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Concentration index

Source: R/concentration.R
iq_concentration.Rd

Computes the concentration index, which measures inequality in a health (or other) variable across the income distribution. Unlike the Gini coefficient, the ranking variable and the outcome variable are different.

Usage

iq_concentration(
  x,
  rank,
  weights = NULL,
  correction = c("none", "erreygers", "wagstaff"),
  bounds = c(0, 1),
  na.rm = FALSE,
  ci = FALSE,
  R = 1000L,
  level = 0.95
)

Arguments

x

Numeric vector of outcome values (e.g. health expenditure).

rank

Numeric vector of ranking values (e.g. income). Must be the same length as x.

weights

Optional numeric vector of survey weights.

correction

Character. "none" (default) for the standard index; "erreygers" for the Erreygers (2009) bounded-variable correction; "wagstaff" for the Wagstaff (2005) normalised index.

bounds

Numeric vector of length 2 giving the lower and upper bounds of x. Required when correction = "erreygers". Default c(0, 1) (suitable for binary or proportion variables).

na.rm

Logical. Remove NA values? Default FALSE.

ci

Logical. Compute bootstrap confidence intervals? Default FALSE.

R

Integer. Number of bootstrap replicates. Default 1000.

level

Numeric. Confidence level. Default 0.95.

Value

An S3 object of class "iq_concentration" with elements:

value

Numeric. The concentration index.

correction

Character. The correction applied.

n

Integer. Number of observations.

se, ci_lower, ci_upper, level

Bootstrap CI fields, NULL unless ci = TRUE.

Details

A positive value indicates the outcome is concentrated among the better-off; a negative value indicates concentration among the worse-off.

For bounded variables (e.g. binary health indicators), the standard concentration index has bounds that depend on the mean. Two corrections are available:

  • correction = "erreygers": the Erreygers (2009) corrected index, E = 4 * mu / (b - a) * C, which has fixed bounds of -1 to 1.

  • correction = "wagstaff": the Wagstaff (2005) normalised index, W = C / (1 - mu / b) for variables bounded above at b, which is the standard normalisation in much of the health-economics literature.

References

Wagstaff, A., Paci, P. and van Doorslaer, E. (1991). "On the Measurement of Inequalities in Health." Social Science and Medicine, 33(5), 545–557.

Erreygers, G. (2009). "Correcting the Concentration Index." Journal of Health Economics, 28(2), 504–515.

Wagstaff, A. (2005). "The Bounds of the Concentration Index when the Variable of Interest is Binary, with an Application to Immunization Inequality." Health Economics, 14(4), 429–432.

Examples

set.seed(1)
income <- rlnorm(200, 10, 0.8)
health_exp <- income * 0.05 + rnorm(200, 500, 100)
iq_concentration(health_exp, rank = income)
#> 
#> ── Concentration Index ─────────────────────────────────────────────────────────
#> • Value: 0.3065
#> • Observations: 200

# With bootstrap CIs
iq_concentration(health_exp, rank = income, ci = TRUE, R = 200)
#> 
#> ── Concentration Index ─────────────────────────────────────────────────────────
#> • Value: 0.3065
#> • Observations: 200
#> • Bootstrap 95% CI: [0.2691, 0.3359]

# Binary outcome with Erreygers correction
sick <- as.numeric(income < median(income)) + rbinom(200, 1, 0.1)
sick <- pmin(sick, 1)
iq_concentration(sick, rank = income, correction = "erreygers")
#> 
#> ── Concentration Index (Erreygers) ─────────────────────────────────────────────
#> • Value: -0.9241
#> • Observations: 200