Concept Architecture
Concept
Theoretically, Concentration Curve is a graphical method used to assess socioeconomic-related inequality in a health variable by plotting the cumulative proportion of the population, ranked by socioeconomic status, against the cumulative proportion of the health variable. It extends the Lorenz curve framework to health economics and provides a visual representation of whether health outcomes, healthcare utilisation or healthcare expenditures are disproportionately concentrated among more or less advantaged population groups. The concept is founded on welfare economics, inequality measurement and cumulative distribution theory.
Mathematically, the concentration curve is constructed by ordering individuals according to a socioeconomic ranking variable, calculating cumulative population shares and cumulative shares of the health variable, and plotting these cumulative proportions. If the health variable is distributed equally across all socioeconomic groups, the concentration curve coincides with the line of equality. Deviations from this line quantify the extent and direction of socioeconomic inequality. The area between the concentration curve and the line of equality forms the basis of the Concentration Index.
In practice, concentration curves are constructed from individual- or household-level survey data after ranking observations by income, wealth or another measure of socioeconomic status. They are widely used to evaluate equity in healthcare financing, healthcare utilisation, disease burden and health outcomes. In health economics, concentration curves support policy evaluation by identifying whether healthcare resources or health outcomes are disproportionately concentrated among disadvantaged or advantaged populations.
Purpose
Used to assess and visualise socioeconomic inequality in health outcomes, healthcare utilisation or healthcare expenditures, providing the graphical foundation for equity analysis and calculation of the Concentration Index.
Mathematical Formulae
Primary Formula
L(p) = (1 / ?) ? ??? y(r) dr
where:
- L(p) = cumulative share of the health variable
- p = cumulative proportion of the population ranked by socioeconomic status
- y(r) = health variable for rank r
- ? = mean of the health variable
Supporting Formulae
Line of equality:
L(p) = p
Concentration Index:
C = 2 ? ??? [L(p) ? p] dp
Discrete approximation:
C = (2 / (n?)) ? ?? y?R? ? 1
where:
- n = sample size
- y? = health variable
- R? = fractional socioeconomic rank
Related Mathematical Methods
- Concentration Index
- Lorenz Curve
- Gini Coefficient
- Equity Analysis
- Horizontal Equity
- Socioeconomic Inequality Measurement
- Dominance Testing
Example
A health economist analyses annual primary care visits for 5,000 individuals ranked by household income. The cumulative proportion of visits rises more rapidly than the cumulative proportion of the population among lower-income groups, causing the concentration curve to lie above the line of equality. The resulting negative Concentration Index indicates that healthcare utilisation is disproportionately concentrated among socioeconomically disadvantaged individuals.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| SORT | =SORT(A2:B5001,1,1) | Rank individuals by socioeconomic status. |
| SUM | =SUM(B$2:B2)/SUM(B$2:B5001) | Calculate cumulative share of the health variable. |
| ROW | =ROW(A2)-ROW($A$2)+1 | Generate cumulative population ranks. |
| SUMPRODUCT | =2*SUMPRODUCT(B2:B5001,C2:C5001)/(COUNT(B2:B5001)*AVERAGE(B2:B5001))-1 | Calculate the Concentration Index from ranked data. |
VBA (Optional)
Automate construction of concentration curves and calculation of Concentration Indices for multiple health outcomes and socioeconomic ranking variables.
Sources
- Wagstaff A, Paci P, van Doorslaer E. On the measurement of inequalities in health. Social Science & Medicine. 1991;33(5):545?557.
- Kakwani NC, Wagstaff A, van Doorslaer E. Socioeconomic inequalities in health: Measurement, computation and statistical inference. Journal of Econometrics. 1997;77:87?103.
- O'Donnell O, van Doorslaer E, Wagstaff A, Lindelow M. Analyzing Health Equity Using Household Survey Data. World Bank.
- Wagstaff A, van Doorslaer E. Equity in health care finance and delivery.
- Drummond MF, et al. Methods for the Economic Evaluation of Health Care Programmes.
Related Concepts (2)
Library
Publications
1
Distributional Cost-Effectiveness Analysis: Quantifying Health Equity Impacts and Trade-Offs — Cookson, Griffin, Norheim & Culyer, 1st Edition ed., 2020 (Oxford University Press)
The definitive practical guide to distributional cost-effectiveness analysis (DCEA), a suite of methods for quantifying who gains and who loses from health programmes and the trade-offs between improving total health and reducing unfair health inequality. Volume 7 in the Handbooks in Health Economic Evaluation series.
BookView source →
Frequently Asked Questions (6)
What is a concentration curve?
A graphical tool plotting the cumulative share of a health variable against the cumulative population share ranked poorest to richest.
Source: O'Donnell et al. 2008
What two cumulative shares does a concentration curve plot against each other?
A concentration curve plots the cumulative share of a health variable against the cumulative share of the population, with people ranked from poorest to richest. The resulting curve shows how that health variable is distributed across the income range: a line bowed above the diagonal means it concentrates among the poor, below it among the rich. This gives a visual reading of socioeconomic inequality that a summary concentration index then reduces to a single figure. Charting a health variable against income rank is what it does. O'Donnell and colleagues (2008) describe the tool.
Source: O'Donnell et al. 2008
What does a concentration curve show?
A concentration curve shows how a health variable is distributed across the population ranked by socioeconomic status, plotting the cumulative share of the variable against the cumulative population share from poorest to richest. So a concentration curve shows the distribution by socioeconomic rank, which is why it plots cumulative shares, since comparing the share of the variable with the population share reveals whether it concentrates among poorer or richer groups, and the curve depicts how the health variable is distributed across socioeconomic groups, indicating inequality.
Source: O'Donnell et al. 2008
How is a concentration curve interpreted?
A concentration curve is interpreted by comparing it with the line of equality: if the curve lies above the line, the health variable is concentrated among poorer groups, and if below, among richer groups, indicating the direction of inequality. So a concentration curve is interpreted relative to the equality line, which is why its position matters, since a curve above or below the line shows concentration among poorer or richer groups, and interpreting the curve's position relative to equality reveals whether and how the health variable is unequally distributed by socioeconomic status.
Source: O'Donnell et al. 2008
Why is a concentration curve used?
A concentration curve is used to depict how a health variable is distributed across socioeconomic groups, showing whether it concentrates among poorer or richer people, which helps assess health inequality. So a concentration curve is used to show socioeconomic distribution, which is why it ranks by wealth, since displaying the cumulative shares reveals inequality in the variable, and using a concentration curve helps assess whether a health variable, such as health status or spending, is distributed equally or concentrated among richer or poorer groups.
Source: O'Donnell et al. 2008
How does a concentration curve relate to a concentration index?
A concentration curve relates to a concentration index in that the concentration index is a summary measure derived from the concentration curve: it quantifies the inequality the curve depicts. So the concentration index summarises the concentration curve, which is why they are connected, since the curve shows the distribution graphically and the index measures it numerically, and the concentration index is derived from the concentration curve, providing a single number that captures the socioeconomic inequality the curve displays, linking the graphical tool to its summary measure.
Source: O'Donnell et al. 2008
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 31 Dec 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/concentration-curve
- Term code
- HS-HP-HE-010
Stable URI · Machine-readable · Resolvable · CC BY 4.0