Signature
I_FG = Delta - sum_(j=1)^J [(1 - u_j) * Delta_j]
| Inputs | Definition | Unit |
|---|---|---|
Delta | Standardised gap in the health outcome between the two groups, including the unexplained remainder | for example percentage points |
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 |
I_FG | Inequity in the gap under the fairness gap: the whole gap minus the explained parts whose causes are judged legitimate | 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
Fairness gap from a decomposed gap in one Excel cell
With the standardised gap in a cell named Gap, 1 or 0 for each cause in UnfairFlag and the explained parts in CausePart, Excel subtracts the legitimate parts from the gap.
=Gap-SUMPRODUCT(1-UnfairFlag,CausePart)
Assumptions
Additive attribution of the health gap to causes for the fairness gap
The explained parts and the unexplained remainder add up to the standardised gap, so removing a cause removes exactly its part. The remainder is whatever the decomposition leaves unexplained.
Same gap and decomposition for the fairness gap and direct unfairness
Both measures are computed from the same standardised gap and the same decomposition, so that the difference between them equals the unexplained remainder in every scenario.
Worked examples
Fairness gap with smoking judged a restricted choice
With smoking and housing and working conditions both judged unfair, no explained cause is legitimate, so the whole 6.4-point gap counts as inequity, the first row of the article's table.
Delta = 6.4; u_j = [1,1]; Delta_j = [2.0,2.0]; I_FG = 6.4
Fairness gap with smoking judged a free choice
Classing smoking as freely chosen makes its 2.0 points legitimate, so the fairness gap is 6.4 minus 2.0, or 4.4 points, the second row of the article's table.
Delta = 6.4; u_j = [0,1]; Delta_j = [2.0,2.0]; I_FG = 4.4
Fairness gap when every explained cause is judged legitimate
If both explained causes are judged legitimate, only the 2.4-point remainder is left, computed here for illustration. The result equals the remainder, a limiting case that checks the implementation.
Delta = 6.4; u_j = [0,0]; Delta_j = [2.0,2.0]; I_FG = 2.4
Common errors
Treating the fairness gap and direct unfairness as interchangeable
In the article's example the two measures differ by the 2.4-point remainder in every scenario: 6.4 against 4.0 points with smoking judged unfair, and 4.4 against 2.0 points with smoking judged a free choice. Fleurbaey and Schokkaert note that the two approaches generally give different results.
Subtracting the illegitimate parts in the fairness gap
The hypothetical distribution removes the illegitimate causes, so its gap holds the legitimate parts, and the fairness gap subtracts those. Subtracting the illegitimate parts instead returns the remainder: with smoking judged unfair, 6.4 minus 4.0 gives 2.4 points, which is not the inequity.
Sources
Fleurbaey and Schokkaert definition of the fairness gap
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 unfair under indirect 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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