rii {healthequal}

Relative index of inequality (RII)

Description

The relative index of inequality (RII) is a relative measure of inequality that represents the ratio of estimated indicator values between the most-advantaged and most-disadvantaged, while taking into consideration the situation in all other subgroups/individuals – using an appropriate regression model. RII 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.

Usage

rii(
  est,
  subgroup_order,
  pop = NULL,
  scaleval = NULL,
  weight = NULL,
  psu = NULL,
  fpc = NULL,
  strata = NULL,
  conf.level = 0.95,
  linear = FALSE,
  force = FALSE,
  ...
)

Arguments

est

The subgroup estimate. Estimates must be available for all subgroups.

subgroup_order

The order of subgroups in an increasing sequence.

pop

The number of people within each subgroup. Population size must be available for all subgroups.

scaleval

The scale of the indicator. For example, the scale of an indicator measured as a percentage is 100. The scale of an indicator measured as a rate per 1000 population is 1000.

weight

Individual sampling weight (required if data come from a survey)

psu

Primary sampling unit (required if data come from a survey)

fpc

Finite population correction

strata

Strata (required if data come from a survey)

conf.level

confidence level of the interval.

linear

TRUE/FALSE statement to specify the use of a linear regression model for RII estimation (default is logistic regression)

force

TRUE/FALSE statement to force calculation with missing indicator estimate values.

...

Further arguments passed to or from other methods.

Details

To calculate RII, a weighted sample of the whole population is ranked from the most-disadvantaged subgroup (at rank 0) to the most-advantaged subgroup (at rank 1). This ranking is weighted, accounting for the proportional distribution of the population within each subgroup. The population of each subgroup is then considered in terms of its range in the cumulative population distribution, and the midpoint of this range. The indicator of interest is then regressed against this midpoint value using an appropriate regression model (e.g., a generalized linear model with logit link), and the predicted values of the indicator are calculated for the two extremes (rank 1 and rank 0). The ratio between the estimated values at rank 1 and rank 0 (covering the entire distribution) generates the RII value. For more information on this inequality measure see Schlotheuber, A., & Hosseinpoor, A. R. (2022) below.

Interpretation: RII has the value of one if there is no inequality. RII has only positive values. Greater absolute values indicate higher levels of inequality. The further the value of RII from one, the higher the level of inequality. For favourable indicators, values larger than one indicate a concentration of the indicator among the advantaged and values smaller than one indicate a concentration of the indicator among the disadvantaged. For adverse indicators, values larger than one indicate a concentration of the indicator among the disadvantaged and values smaller than one indicate a concentration of the indicator among the advantaged. RII is a multiplicative measure and has to be displayed on a logarithmic scale (values larger than one are equivalent in magnitude to their reciprocal values smaller than one, e.g., a value of 2 is equivalent in magnitude to a value of 0.5).

Type of summary measure: Complex; relative; weighted

Applicability: Ordered; more than two subgroups

Warning: The confidence intervals are approximate and might be biased.

Value

The estimated RII value, corresponding estimated standard error, and confidence interval as a data.frame.

References

Schlotheuber, A., & Hosseinpoor, A. R. (2022). Summary measures of health inequality: A review of existing measures and their application. International journal of environmental research and public health, 19 (6), 3697.

Examples

# example code
data(IndividualSample)
head(IndividualSample)
with(IndividualSample,
     rii(est = sba,
         subgroup_order = subgroup_order,
         weight = weight,
         psu = psu,
         strata = strata
         )
     )