The absolute concentration index (ACI) is an absolute measure of inequality that indicates the extent to which an indicator is concentrated among disadvantaged or advantaged subgroups, on an absolute scale.
Usage
aci(
est,
subgroup_order,
pop = NULL,
weight = NULL,
psu = NULL,
strata = NULL,
fpc = NULL,
lmin = NULL,
lmax = NULL,
conf.level = 0.95,
force = FALSE,
...
)Arguments
- est
The indicator estimate. Estimates must be available for all subgroups/individuals (unless force=TRUE).
- subgroup_order
The order of subgroups/individuals in an increasing sequence.
- pop
For disaggregated data, the number of people within each subgroup. This must be available for all subgroups.
- weight
The individual sampling weight, for individual-level data from a survey. This must be available for all individuals.
- psu
Primary sampling unit, for individual-level data from a survey.
- strata
Strata, for individual-level data from a survey.
- fpc
Finite population correction, for individual-level data from a survey where sample size is large relative to population size.
- lmin
Minimum limit for bounded indicators (i.e., variables that have a finite upper and/or lower limit).
- lmax
Maximum limit for bounded indicators (i.e., variables that have a finite upper and/or lower limit).
- conf.level
Confidence level of the interval. Default is 0.95 (95%).
- force
TRUE/FALSE statement to force calculation with missing indicator estimate values.
- ...
Further arguments passed to or from other methods.
Value
The estimated ACI value, corresponding estimated standard error,
and confidence interval as a data.frame.
Details
ACI can be calculated using disaggregated data and individual-level data. Subgroups in disaggregated data are weighted according to their population share, while individuals are weighted by sample weight in the case of data from surveys.
The calculation of ACI is based on a ranking of the whole population from the most disadvantaged subgroup (at rank 0) to the most advantaged subgroup (at rank 1), which is inferred from the ranking and size of the subgroups. ACI can be calculated as twice the covariance between the health indicator and the relative rank. Given the relationship between covariance and ordinary least squares regression, ACI can be obtained from a regression of a transformation of the health variable of interest on the relative rank. For more information on this inequality measure see Schlotheuber (2022) below.
Interpretation: ACI is 0 if there is no inequality. The larger the absolute value of ACI, the higher the level of inequality. Positive values indicate a concentration of the indicator among advantaged subgroups, and negative values indicate a concentration of the indicator among disadvantaged subgroups.
Type of summary measure: Complex; absolute; weighted
Applicability: Ordered dimension of inequality with more than two subgroups
Warning: The confidence intervals are approximate and might be biased.
References
Schlotheuber, A, Hosseinpoor, AR. Summary measures of health inequality: A review of existing measures and their application. Int J Environ Res Public Health. 2022;19(6):3697. doi:10.3390/ijerph19063697.
Examples
# example code
data(IndividualSample)
head(IndividualSample)
#> id psu strata weight subgroup subgroup_order sba dtp3
#> 1 1 88 1 0.351672 Quintile 3 3 1 NA
#> 2 2 1337 38 0.431545 Quintile 1 (poorest) 1 1 1
#> 3 3 450 18 0.482483 Quintile 2 2 1 NA
#> 4 4 1692 56 0.407390 Quintile 1 (poorest) 1 0 NA
#> 5 5 752 23 1.547062 Quintile 5 (richest) 5 1 NA
#> 6 6 1033 30 2.429523 Quintile 5 (richest) 5 1 NA
#> favourable_indicator indicator_scale
#> 1 1 100
#> 2 1 100
#> 3 1 100
#> 4 1 100
#> 5 1 100
#> 6 1 100
with(IndividualSample,
aci(est = sba,
subgroup_order = subgroup_order,
weight = weight,
psu = psu,
strata = strata))
#> measure estimate se lowerci upperci
#> 1 aci 0.07801353 0.002950566 0.07223053 0.08379654
# example code
data(OrderedSample)
head(OrderedSample)
#> indicator
#> 1 Births attended by skilled health personnel (%)
#> 2 Births attended by skilled health personnel (%)
#> 3 Births attended by skilled health personnel (%)
#> 4 Births attended by skilled health personnel (%)
#> 5 Births attended by skilled health personnel (%)
#> dimension subgroup subgroup_order
#> 1 Economic status (wealth quintile) Quintile 1 (poorest) 1
#> 2 Economic status (wealth quintile) Quintile 2 2
#> 3 Economic status (wealth quintile) Quintile 3 3
#> 4 Economic status (wealth quintile) Quintile 4 4
#> 5 Economic status (wealth quintile) Quintile 5 (richest) 5
#> estimate se population setting_average favourable_indicator
#> 1 75.60530 1.5996131 2072.436 91.59669 1
#> 2 91.01997 1.1351504 2112.204 91.59669 1
#> 3 96.03959 0.6461946 1983.059 91.59669 1
#> 4 97.04223 0.5676206 2052.124 91.59669 1
#> 5 99.22405 0.2237683 1884.510 91.59669 1
#> ordered_dimension indicator_scale
#> 1 1 100
#> 2 1 100
#> 3 1 100
#> 4 1 100
#> 5 1 100
with(OrderedSample,
aci(est = estimate,
subgroup_order = subgroup_order,
pop = population))
#> measure estimate se lowerci upperci
#> 1 aci 4.30052 1.284031 1.783865 6.817174