Signature
R_g = sum_(k=1)^K [w_k * r_gk]
| Inputs | Definition | Unit |
|---|---|---|
w_k | Share of the standard population in age band k; the shares sum to 1 across the K bands | proportion |
r_gk | Rate of the health outcome in social group g and age band k | for example the percentage of adults |
R_g | Directly age-standardised rate of the health outcome in social group g | the unit of the age-specific rates, for example the percentage of adults with a limiting long-term illness |
|---|
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.
Try this function
Implementations
Excel
Directly standardised rate of a social group in one Excel cell
With the standard population shares in a range named StdShare and the group's age-specific rates in a range named GroupRate, in the same band order, Excel returns the standardised rate.
=SUMPRODUCT(StdShare,GroupRate)
Assumptions
One standard population for every social group compared
Every group is standardised to the same weights w_k. The result depends on the standard chosen, so a different standard gives different rates, and a different gap whenever the difference between groups is not the same in every age band.
Age classed as a legitimate source of difference in the inequity analysis
Standardising for age removes the age-related part of the difference from the comparison. This is a fairness judgement as well as a statistical step: a factor standardised away is treated as a legitimate cause and is not counted as inequity.
Same age bands and comparable age-specific rates in every social group
The age bands are defined in the same way in every group, and each age-specific rate is estimated from the same kind of data. Sampling error in a rate for a small band carries through to the standardised rate.
Worked examples
Age-standardised rate of limiting illness in the most deprived group D
In the article's illustrative example group D has rates of 12% under 50 and 40% at 50 and over. With a standard population of 60% under 50 and 40% aged 50 and over, the standardised rate is 7.2 plus 16.0, or 23.2%.
w_k = [0.6,0.4]; r_gk = [12,40]; R_g = 23.2
Age-standardised rate of limiting illness in the least deprived group A
Group A has rates of 8% under 50 and 30% at 50 and over, so the same standard gives 4.8 plus 12.0, or 16.8%. Because the outcome is ill health, the article puts the deprived group's rate first, giving a standardised gap of 6.4 points and a ratio of 23.2 / 16.8 = 1.38. The gap formulas of HE-FM-HINQ-001 subtract the most disadvantaged group's value from the most advantaged group's, so applied to these rates in that order they give minus 6.4 points and 16.8 / 23.2 = 0.72.
w_k = [0.6,0.4]; r_gk = [8,30]; R_g = 16.8
Crude rate of group D from its own age structure
Using group D's own age shares of 50% and 50% as the weights returns its crude rate of 26.0%, as in step 1 of the article. Group A's own shares of 40% and 60% give its crude rate of 21.2%, so the crude gap of 4.8 points is smaller than the standardised gap of 6.4 points because group D is younger.
w_k = [0.5,0.5]; r_gk = [12,40]; R_g = 26.0
Common errors
Comparing crude rates of social groups with different age structures
Crude rates weight each group's age-specific rates by its own age structure, so part of the comparison reflects age. In the article's example the crude gap is 4.8 points against a standardised gap of 6.4 points, because the deprived group is younger.
Reporting a standardised health gap without its standard population
The standardised gap depends on the standard. With a standard of 50% under 50 and 50% aged 50 and over, computed here for illustration, group D's rate is 26.0% and group A's 19.0%, a gap of 7.0 points instead of 6.4. The standard is stated with the result.
Sources
WHO paper on direct age standardisation of rates
Ahmad OB, Boschi-Pinto C, Lopez AD, Murray CJL, Lozano R, Inoue M. Age standardization of rates: a new WHO standard. GPE Discussion Paper Series No. 31. Geneva: World Health Organization; 2001. Introduction, which defines the directly standardised rate as a weighted average of the age-specific rates with the age distribution of the standard population as the weights, gives the formula, and notes that the comparison and the conclusions drawn are influenced by the chosen standard.
World Bank guide on direct standardisation across socioeconomic groups
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, section on direct and indirect standardisation, which describes direct standardisation, in its regression-based variant, as giving the distribution of health across socioeconomic groups that would be observed if all groups had the same age structure (equations 5.4 and 5.5).
Canonical Identity
Stable URI · Machine-readable · Resolvable · CC BY 4.0