Calculating Health Inequality in Complex Surveys

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.