The relative concentration index (RCI) is a relative measure of inequality that indicates the extent to which an indicator is concentrated among disadvantaged or advantaged subgroups, on a relative scale.
rci(
est,
subgroup_order,
pop = NULL,
weight = NULL,
psu = NULL,
strata = NULL,
fpc = NULL,
method = NULL,
lmin = NULL,
lmax = NULL,
conf.level = 0.95,
force = FALSE,
...
)The estimated RCI value, corresponding estimated standard error,
and confidence interval as a data.frame.
The indicator estimate. Estimates must be available for all subgroups/individuals (unless force=TRUE).
The order of subgroups/individuals in an increasing sequence.
For disaggregated data, the number of people within each subgroup. This must be available for all subgroups.
The individual sampling weight, for individual-level data from a survey. This must be available for all individuals.
Primary sampling unit, for individual-level data from a survey.
Strata, for individual-level data from a survey.
Finite population correction, for individual-level data from a survey where sample size is large relative to population size.
Normalisation method for bounded indicators. Options available
are Wagstaff (wagstaff) or Erreygers (erreygers) correction. Must be
used in conjunction with minimum and maximum limits (lmin and lmax).
Minimum limit for bounded indicators (i.e., variables that have a finite upper and/or lower limit).
Maximum limit for bounded indicators (i.e., variables that have a finite upper and/or lower limit).
Confidence level of the interval. Default is 0.95 (95%).
TRUE/FALSE statement to force calculation with missing indicator estimate values.
Further arguments passed to or from other methods.
RCI 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 RCI 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. RCI can be calculated as twice the covariance between the health indicator and the relative rank, divided by the indicator mean. Given the relationship between covariance and ordinary least squares regression, RCI 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: RCI is bounded between -1 and +1 (or between -100 and +100, when multiplied by 100). The larger the absolute value of RCI, 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. RCI is 0 if there is no inequality.
Type of summary measure: Complex; relative; weighted
Applicability: Ordered dimension of inequality with more than two subgroups
Warning: The confidence intervals are approximate and might be biased.
Erreygers G. Correcting the Concentration Index. J Health Econ. 2009;28(2):504-515. doi:10.1016/j.jhealeco.2008.02.003.
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.
Wagstaff A. The bounds of the concentration index when the variable of interest is binary, with an application to immunization inequality. Health Econ. 2011;20(10):1155-1160. doi:10.1002/hec.1752.
# example code
data(IndividualSample)
head(IndividualSample)
with(IndividualSample,
rci(est = sba,
subgroup_order = subgroup_order,
weight = weight,
psu = psu,
strata = strata))
# example code
data(OrderedSample)
head(OrderedSample)
with(OrderedSample,
rci(est = estimate,
subgroup_order = subgroup_order,
pop = population))
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