Title:	Concentration Index and Decomposition for Health Inequalities
Version:	0.3.0
Date:	2025-01-10
Description:	Relative, generalized, and Erreygers corrected concentration index; plot Lorenz curves; and decompose health inequalities into contributing factors. The package currently works with (generalized) linear models, survival models, complex survey models, and marginal effects probit models. originally forked by Brecht Devleesschauwer from the 'decomp' package (no longer on CRAN), 'rineq' is now maintained by Kaspar Walter Meili. Compared to the earlier 'rineq' version on 'github' by Brecht Devleesschauwer (https://github.com/brechtdv/rineq), the regression tree functionality has been removed. Improvements compared to earlier versions include improved plotting of decomposition and concentration, added functionality to calculate the concentration index with different methods, calculation of robust standard errors, and support for the decomposition analysis using marginal effects probit regression models. The development version is available at https://github.com/kdevkdev/rineq.
Depends:	R (≥ 3.5.0)
Imports:	stats, graphics
Suggests:	sandwich, lmtest, mfx, survey, survival
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
LazyData:	true
RoxygenNote:	7.3.2
Encoding:	UTF-8
Language:	en-Us
URL:	https://github.com/kdevkdev/rineq
BugReports:	https://github.com/kdevkdev/rineq/issues
NeedsCompilation:	no
Packaged:	2025-01-10 14:11:03 UTC; kaspar
Author:	Brecht Devleesschauwer [aut, cph], Saveria Willimès [aut, cph], Carine Van Malderen [aut, cph], Peter Konings [aut, cph], Niko Speybroeck [aut, cph], Kaspar Meili [aut, cre, cph]
Maintainer:	Kaspar Meili <meilikaspar@yahoo.de>
Repository:	CRAN
Date/Publication:	2025-01-13 17:30:10 UTC

Calculates different type of concentration indexes

Description

This function calculates the relative concentration index (Kakwani et al.), the generalized concentration index (Clarke et al., 2002), the Wagstaff index for bounded variables (Owen et al. 2016), and the concentration index with Erreygers' correction (Erreygers et al., 2009). It returns an object of class hci for which confidence intervals, summaries and plots are defined.

Usage

ci(
  ineqvar,
  outcome,
  weights = NULL,
  type = c("CI", "CIg", "CIc", "CIw"),
  method = c("linreg_delta", "linreg_convenience", "cov_convenience", "direct"),
  df_correction = TRUE,
  robust_se = FALSE,
  rse_type = "HC3",
  rank_function = rineq::rank_wt
)

Arguments

Value

An S3 object of class hci. Contains:

• concentration_index The concentration index

• type The type

• method The method used for calculation

• variance The variance,used for calculation of confidence intervals

• fractional_rank Computed fractional rank NA

• outcome Outcome after removing NA

• call Call signature

• n Number of observations after removing NA

• robust_se Were robust standard errors calculated?

• rse_type Type of robust standard errors.

• df_correction Do the degrees of freedom correspond to a sample?

References

Clarke, P. M., Gerdtham, U. G., Johannesson, M., Bingefors, K., & Smith, L. (2002). On the measurement of relative and absolute income-related health inequality. Social Science & Medicine, 55(11), 1923-1928

Erreygers, G. (2009). Correcting the concentration index. Journal of health economics, 28(2), 504-515

Kakwani, N., Wagstaff, A., & Van Doorslaer, E. (1997). Socioeconomic inequalities in health: measurement, computation, and statistical inference. Journal of econometrics, 77(1), 87-103.

O'Donnel, O., O'Neill S., Van Ourti T., & Walsh B. (2016). Conindex: Estimation of Concentration Indices. The Stata Journal, 16(1): 112-138.

O’Donnell, O., Van Doorslaer, E. , Wagstaff, A., Lindelow, M., 2008. Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation, World Bank Publications. The World Bank.

van Ourti, T., 2004. Measuring horizontal inequity in Belgian health care using a Gaussian random effects two part count data model. Health Economics, 13: 705–724.

Examples

# Direct
data(housing)
ci.bmi <- ci(ineqvar = housing$income, outcome = housing$bmi, method = "direct")
summary(ci.bmi)

# retrieve value
ci.bmi$concentration_index

# obtain confidence intervals
confint(ci.bmi, level = 0.95) 
plot(ci.bmi)

# Wagstaff type with binary outcome and robust standard errors 
# that should correspond to Stata (depends on 'sandwich'):
ci.bmi.b <- ci(housing$income, housing$high.bmi, type = "CIw", robust_se = TRUE, 
   rse_type = "HC1")

Confidence intervals for hci objects

Description

Confidence intervals for hci objects

Usage

## S3 method for class 'hci'
confint(object, parm = NULL, level = 0.95, ...)

Arguments

Value

A confidence interval in a numeric vector of length 2

Examples

data(housing)
ci.bmi <- ci(ineqvar = housing$income, outcome = housing$bmi, method = "direct")
confint(ci.bmi)

Function to decompose the Relative Concentration Index into its components

Description

Currently compatible with lm, glm logit and probit, svyglm, coxph and mfx marginal effects probit.

