Analyzing Health Equity Using
Household Survey Data
Lecture 7
Concentration Curves
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
How to measure health
disparities?
• Measures of dispersion like the variance, coefficient of
variation, or Theil’s entropy inform of total, not
socioeconomic-related health inequality
• Relative risk ratios, e.g. mortality in top to bottom
occupation class, do not take account of group sizes
• Rate ratios of top to bottom quintiles do not reflect the
complete distribution
• Borrow rank-dependent measures—Lorenz curve and Gini
Index—and their bivariate extensions—concentration
curve and index—from income distribution literature and
apply to socioeconomic-related inequality in health
variables
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
U5MR per 1000 live births
In which country are child deaths
distributed most unequally?
300
Poorest
"quintile"
2nd poorest
"quintile
Middle "quintile"
250
200
150
2nd richest
"quintile"
Richest
"quintile"
100
50
0
India
Mali
Comparison made difficult by differences in levels.
And have to rely on top versus bottom relativities.
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Comparison is easier using cumulative
distributions - Concentration curves
Child deaths are
disproportionately
concentrated on the poor
in both countries
100%
cumul % under-five deaths
80%
60%
Line of equality
India
Mali
40%
But the disproportionate
concentration (inequality)
appears greater in India
20%
0%
0%
20%
40%
60%
80%
100%
cumul % births, ranked by wealth
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
In general, concentration curve plots the cumulative
% of health variable against the cumulative % of
population ranked by socioeconomic status
Must be possible to sum
health variable.
Living standards variable only
needs to provide a ranking.
L(s)
1
cumulative
proportion
of ill-health
Curve above the diagonal 
concentration among the poor
Curve below the diagonal 
concentration among the rich
1
0
cumulative proportion of population
ranked by socioeconomic status
Curve on the diagonal = equality
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Graphing concentration curves from
grouped data
1. Rank indvs/HHs by living standards
variable, into quintiles (or deciles)
2. Obtain for each quintile the mean of
variable of interest and # relevant cases
3. Paste quintile means and counts into Excel;
form cumulative % relevant cases and
corresponding cumulative % of total value
of variable of interest; graph concentration
curve using xy chart
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Under-five deaths in India
Wealth
group
No. of rel % cumul % U5MR No. of rel % cumul %
births births births per 1000 deaths deaths deaths
Poorest
29939
2nd
28776
Middle
26528
4th
24689
Richest
19739
Total/average 129671
23%
22%
20%
19%
15%
0%
23% 154.7 4632
45% 152.9 4400
66% 119.5 3170
85% 86.9 2145
100% 54.3 1072
118.8 15419
30%
29%
21%
14%
7%
0%
30%
59%
79%
93%
100%
In excel
Equality L(s) India L(s) Mali
0%
0%
0%
23%
23%
30%
45%
45%
59%
66%
66%
79%
85%
85%
93%
100%
100%
100%
0%
0%
21%
25%
42%
49%
63%
69%
83%
89%
100%
100%
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
But the advantage of the concentration is that it
can be computed from individual level data and
so gives a picture of the complete distribution
1
Concentration Curve for Child Malnutrition in Vietnam
.6
.8
glcurve neghaz, glvar(yord) pvar(rank)
sortvar(lnpcexp) replace by(year)
split lorenz
0
.2
.4
or use twoway graph routines to plot the
co-ordinates yord & rank
0
.2
.4
.6
.8
cumul share of children (poorest first)
1992/93
1997/98
line of equality
1
Assessing inequality in the
standardized distribution of health
• Concentration curve L(s) lies
below diagonal  health is
0.8
concentrated among the rich;
• L*(s) is the indirectly standardized
0.6
concentration curve, i.e. the
0.4
(unavoidable) inequality to be
expected on the basis of the age0.2
sex distribution
• Inequality favoring the rich if L(s)
0.0
0.0 0.2 0.4 0.6 0.8 1.0
lies below L*(s)
cum. prop. sample,
Cum. prop. of health
1.0
ranked by income
L(s)
L*(s)
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Concentration curve (Lorenz)
dominance tests
• Concentration curve A dominates the 45o line
/Lorenz curve/conc. curve B if it lies above the
other line/curve
• Comparing the point estimates of curves is not
sufficient to establish dominance
• Concentration curves are estimated from survey
data and so display sampling variability
• Need to conduct formal tests of significance of
difference between curves
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Testing dominance b/w
dependent curves
•
•
•
•
•
Test significance of difference between ordinates of
curves at a number of quantiles
If the curves are independent, just requires the standard
errors for the point estimates of the ordinates of each
curve
But often the curves are dependent e.g. conc. & Lorenz
curves, 2 conc. curves estimated from same sample
Requires standard errors for the difference between
ordinates allowing for dependence
See Bishop, Chow & Formby (IER, 1994) & Davidson &
Duclos (Econometrica, 1997)
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Decision rule
• What constitutes a significant difference b/w two curves?
• At least one significant difference in one direction and no
significant difference in the other?
• This will over reject the null (for given significance level)
since are making multiple comparisons
• Can use same decision rule but correct critical values
(using Studentised Maximum Modulus)
• Or require significant difference at all quantiles compared
– (Intersection Union Principle)
• Dardanoni & Forcina (Econometrics J. 1999) show IUP is
less likely to falsely reject null but has much lower power
to find dominance when exists
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Tests can also find
• Non-dominance if no significant difference
at any quantile (with MCA rule)
• Curves cross if at least one significant
difference in each direction
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Number of comparison points
• If too few, not testing dominance across full
range of distribution
• But always difficult to find significant
differences at extremes of curves
• Common choice is to test at 19 evenly
spaced quantiles from 5% to 95%
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Stata ado for dominance testing
dominance varlist [if] [in] [weight]
[using filename], sortvar() [options]
Dominance of CC against 45o line and Lorenz:
dominance totsub [aw=wght], sortvar(hhexp_eq)
Dominance of one CC against another:
dominance nonhsub ipsub [aw=wght], sortvar(hhexp_eq)
Dominance of independent CC:
use India
dominance totsub [aw=weight] using Vietnam,
sortvar(hhexp_eq) labels(India Vietnam)
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity
Concentration curves for subsidies to
inpatient and non-hospital care in India
“Analyzing Health Equity Using Household Survey Data” Owen O’Donnell, Eddy van Doorslaer, Adam Wagstaff and
Magnus Lindelow, The World Bank, Washington DC, 2008, www.worldbank.org/analyzinghealthequity