Inequalities in health CI and CC
Lecture 1:
Inequalities and inequities in health
and health care utilization
Concentration curve and
concentration index
1
Health inequality and inequity
• Rich-poor inequalities in health largely, if not
entirely, derive from differences in constraints
(e.g. incomes, time costs, health insurance,
environment) rather than in preferences.
• Hence they are often considered to represent
inequities.
• But in high-income countries the poor often use
more health care and this may not represent
inequity.
• Drawing conclusions about health equity involves
consideration of the causes of health inequalities.
Equity of what?
• Health outcomes, e.g. infant mortality, child growth,
disability, incidence of illness, general health, life
expectancy.
• Health care utilisation, e.g. doctor visits, inpatient
stays, vaccinations, maternity care.
• Subsidies received through use of public health care.
• Payments for health care (both direct and indirect).
Equity in relation to what?
• Equity in health, health care and health payments
could be examined in relation to gender, ethnicity,
geographic location, education, income….
• This course focuses on equity by socioeconomic
status, usually measured by income, wealth or
consumption.
• Many of the techniques are applicable to equity in
relation to other characteristics but they often
require that individuals can be ranked by that
characteristic.
The basic idea
The basic idea
• The poor typically lag behind the better off in
terms of health outcomes and utilization of
health services
• Policymakers would like to track progress – is the
gap narrowing? – and see how their country
compares to other countries
• Data are often presented in terms of economic or
socioeconomic groups
• With several groups, it’s not easy to see how
inequalities compare or have changed
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
Rate ratios can be used: but don’t consider how skewed the distribution is in the
middle quintiles
Comparison made difficult by differences in average levels
In which country is child stunting distributed most
unequally? Which country has made the largest
progress in reducing inequalities?
Let’s get measuring!
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
Cumulative % of illness
Illness concentration curve
Here inequality
disfavors the poor:
they bear a greater
share of illness
than their share in
the population
The further the CC
is from the line of
equality, the
greater the
inequality!
75% of
disease
burden
Poorest 50% of population
Cumulative % population,
ranked in ascending order of income, wealth, etc.
Comparing too many concentration
curves is bad for your eyes!
100%
Equality
Brazil
Cote d'Ivoire
Ghana
Nepal
Nicaragua
Pakistan
Cebu
S Africa
Vietnam
cumul %
under-5 deaths
80%
60%
40%
20%
Brazil is most unequal,
but how do the rest
compare?
0%
0%
20%
40%
60%
80%
cumul % live births,
ranked by equiv consumption
100%
Cumulative proportion of illness
The concentration index
is a useful tie-breaker
Concentration index (CI) = 2 x
shaded area
75% of
disease
burden
CI lies in range (-1,1)
CI < 0 because variable
is “concentrated” among the
poor
Poorest 50% of population
Cumulative proportion of illness
The case where inequalities in illness
favor the poor
Concentration index (=2 x
shaded area, as before) is
positive in this case because
variable is “concentrated”
among the better off
25% of
disease
burden
Poorest 50% of population
Here inequality
favors the poor:
they bear a smaller
share of illness
than their share in
the population
Beware!
A negative CI doesn’t necessarily imply poor
outcomes for the poor. It depends on whether
the health variable being analyzed is a “good”
outcome or a “bad” outcome.
Concentration index defined
C = 2 x area
between 450 line and concentration
curve
= 2A=2(0.5 - B) = 1 - 2B
cum. % of health variable
100%
75%
C>0 (0,
g>0
– Mirror: E(h)=-E(s), s=bh-h
– Monotonicity
– Transfer
Total inequality in health and
socioeconomic-related health inequality
By definition, the
health Lorenz curve
must lie below the
concentration curve.
100%
cum % of health
80%
60%
That is, total health
inequality is greater
than income-related
health inequality.
40%
20%
0%
0%
10%
20%
30%
40%
50%
60%
70%
80%
cum % of pop, ranked by health or income
diagonal
Lorenz curve
Conc curve
90%
100%
Total inequality in health is larger than
socioeconomic-related health inequality
Gini index of total health inequality
2
G = cov(h , rh )
rh is rank in health distribution
µ
cov(h , rh )
Then G
C
=
cov(h , r )
≥1
Thus, G = C + R, where R>=0 and measures the outward move from
the health concentration curve to the health Lorenz curve, or the
re-ranking in moving from the SES to the health distribution
“even if the social class gradient was magically eliminated,
dispersion in health outcomes in the population would remain
very much the same”
Smith J, 1999, Healthy bodies and thick wallets”, J Econ Perspectives
Estimating the concentration index from
micro data
• Use “convenient covariance” formula C=2cov(h,r)/μ
– Weights applied in computation of mean, covar and rank
• Equivalently, use “convenient regression”
2 hi
2σ r
= α + β ri + ε i
µ
– Where the fractional rank (r) is calculated as follows if there are weights (w)
i −1
wi
ri = w j + ,
2
j =0
w0 = 0
– OLS estimate of β is the estimate of the concentration index
Sensitivity of the concentration index to
the living standards measure
• C reflects covariance between health and rank in
the living standards distribution
• C will differ across living standards measures if reranking of individuals is correlated with health
(Wagstaff & Watanabe, 2003)
From OLS estimate of
2σ ∆2r
hi
µ
= α + γ∆ri + ε i
where ∆ri = r1i − r2i is the re-ranking and σ ∆2r its variance,
the difference in concentration indices is
C1 − C2 = γˆ
Evidence on sensitivity of concentration
index
Wagstaff & Watanabe (2003) – signif. difference b/w C estimated
from consumption and assets index in only 6/19 cases for
underweight and stunting
But Lindelow (2006) finds greater sensitivity in concentration
indices for health service utilization in Mozambique
-
!