Usage

contribution(object, ranker, correction = TRUE, type = "CI", intercept = "exclude")

Arguments

Details

These functions decompose the Relative Concentration Index into its components using a (generalized) linear model, optionally using a survey design, or a Cox Proportional Hazards model. Print, summary and plot methods have been defined for the results.

If correction is TRUE negative values of components or outcome are corrected using correct_sign() with option shift = FALSE.

For non-linear models the decomposition needs to rely on a linear approximations of the effects. There are different approaches. One is to work on the scale of the glm coefficients and calculate the concentration index based on the predicted outcome. (Konings et al., 2010, Speybroeck et al., 2010). Another approach is to use marginal effects as beta coefficients and the original outcome (O'Donnel et al. 2008).

This function supports both. For glm, coxph, and svyglm models, the first approach is used. The second approach is implemented for model objects of type probitmfx and logitmfx from the 'mfx' package. See examples.

Per default, the intercept in models is excluded, but this can be changed by setting the the intercept argument to include, but this may conceptually make less sense and is more appropriate if the model does not contain an intercept.

Use decomposition() function directly to manually specify coefficients, outcomes, and model matrices for arbitrary models.

NOTE: Be careful with automatically omitted rows in models. Only models with data with ordinary indexes are supported (starting from 1, sequentially increasing by increments of 1). For the case were rows with NA are automatically omitted by the model function, the used indices are guessed based on the row names of the model matrix and then used for accessing the ranker variable. However, this may lead to issues if the row names do not correspond to ordinary integer indexes. For example, if a model such as lm uses the default na.omit action and removes rows, the data in the model might not be consistent with the ranker vector anymore.

Value

An object of class decomposition containing the following components:

• betas A numeric vector containing regression coefficients

• partial_cis A numeric vector containing partial confidence intervals

• confints A numeric vector containing 95\

• averages Weighted averages of every variable in the model

• ci_contribution Confidence intervals for contributions

• overall_ci Confidence intervals for the concentration index

• corrected_coefficients Corrected coefficients using correct_sign() if, requested FALSE otherwise

• outcome_corrected Corrected outcome correct_sign() if requested, FALSE otherwise

• rows Rownames of used rows in the model

Warning

ranker should be chosen with care. Ideally, it is a variable from the same dataframe as the other variables. If not, redefine the row names in the model.

Author(s)

Peter Konings

References

Konings, P., Harper, S., Lynch, J., Hosseinpoor, A.R., Berkvens, D., Lorant, V., Geckova, A., Speybroeck, N., 2010. Analysis of socioeconomic health inequalities using the concentration index. Int J Public Health 55, 71–74. https://doi.org/10.1007/s00038-009-0078-y

Speybroeck, N., Konings, P., Lynch, J., Harper, S., Berkvens, D., Lorant, V., Geckova, A., Hosseinpoor, A.R., 2010. Decomposing socioeconomic health inequalities. Int J Public Health 55, 347–351. https://doi.org/10.1007/s00038-009-0105-z

O’Donnell, O., Doorslaer, E. van, Wagstaff, A., Lindelow, M., 2008. Analyzing Health Equity Using Household Survey Data: A Guide to Techniques and Their Implementation, World Bank Publications. The World Bank.

Examples

data(housing)

## Linear regression direct decomposition
fit.lm <- lm(bmi ~ sex + tenure + place + age,data = housing)
       
# decompose relative concentration index
contrib.lm <- contribution(fit.lm, housing$income) 
summary(contrib.lm)
plot(contrib.lm, decreasing = FALSE, horiz = TRUE)

    
# GLM: Decomposition based on predicted outcome
fit.logit <-glm(high.bmi ~ sex + tenure + place + age, data = housing)

contrib.logit <- contribution(fit.logit, housing$income) 
summary(contrib.logit)
plot(contrib.logit, decreasing = FALSE,horiz = TRUE)


# GLM probit: Decomposition based on predicted outcome
fit.probit <-glm(high.bmi ~ sex + tenure + place + age, data = housing, 
                family = binomial(link = probit))

