contribution {rineq}

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

object

The model result object. class coxph, glm, lm or svyglm, probitmfx, logitmfx; the outcome should be the health variable and the predictors the components.

ranker

Ranking variable with the same length as the outcome.

correction

A logical indicating whether the global and partial confidence should be corrected for negative values using imputation.

type

Character, concentration index type that the decomposition should be applied to. Defaults to CI. Use CIw for binary outcomes.

intercept

Character, one of exclude or include, defaults to exclude. If exclude, the intercept coefficient will not included in the decomposition analysis, if set to include, it will be included.

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.

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)


# adopted 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(survival::Surv(time, status) ~ x + survival::strata(sex), testcph) 
contrib.coxph = contribution(fit.coxph, testcph$income)