Health Economics Metrics

Topic 91 of 91· Consumer health apps and devices

Concentration Index

The Concentration Index (Wagstaff, Paci, van Doorslaer, 1991) is the standard statistical measure of socioeconomic-related inequality in a health variable, ranging from -1 to 1. Negative means the health variable is concentrated among the socioeconomically disadvantaged, positive means it is concentrated among the better-off, and zero means no consistent socioeconomic gradient — it turns a suspicion about unequal distribution into a single, comparable number.

Why it matters

A program can look effective on aggregate and still deliver its benefit almost entirely to people who were already better off. Distributional concerns like this are exactly what reach and equity tracks descriptively — reach stratified by deprivation quintile, an equity gap between top and bottom groups — but a stratified table doesn't compress to a single trend line, and it can't easily be compared across two completely different interventions measured on different scales. The Concentration Index solves both problems: it is computed the same way for any health variable against any socioeconomic ranking, so a national health service can track whether a specific digital service's inequality is widening or narrowing release over release, and can compare the distributional fairness of an app roll-out against, say, a screening program, on the same normalized scale.

The math

CI = (2 / mean(health_values)) × Cov(health_values, socioeconomic_ranks)

Cov(X, Y) = mean(X × Y) − mean(X) × mean(Y)   (population covariance)

socioeconomic_ranks: each person's fractional rank in the socioeconomic
distribution, in [0, 1] (0 = most disadvantaged, 1 = most advantaged;
for grouped/banded data, conventionally the midpoint rank of each group)

This is the "convenient covariance formula" (O'Donnell, van Doorslaer, Wagstaff, Lindelow, World Bank 2008) — the standard practitioner shortcut for computing the Concentration Index directly from paired observations, without first drawing and integrating under a concentration curve.

Worked example

A self-reported good-health score (1 = worst, 4 = best) observed across four equal-sized socioeconomic quartiles, each represented by its quartile midpoint rank:

health_values        = [1.0, 2.0, 3.0, 4.0]
socioeconomic_ranks  = [0.125, 0.375, 0.625, 0.875]

mean(health_values)        = 2.5
mean(health × rank)        = mean([0.125, 0.75, 1.875, 3.5]) = 1.5625
mean(socioeconomic_ranks)  = 0.5

Cov = 1.5625 − 2.5 × 0.5 = 0.3125

CI = 2 × 0.3125 / 2.5 = 0.25

A positive 0.25 means this health score is concentrated among the socioeconomically advantaged group — the higher-scoring respondents skew toward the better-off end of the ranking.

Software engineering connection

This is the same covariance-based inequality measurement used in economics generally (the Gini coefficient's cousin), and it maps onto measuring whether a software product's benefits are concentrated among already-advantaged user segments rather than spread equitably — a direct extension of reach and equity (RE-AIM's "reach" dimension) into a formal statistical measure rather than a described gap. Where reach-and-equity reports impact per stratum, the Concentration Index compresses the whole distribution into one signed number, suitable as a single tracked KPI across releases — practical for a dashboard, where a full stratified breakdown isn't.

Pitfalls

  • Sign convention drift: the sign depends on how both the health variable and the rank are defined — flipping either flips the sign, so the convention used must always be stated explicitly alongside any reported value.
  • Boundary ranks instead of midpoint ranks: grouped or banded socioeconomic data (e.g. quintiles) requires using each group's fractional rank at its midpoint, not its boundary, or the index is biased.
  • Reading "near zero" as "no inequality": a Concentration Index near zero means "no consistent socioeconomic gradient", not "no inequality" in an absolute sense — offsetting inequalities in different directions can cancel out.

Sources