# binary, set type to 'CIw'
contrib.probit <- contribution(fit.probit, housing$income, type = "CIw") 
summary(contrib.probit)
plot(contrib.probit, decreasing = FALSE,horiz = TRUE)


# Marginal effects probit using package 'mfx': Decomposition based on predicted outcome
fit.mfx <-mfx::probitmfx(high.bmi ~ sex + tenure + place + age, data = housing)

contrib.mfx <- contribution(fit.mfx, housing$income, type = "CIw") 
summary(contrib.mfx, type="CIw")
plot(contrib.mfx, decreasing = FALSE, horiz = TRUE)


# package survey svy 
des = survey::svydesign(~1, data= housing, weights = rep(1, NROW(housing)))
fit.svy = survey::svyglm(bmi ~ tenure+height+weight, design = des)
contrib.svy = contribution(fit.svy, housing$income)


# adapted from the `coxph` example in survival package 
testcph <- data.frame(time = c(4,3,1,1,2,2,3), 
              status = c(1,1,1,0,1,1,0), 
              x      = c(0,2,1,1,1,0,0), 
              sex    = c(0,0,0,0,1,1,1),
              income = c(100,50, 20, 20, 50, 60,100))
              
# Fit a stratified model 
fit.coxph = survival::coxph(Surv(time, status) ~ x + strata(sex), testcph) 
contrib.coxph = contribution(fit.coxph, testcph$income) 

Corrects negative values in the health variable

Description

The Relative Concentration Index is not bonded between [-1,1] if the health variable contains both negative and positive values. This function corrects for this either by imputing a value of 0 for all negative values or by subtracting the minimum value.

Usage

correct_sign(x, shift = TRUE)

corrected_value(x)

is_corrected(x)

Arguments

Value

correct_sign() returns a list with 2 components:

• corrected: corrected version of x

• modified: logical, TRUE when any of the elements of x have been changed

corrected_value(): returns the corrected value if passed the result of 'correct_sign().

is_corrected(): returns TRUE if a modifications was made and FALSE otherwise. Takes as argument the result of correct_sign(),

Functions

• corrected_value(): Return the corrected value

• is_corrected(): Check if the sign was corrected

Author(s)

Peter Konings

Examples

data("housing")

# standardize & normalize bmi, will introduce negative values
housing$bmi.std <- (housing$bmi - mean(housing$bmi))/ sd(housing$bmi)

housing$bmi.std.shifted <- corrected_value(correct_sign(housing$bmi.std, shift = TRUE))
housing$bmi.std.imputed <- corrected_value(correct_sign(housing$bmi.std, shift = FALSE))

## compare the effect of both methods
plot(density(housing$bmi.std, na.rm = TRUE))
points(density(housing$bmi.std.shifted, na.rm = TRUE), col = 'blue')
points(density(housing$bmi.std.imputed, na.rm = TRUE), col = 'green')

Decomposition analysis

Description

Used by the wrapper contribution() but can be used manually. Calculates the decomposition for a given regression model.

Usage

decomposition(outcome, betas, mm, ranker, wt, correction, citype = "CI")

Arguments

Details

NOTE: Only models with data with ordinary indexes are supported (starting from 1, sequentially increasing by increments of 1). For the case were rows with NA are automatically omitted by the model function, the used indices are guessed based on the row names of the model matrix and then used for accessing the ranker variable. However, this may lead to issues if the row names do not correspond to ordinary integer indexes.

Value

S3 object of class decomposition

Examples

fit.lm = lm(mtcars$mpg ~ mtcars$cyl)
decomp = decomposition(mtcars$mpg, coefficients(fit.lm), fit.lm$model, 
                       mtcars$hp, wt = rep(1, nrow(mtcars)), correction = FALSE) 
summary(decomp)

Artificial example data on housing conditions

Description

Microdata with a permissive license that includes continuous data on health and income is hard to come by. In stead of real data, the package thus includes an imaginary dataset.

Usage

data(housing)

Format

data.frame object.

Variable list:

id

unique identifier per person

sex

female or male

age

integer, from 20 to 94

tenure

categorical. One of homeless, irregular, own_apartment, own_house, or rent

height

height in cm

weight

weight in kg

bmi

weight/(height/100)^2

income

continuous, imaginary currency without unit

Source

Artificially generated by the package authors

Plots a barplot of the contribution percentages in a decomposition object. Sets custom plot margins and uses the graphical parameters xlim, horiz, las and xlab which therefore cannot be customized

Description

Plots a barplot of the contribution percentages in a decomposition object. Sets custom plot margins and uses the graphical parameters xlim, horiz, las and xlab which therefore cannot be customized

Usage

## S3 method for class 'decomposition'
plot(x, decreasing = TRUE, horiz = FALSE, ...)

Arguments

Value

Invisibly returns x as the function is called for side effects (plotting).