"
#
!
-
-
-
-
-
-
C and 95% conf interval
Nicaragua 1983-88
25
Brazil (NE & SE) 198792
Concentration indices for U5MR
Phillipines (Cebu)
1981-91
0.1
South Africa 1985-89
0.0
Nepal 1985-96
-0.1
Cote d’Ivoire 1978-89
-0.2
Ghana 1978-89
-0.3
Pakistan 1981-90
-0.4
-0.5
Vietnam 1982-93
Changes in CIs of stunting
Taking account of the level and the
distribution of health
If there is concern for the level of health, and not only socioeconomicrelated inequality in its distribution, then may want a summary statistic
to reflect mean health in addition to this inequality.
Might refer to such a measure as an index of ‘health achievement’.
An index of health achievement can be obtained by taking a weighted
average of levels of health, rather than of health shares, as follows:
I (ν ) =
1
n
n
i =1
hi ν (1 − ri
)
(ν −1)
(
= µ 1 − C (ν )
)
That is simply the product of the mean and one minus the extended CI.
So, for a desirable health variable, increases in the mean may be traded-off
against increases in pro-rich inequality
For a non-desirable health variable, decreases in the mean can be tradedoff against increases in its concentration on the poor.
Mean and inequality-weighted mean in
under-five mortality
Mean and inequality-weighted
mean of medically attended births
100
90
80
70
60
Mean
Achievement
50
40
30
20
10
Dominican
Rep.
Brazil
Colombia
Nicaragua
Bolivia
Peru
Haiti
0
Guatemala
% babies delivered by a medically-trained person
Deliveries by a medically-trained person
Where to go from here?
• Analyses of equity in health requires data on
– Health
• Infant mortality, stunting/wasting, self-assessed health
• Chronic conditions -> reporting bias!
• Measured hypertension, grip strength, blood tests
– Socioeconomic status
• Need to be able to rank people from poor to reach
• Consumption, expenditure, wealth index
Inequalities and inequities in health
and health care utilization
Concentration curve and
concentration index
1
Health inequality and inequity
• Rich-poor inequalities in health largely, if not
entirely, derive from differences in constraints
(e.g. incomes, time costs, health insurance,
environment) rather than in preferences.
• Hence they are often considered to represent
inequities.
• But in high-income countries the poor often use
more health care and this may not represent
inequity.
• Drawing conclusions about health equity involves
consideration of the causes of health inequalities.
Equity of what?
• Health outcomes, e.g. infant mortality, child growth,
disability, incidence of illness, general health, life
expectancy.
• Health care utilisation, e.g. doctor visits, inpatient
stays, vaccinations, maternity care.
• Subsidies received through use of public health care.
• Payments for health care (both direct and indirect).
Equity in relation to what?
• Equity in health, health care and health payments
could be examined in relation to gender, ethnicity,
geographic location, education, income….
• This course focuses on equity by socioeconomic
status, usually measured by income, wealth or
consumption.
• Many of the techniques are applicable to equity in
relation to other characteristics but they often
require that individuals can be ranked by that
characteristic.
The basic idea
The basic idea
• The poor typically lag behind the better off in
terms of health outcomes and utilization of
health services
• Policymakers would like to track progress – is the
gap narrowing? – and see how their country
compares to other countries
• Data are often presented in terms of economic or
socioeconomic groups
• With several groups, it’s not easy to see how
inequalities compare or have changed
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
Rate ratios can be used: but don’t consider how skewed the distribution is in the
middle quintiles
Comparison made difficult by differences in average levels
In which country is child stunting distributed most
unequally? Which country has made the largest
progress in reducing inequalities?
Let’s get measuring!
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
Cumulative % of illness
Illness concentration curve
Here inequality
disfavors the poor:
they bear a greater
share of illness
than their share in
the population
The further the CC
is from the line of
equality, the
greater the
inequality!
75% of
disease
burden
Poorest 50% of population
Cumulative % population,
ranked in ascending order of income, wealth, etc.
Comparing too many concentration
curves is bad for your eyes!
100%
Equality
Brazil
Cote d'Ivoire
Ghana
Nepal
Nicaragua
Pakistan
Cebu
S Africa
Vietnam
cumul %
under-5 deaths
80%
60%
40%
20%
Brazil is most unequal,
but how do the rest
compare?
