Calculating Health Inequality in Complex Surveys

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Sujon Mia - StatAid Research Lab

Introduction

Analyzing health inequalities—such as the concentration of childhood malnutrition among the poorest wealth quintiles—is a critical component of global health research. However, calculating standardized metrics like the Concentration Index using data from complex, multi-stage stratified cluster surveys (such as DHS or MICS) is methodologically challenging.

The SurveyNCD package, developed by the StatAid Research Lab, provides a streamlined, mathematically rigorous pipeline to automate these calculations.

This vignette demonstrates how to process raw anthropometric data and calculate survey-weighted health inequality metrics in just a few lines of code.

Setup and Package Loading

First, load SurveyNCD along with the standard tidyverse and srvyr packages for data manipulation and survey design handling.

library(SurveyNCD)
library(dplyr)
library(srvyr)

Phase 1: Cleaning Anthropometric Data

Raw survey datasets often store Z-scores as integers (e.g., -254 instead of -2.54) and use specific numerical flags (like 9999) to indicate missing or biologically implausible data. Failing to account for these flags will severely distort your means and indices.

The who_anthro_score() function automatically cleans these values and categorizes them according to strict WHO child growth standards.

# Simulating raw survey data with a missing flag (9999)
raw_survey_data <- tibble(
  cluster_id = c(1, 1, 2, 2),
  strata = c(1, 1, 2, 2),
  sample_weight = c(1.2, 0.8, 1.1, 0.9),
  wealth_score = c(-1.5, -0.2, 0.5, 1.8),
  raw_hw70 = c(-310, -254, 50, 9999) # Raw Height-for-Age
)

# Apply the SurveyNCD cleaning function
cleaned_data <- raw_survey_data %>%
  mutate(
    stunting_category = who_anthro_score(raw_hw70, indicator = "stunting"),
    is_stunted = case_when(
      stunting_category %in% c("Severe stunting", "Moderate stunting") ~ 1,
      stunting_category == "Normal stunting" ~ 0,
      TRUE ~ NA_real_
    )
  )

cleaned_data %>% select(raw_hw70, stunting_category, is_stunted)
#> # A tibble: 4 × 3
#>   raw_hw70 stunting_category is_stunted
#>      <dbl> <fct>                  <dbl>
#> 1     -310 Severe stunting            1
#> 2     -254 Moderate stunting          1
#> 3       50 Normal stunting            0
#> 4     9999 <NA>                      NA

Phase 2: Specifying the Complex Survey Design

Before calculating inequality, we must declare the complex survey design.

svy_design <- cleaned_data %>%
  as_survey_design(
    ids = cluster_id,
    strata = strata,
    weights = sample_weight
  )

Phase 3: Calculating the Concentration Index

The survey_concentration_index() function handles the internal complexities of calculating weighted fractional ranks and covariances across the survey design.

stunting_inequality <- svy_design %>%
  survey_concentration_index(
    outcome = is_stunted,
    wealth = wealth_score
  )

print(stunting_inequality)
#> # A tibble: 1 × 7
#>   Concentration_Index Standard_Error Lower_CI Upper_CI     p_value Outcome_Mean
#>                 <dbl>          <dbl>    <dbl>    <dbl>       <dbl>        <dbl>
#> 1              -0.355         0.0711   -0.494   -0.215 0.000000606        0.645
#> # ℹ 1 more variable: n <int>

Interpretation

The output provides both the weighted prevalence of the outcome and the precise Concentration_Index. A negative index confirms a pro-poor inequality in child stunting.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.