lunaineq

lunaineq estimates health inequality metrics for ecological or grouped data. The package is intended for analyses where each row represents an aggregate unit—such as a region, province, department, municipality, district, country, quintile, or other population group—and the analyst wants to quantify how a health indicator varies across a socioeconomic or equity stratifier.

The package implements six metrics:

Function	Metric	Question answered
ag_ineqeco()	Absolute Gap (AG)	How large is the absolute difference between the most disadvantaged and most advantaged groups?
rg_ineqeco()	Relative Gap (RG)	How many times higher/lower is the indicator in the disadvantaged group compared with the advantaged group?
aci_ineqeco()	Absolute Concentration Index (ACI)	How much absolute inequality is distributed across the full socioeconomic ranking?
rci_ineqeco()	Relative Concentration Index (RCI)	Is the outcome concentrated among disadvantaged or advantaged units across the full distribution?
sii_ineqeco()	Slope Index of Inequality (SII)	What is the model-predicted absolute difference between the top and bottom of the social hierarchy?
rii_ineqeco()	Relative Index of Inequality (RII)	What is the model-predicted ratio between the top and bottom of the social hierarchy?

Installation

# install.packages("devtools")
devtools::install_github("adrianvasquezmd/lunaineq", build_vignettes = TRUE)

Core data requirements

Each analysis requires:

1. one row per ecological unit or group;
2. an equity stratifier supplied through equity_stratifier_var;
3. either a precomputed health indicator (health_indicator_var) or raw numerator/denominator columns (health_numerator_var, health_denominator_var);
4. a population or exposure weight, supplied explicitly through population_weights_var or implicitly through health_denominator_var when counts are used.

If the same ecological unit appears in multiple years, subset before analysis:

df_2020 <- subset(paho_data, year == 2020)

Direction of the equity stratifier

The argument higher_ineq_is_favorable controls how the equity stratifier is ordered.

Use higher_ineq_is_favorable = TRUE when higher values of the stratifier mean greater advantage, such as income, wealth, education, or HDI.

Use higher_ineq_is_favorable = FALSE when higher values mean greater disadvantage, such as poverty, deprivation, marginalization, vulnerability, or unsatisfied basic needs.

Example: if equity_stratifier_var = "ubn" and higher UBN means greater deprivation, use:

higher_ineq_is_favorable = FALSE

Health indicator input modes

Count-based input

Preferred when numerator and denominator are available:

health_indicator_type  = "rate"
health_numerator_var   = "maternal_death"
health_denominator_var = "live_births"
rate_scaling_factor    = 100000

Precomputed indicator input

Use when the rate, percentage, proportion, or ratio is already calculated:

health_indicator_var   = "mmr"
population_weights_var = "live_births"
health_indicator_type  = "rate"

If available, health_se_var can be supplied for AG/RG/ACI/RCI analytic variance workflows. The current SII/RII functions do not accept health_se_var; they estimate uncertainty using Wald, bootstrap, or jackknife methods.

Quick examples

Absolute gap

ag <- ag_ineqeco(
  data = df_2020,
  health_indicator_type = "rate",
  health_numerator_var = "maternal_death",
  health_denominator_var = "live_births",
  rate_scaling_factor = 100000,
  analysis_unit_var = "state",
  equity_stratifier_var = "ubn",
  higher_ineq_is_favorable = FALSE,
  grouping_approach = "fractional",
  n_groups = 5,
  ci_method = "delta"
)

ag$summary_stats
ag$results_groups

Interpretation: if AG is 40 deaths per 100,000 live births, the maternal mortality ratio is 40 deaths per 100,000 live births higher in the most disadvantaged group than in the most advantaged group.

Relative concentration index

rci <- rci_ineqeco(
  data = df_2020,
  health_indicator_type = "rate",
  health_numerator_var = "maternal_death",
  health_denominator_var = "live_births",
  rate_scaling_factor = 100000,
  analysis_unit_var = "state",
  equity_stratifier_var = "ubn",
  higher_ineq_is_favorable = FALSE,
  bounded_corrections = "none",
  ci_method = "analytic"
)

rci$summary_stats
rci$results_curve

Interpretation: the RCI summarizes whether the indicator is concentrated toward the disadvantaged or advantaged end of the socioeconomic distribution. For adverse indicators, concentration among disadvantaged units indicates an inequitable distribution of health burden.

Slope index of inequality

sii <- sii_ineqeco(
  data = df_2020,
  health_indicator_type = "rate",
  health_numerator_var = "maternal_death",
  health_denominator_var = "live_births",
  rate_scaling_factor = 100000,
  analysis_unit_var = "state",
  equity_stratifier_var = "ubn",
  higher_ineq_is_favorable = FALSE,
  models = NULL,
  model_selection_metric = "RMSE",
  social_position_method = "classic",
  ci_method = "wald",
  vcov_type = "HC1"
)

sii$summary_stats
sii$model_selection_table

Interpretation: SII is the model-predicted absolute difference between the advantaged and disadvantaged ends of the social hierarchy. Inspect model_selection_table to verify which model was selected and why.

Choosing among functions

Use AG/RG when you need a clear comparison between extreme groups. Use ACI/RCI when you want the full ranked distribution, not only extremes. Use SII/RII when you want a regression-based social-gradient estimate that predicts values at the bottom and top of the social hierarchy.

For reporting, use absolute and relative measures together. A relative gap can be large even when the absolute difference is small; an absolute gap can be large even when the relative ratio is modest.

Main methodological choices

Grouping for AG/RG

grouping_approach controls how the extreme groups are constructed:

• "territorial": groups ecological units based on the distribution of units;
• "weighted_cut": groups using population/exposure weighting;
• "weighted_midpoint": groups using weighted midpoints in the ranked distribution;
• "fractional": uses fractional-rank information to form the comparison.

When grouping_approach = "territorial", territorial_method can be "quantile", "kmeans", "fisher", "manual", or "equal".

Bounded corrections for RCI

bounded_corrections controls whether Wagstaff and/or Erreygers corrections are returned for bounded outcomes. Use these mainly for proportions or percentages. For unbounded rates such as mortality rates, use bounded_corrections = "none" unless a meaningful lower and upper bound is explicitly justified.

Model selection for SII/RII

SII/RII select among candidate models using model_selection_metric. Prediction-error metrics (MSE, RMSE, MAE, MAPE) are computed on the final outcome scale and weighted by population/exposure weights. AIC and BIC are used only for likelihood-comparable model sets.

For most applied workflows, start with:

models = NULL
model_selection_metric = "RMSE"
social_position_method = "classic"
ci_method = "wald"

Then inspect diagnostics and consider bootstrap/jackknife as sensitivity analyses.

Vignette

vignette("lunaineq", package = "lunaineq")

The vignette provides function-by-function documentation, argument-level guidance, and epidemiological interpretation templates.

Authors and license

Authors: Adrian Vasquez-Mejia, Oscar J. Mujica, Antonio Sanhueza.

License: AGPL (>= 3).