0%
0%
20%
40%
60%
80%
cumul % live births,
ranked by equiv consumption
100%
Cumulative proportion of illness
The concentration index
is a useful tie-breaker
Concentration index (CI) = 2 x
shaded area
75% of
disease
burden
CI lies in range (-1,1)
CI < 0 because variable
is “concentrated” among the
poor
Poorest 50% of population
Cumulative proportion of illness
The case where inequalities in illness
favor the poor
Concentration index (=2 x
shaded area, as before) is
positive in this case because
variable is “concentrated”
among the better off
25% of
disease
burden
Poorest 50% of population
Here inequality
favors the poor:
they bear a smaller
share of illness
than their share in
the population
Beware!
A negative CI doesn’t necessarily imply poor
outcomes for the poor. It depends on whether
the health variable being analyzed is a “good”
outcome or a “bad” outcome.
Concentration index defined
C = 2 x area
between 450 line and concentration
curve
= 2A=2(0.5 - B) = 1 - 2B
cum. % of health variable
100%
75%
C>0 (0,
g>0
– Mirror: E(h)=-E(s), s=bh-h
– Monotonicity
– Transfer
Total inequality in health and
socioeconomic-related health inequality
By definition, the
health Lorenz curve
must lie below the
concentration curve.
100%
cum % of health
80%
60%
That is, total health
inequality is greater
than income-related
health inequality.
40%
20%
0%
0%
10%
20%
30%
40%
50%
60%
70%
80%
cum % of pop, ranked by health or income
diagonal
Lorenz curve
Conc curve
90%
100%
Total inequality in health is larger than
socioeconomic-related health inequality
Gini index of total health inequality
2
G = cov(h , rh )
rh is rank in health distribution
µ
cov(h , rh )
Then G
C
=
cov(h , r )
≥1
Thus, G = C + R, where R>=0 and measures the outward move from
the health concentration curve to the health Lorenz curve, or the
re-ranking in moving from the SES to the health distribution
“even if the social class gradient was magically eliminated,
dispersion in health outcomes in the population would remain
very much the same”
Smith J, 1999, Healthy bodies and thick wallets”, J Econ Perspectives
Estimating the concentration index from
micro data
• Use “convenient covariance” formula C=2cov(h,r)/μ
– Weights applied in computation of mean, covar and rank
• Equivalently, use “convenient regression”
2 hi
2σ r
= α + β ri + ε i
µ
– Where the fractional rank (r) is calculated as follows if there are weights (w)
i −1
wi
ri = w j + ,
2
j =0
w0 = 0
– OLS estimate of β is the estimate of the concentration index
Sensitivity of the concentration index to
the living standards measure
• C reflects covariance between health and rank in
the living standards distribution
• C will differ across living standards measures if reranking of individuals is correlated with health
(Wagstaff & Watanabe, 2003)
From OLS estimate of
2σ ∆2r
hi
µ
= α + γ∆ri + ε i
where ∆ri = r1i − r2i is the re-ranking and σ ∆2r its variance,
the difference in concentration indices is
C1 − C2 = γˆ
Evidence on sensitivity of concentration
index
Wagstaff & Watanabe (2003) – signif. difference b/w C estimated
from consumption and assets index in only 6/19 cases for
underweight and stunting
But Lindelow (2006) finds greater sensitivity in concentration
indices for health service utilization in Mozambique
-
!
"
#
!
-
-
-
-
-
-
C and 95% conf interval
Nicaragua 1983-88
25
Brazil (NE & SE) 198792
Concentration indices for U5MR
Phillipines (Cebu)
1981-91
0.1
South Africa 1985-89
0.0
Nepal 1985-96
-0.1
Cote d’Ivoire 1978-89
-0.2
Ghana 1978-89
-0.3
Pakistan 1981-90
-0.4
-0.5
Vietnam 1982-93
Changes in CIs of stunting
Taking account of the level and the
distribution of health
If there is concern for the level of health, and not only socioeconomicrelated inequality in its distribution, then may want a summary statistic
to reflect mean health in addition to this inequality.
Might refer to such a measure as an index of ‘health achievement’.
An index of health achievement can be obtained by taking a weighted
average of levels of health, rather than of health shares, as follows:
I (ν ) =
1
n
n
i =1
hi ν (1 − ri
)
(ν −1)
(
= µ 1 − C (ν )
)
That is simply the product of the mean and one minus the extended CI.
So, for a desirable health variable, increases in the mean may be traded-off
against increases in pro-rich inequality
For a non-desirable health variable, decreases in the mean can be tradedoff against increases in its concentration on the poor.
Mean and inequality-weighted mean in
under-five mortality
Mean and inequality-weighted
mean of medically attended births
100
90
80
70
60
Mean
Achievement
50
40
30
20
10
Dominican
Rep.
Brazil
Colombia
Nicaragua
Bolivia
Peru
Haiti
0
Guatemala
% babies delivered by a medically-trained person
Deliveries by a medically-trained person
Where to go from here?
• Analyses of equity in health requires data on
– Health
• Infant mortality, stunting/wasting, self-assessed health
• Chronic conditions -> reporting bias!
• Measured hypertension, grip strength, blood tests
– Socioeconomic status
• Need to be able to rank people from poor to reach
• Consumption, expenditure, wealth index