-001); neither is repeated here.
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Implementations
Excel
Direct unfairness from a decomposed gap in one Excel cell
With 1 or 0 for each cause in a range named UnfairFlag and the parts of the gap in a range named CausePart, in the same order, Excel returns the direct unfairness measure.
=SUMPRODUCT(UnfairFlag,CausePart)
Assumptions
Additive attribution of the health gap to causes for direct unfairness
The gap is split into parts that add up, as in a linear regression decomposition, so that setting a legitimate cause to the same value in both groups removes exactly its part. With interactions between causes, holding one cause constant changes the other parts as well, and the result depends on the reference value chosen.
Fairness judgements stated before direct unfairness is computed
Each cause is classed as legitimate or illegitimate by an explicit value judgement, for example by Whitehead's criterion of the degree of choice involved. The classification is reported with the result, since the same gap gives different inequity under different judgements.
Worked examples
Direct unfairness with smoking judged a restricted choice
In the article's illustrative example the 6.4-point standardised gap is attributed 2.0 points to smoking, 2.0 points to housing and working conditions and 2.4 points to the unexplained remainder. With both explained causes judged unfair, direct unfairness counts 2.0 + 2.0 = 4.0 points, the third row of the article's table.
u_j = [1,1]; Delta_j = [2.0,2.0]; I_DU = 4.0
Direct unfairness with smoking judged a free choice
Classing smoking as freely chosen sets its indicator to 0 and leaves only housing and working conditions, 2.0 points, the fourth row of the article's table.
u_j = [0,1]; Delta_j = [2.0,2.0]; I_DU = 2.0
Direct unfairness when every explained cause is judged legitimate
If every explained cause is judged legitimate, direct unfairness is zero whatever the size of the gap, a limiting case that checks the implementation.
u_j = [0,0]; Delta_j = [2.0,2.0]; I_DU = 0
Common errors
Counting the unexplained remainder under direct unfairness
Adding the 2.4-point remainder turns the direct unfairness figure of 4.0 points into 6.4 points, which is the fairness gap result, not direct unfairness. The two measures treat the remainder differently and are labelled accordingly.
Reporting direct unfairness without the fairness judgements behind it
Reclassifying smoking from a restricted to a free choice halves the result from 4.0 to 2.0 points with the same data. A figure reported without the classification of each cause cannot be interpreted.
Sources
Fleurbaey and Schokkaert definition of direct unfairness
Fleurbaey M, Schokkaert E. Unfair inequalities in health and health care. Journal of Health Economics. 2009;28(1):73-90. Abstract, which distinguishes causal variables leading to ethically legitimate inequalities from those leading to illegitimate ones, defines direct unfairness by the hypothetical distribution in which all legitimate sources of variation are kept constant and the fairness gap by the difference between the actual distribution and the hypothetical one in which all illegitimate sources have been removed, notes that the two generally give different results, and relates them to direct and indirect standardisation.
Unexplained inequality treated as acceptable under direct standardisation
Asada Y, Hurley J, Norheim OF, Johri M. Unexplained health inequality: is it unfair? International Journal for Equity in Health. 2015;14:11. Abstract, which treats unexplained inequality as ethically acceptable under direct standardisation and as unfair under indirect standardisation, and reports that about 75% of the variation in the Health Utilities Index was unexplained and that about 60% of health inequality was inequitable under direct standardisation against almost all of it under indirect standardisation.
Canonical Identity
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