Examples

data(housing)
# Linear regression & decompose 
fit.lm <- lm(bmi ~ sex + tenure + place + age,data = housing)
contrib.lm <- contribution(fit.lm, housing$income)

# plot horizontally, in increasing order
plot(contrib.lm, decreasing = FALSE, horiz = TRUE)

Plots the concentration curve for an hci object.

Description

Plots the concentration curve for an hci object.

Usage

## S3 method for class 'hci'
plot(x, ...)

Arguments

Value

Invisibly returns x as the function is called for side effects (plotting).

Examples

data(housing)
ci.bmi <- ci(ineqvar = housing$income, outcome = housing$bmi, method = "direct")
plot(ci.bmi)
 

Print function for decomposition objects.

Description

Print function for decomposition objects.

Usage

## S3 method for class 'decomposition'
print(x, ...)

Arguments

Value

Invisibly returns x as the function is called for side effects.

Examples

data(housing)
# Linear regression &  decompose 
fit.lm <- lm(bmi ~ sex + tenure + place + age,data = housing)
contrib.lm <- contribution(fit.lm, housing$income)

# print
print(contrib.lm)

Prints an hci object.

Description

Prints an hci object.

Usage

## S3 method for class 'hci'
print(x, ...)

Arguments

Value

Invisibly returns x as the function is called for side effects.

Examples

data(housing)
ci.bmi <- ci(ineqvar = housing$income, outcome = housing$bmi, method = "direct")
print(ci.bmi)

Generalized weighted ranking function

Description

In the case of ties, the ordinary rank_wt() function uses the order in the original data. This is the same approach as in the Stata code provided by O’Donnell et al. (2008) in the original World Bank publication, but depends on the arbitrary initial order in the data The Stat conindex code however uses uses the generalized weighted rank implementation published by van Ourti (2004). For Stata compatibility use rank_gwt()

Usage

rank_gwt(x, wt)

Arguments

Details

The formula notation in van Ourti (2004) seems to rely on absolute an absolute deduction of 1 unit of monetary income value. This only works in the integer case. Instead, this this implementation uses the next lowest x value, respectively the next lowest rank, to calculate the proportion of the inequality variable up to the respective value

Value

A numeric vector containing weighted fractional ranks of the elements of x.

References

van Ourti, T., 2004. Measuring horizontal inequity in Belgian health care using a Gaussian random effects two part count data model. Health Economics, 13: 705–724.

Examples

x <- sample(1:10, size = 10, replace = TRUE)
x.weight <- seq(0, 1, length.out = 10)
rank_gwt(x, wt = x.weight)

Calculates the weighted rank

Description

Calculates the weighted rank

Usage

rank_wt(x, wt)

Arguments

Value

A numeric vector containing weighted fractional ranks of the elements of x.

Author(s)

Peter Konings

References

Kakwani et al., 1997.

Examples

x <- sample(1:10, size = 10, replace = TRUE)
x.weight <- seq(0, 1, length.out = 10)
rank_wt(x, wt = x.weight)

Prints and returns a summary for a decomposition object.

Description

Prints and returns a summary for a decomposition object.

Usage

## S3 method for class 'decomposition'
summary(object, digits = getOption("digits"), addcoefs = FALSE, ...)

Arguments

Value

A data frame frame with columns for the absolute and relative contribution, elasticity, concentration index including confidence intervals, and whether correction was applied. If specified using addcoefs, the coefficients are included as the first column.

Examples

data(housing)
# Linear regression & decompose 
fit.lm <- lm(bmi ~ sex + tenure + place + age,data = housing)
contrib.lm <- contribution(fit.lm, housing$income)

# print
print(contrib.lm)

Prints the a summary of the concentration index object hci

Description

Prints the a summary of the concentration index object hci

Usage

## S3 method for class 'hci'
summary(object, ...)

Arguments

Value

No returns value. Directly prints to the standard output connection.

Examples

data(housing)
ci.bmi <- ci(ineqvar = housing$income, outcome = housing$bmi, method = "direct")
summary(ci.bmi)

Calculates the weighted variance

Description

Calculates the weighted variance

Usage

var_wt(x, wt, na.rm = FALSE)

Arguments

Value

A numeric vector containing weighted variance of the elements of x

Examples

x <- sample(1:10, size = 10, replace = TRUE)
x.weight <- seq(0, 1, length.out = 10)
var_wt(x, wt = x.weight)