Signature
yIS_i = y_i - yX_i + y_bar
| Inputs | Definition | Unit |
|---|---|---|
y_i | Actual use of care by person i, or the group mean | units of use |
yX_i | Need-expected use of person i from HE-FM-HEQ-001, or the group mean | units of use |
y_bar | Sample mean of actual use | units of use |
yIS_i | Need-standardised use of care by person i, or the group mean when group means are entered | units of use, for example doctor visits per person per year |
|---|
Function
Horizontal equity measurement function for health care delivery and finance
Maps data on the use of health care, proxies of need and compulsory health payments, for people ranked by income or another measure of living standards, to measures of horizontal equity: need-expected use from a need regression, need-standardised use, the horizontal inequity index for the delivery of care, its rule-of-75 reading, and the horizontal inequity term in the decomposition of the redistributive effect of health finance. Equal treatment for equal need is judged against the average relationship between need and use in the sample, so the vertical norm is assumed rather than tested. The grouped-data concentration index (HE-FM-HINQ-005 on the Health Inequality page and HE-FM-VEQ-002 on the Vertical Equity page) and the Kakwani index (HE-FM-VEQ-001) have their own records and are not repeated here.
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Implementations
Excel
Need-standardised use of health care in one Excel cell
With actual use in a cell named ActualUse, need-expected use in NeedExpected and the sample mean of actual use in MeanUse, Excel returns need-standardised use. Filled down a column of people or groups, MeanUse stays fixed.
=ActualUse-NeedExpected+MeanUse
Assumptions
Linear standardisation with the mean of actual use added
The need-expected values come from a linear regression, so their mean equals y_bar and standardised use has the same mean as actual use. With a nonlinear model the mean of the predictions is added instead of y_bar, so that the mean of standardised use still equals that of actual use.
Group means standardised in the same way as individual values
Applying the formula to group means of actual and need-expected use gives the same result as standardising each person and then averaging within the group, because the formula is linear and y_bar is the same constant for everyone.
Worked examples
Need-standardised visits for the poorest income quintile
In the article's example the poorest quintile makes 4.4 visits a year against 5.0 expected given its need, with an overall mean of 4.0, so its need-standardised use is 3.4 visits.
y_i = 4.4; yX_i = 5.0; y_bar = 4.0; yIS_i = 3.4
Need-standardised visits for the richest income quintile
The richest quintile makes 3.6 visits against 3.0 expected, so its need-standardised use is 4.6 visits, about 35 per cent more than the poorest quintile at the same average need.
y_i = 3.6; yX_i = 3.0; y_bar = 4.0; yIS_i = 4.6
Common errors
Leaving out the mean when standardising use for need
Actual minus need-expected use alone averages zero, so its concentration index, which divides by the mean, cannot be computed. In the article's example the poorest quintile would show minus 0.6 visits and the richest 0.6 visits.
Subtracting actual use from need-expected use
Reversing the subtraction mirrors the pattern: the poorest quintile would receive 4.6 standardised visits and the richest 3.4, and the horizontal inequity index would be minus 0.06, showing pro-poor inequity where the correct result is pro-rich.
Sources
World Bank guide on indirectly standardised values
O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation. Washington, DC: World Bank; 2008. Chapter 5, equation 5.3: indirectly standardised values as the difference between actual and x-expected values plus the overall sample mean, and group figures as averages of the standardised values.
World Bank guide on standardised use with nonlinear models
O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation. Washington, DC: World Bank; 2008. Chapter 15, page 179: with nonlinear models the mean of the predictions is added, rather than the mean of the actual variable, so that standardised use has the same mean as actual use.
Canonical Identity
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