Signature
Delta = sum_(j=1)^J [Delta_j] + Delta_res; s = (sum_(j=1)^J [u_j * Delta_j] + u_res * Delta_res) / Delta
| Inputs | Definition | Unit |
|---|---|---|
Delta_j | Part of the standardised gap attributed to cause j | the unit of the gap |
Delta_res | Part of the standardised gap that the decomposition does not explain | the unit of the gap |
u_j | Judgement on cause j: 1 if judged unfair, 0 if judged legitimate | indicator |
u_res | Judgement on the unexplained remainder: 1 if it is treated as unfair, as under the fairness gap, 0 if it is treated as acceptable, as under direct unfairness | indicator |
Delta | Standardised gap between the two groups, equal to the explained parts plus the unexplained remainder | the unit of the gap, for example percentage points |
|---|---|---|
s | Inequity as a share of the standardised gap | proportion |
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
Inequity share of a decomposed health gap in one Excel cell
With 1 or 0 for each cause in UnfairFlag, the explained parts in CausePart, the remainder in a cell named Remainder and 1 or 0 for the remainder in a cell named RemainderFlag, Excel returns the share.
=(SUMPRODUCT(UnfairFlag,CausePart)+RemainderFlag*Remainder)/(SUM(CausePart)+Remainder)
Assumptions
Parts that add up to the standardised gap for the inequity share
The explained parts and the remainder sum to the gap after standardisation, so the share depends on the standard population and on which factors were standardised away before the decomposition.
Positive standardised gap for the inequity share
The share is defined only when the gap is not zero, and it is read most easily when the gap and all its parts have the same sign.
Worked examples
Inequity share with smoking restricted and the remainder unfair
The parts 2.0 + 2.0 + 2.4 rebuild the article's 6.4-point gap, and with every part judged unfair the whole gap counts as inequity, a share of 1.
Delta_j = [2.0,2.0]; Delta_res = 2.4; u_j = [1,1]; u_res = 1; Delta = 6.4; s = 1
Inequity share with smoking freely chosen and the remainder unfair
The article's 4.4 points out of 6.4 give a share of 0.6875, computed here for illustration.
Delta_j = [2.0,2.0]; Delta_res = 2.4; u_j = [0,1]; u_res = 1; Delta = 6.4; s = 0.6875
Inequity share with smoking restricted and the remainder acceptable
The article's 4.0 points out of 6.4 give a share of 0.625, computed here for illustration.
Delta_j = [2.0,2.0]; Delta_res = 2.4; u_j = [1,1]; u_res = 0; Delta = 6.4; s = 0.625
Inequity share with smoking freely chosen and the remainder acceptable
The article's 2.0 points out of 6.4 give a share of 0.3125, computed here for illustration.
Delta_j = [2.0,2.0]; Delta_res = 2.4; u_j = [0,1]; u_res = 0; Delta = 6.4; s = 0.3125
Common errors
Reading the inequity share as fixed by the data
The same standardised gap gives shares of 1, 0.6875, 0.625 and 0.3125 under the four combinations of judgements in the article's table, computed here for illustration. Asada and colleagues found the same dependence in survey data, with about 60% of inequality inequitable under direct standardisation and almost all of it under indirect standardisation.
Carrying an individual-level judgement on unexplained variation over to groups without saying so
Asada and colleagues considered unexplained variation between individuals. Treating a residual gap between groups in the same way is an analogy, as the article notes, and is reported as an assumption of the analysis.
Sources
Shares of health inequality judged inequitable under two treatments of the unexplained part
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.
Legitimate and illegitimate sources of health inequality
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.
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0