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

In which country are child deaths

distributed most unequally?

0

50

100

150

200

250

300

India Mali

U5M

R p

er

1000 liv

e b

irth

s

Poorest"quintile"

2nd poorest"quintile

Middle "quintile"

2nd richest"quintile"

Richest"quintile"

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 GiniIndex—and their bivariate extensions—concentration curve and index—from income distribution literature and apply to socioeconomic-related inequality in health variables

Illness concentration curve

Poorest 50% of population

75% of

disease

burden

Cu

mu

lati

ve %

of

illn

ess

Cumulative % population,

ranked in ascending order of income, wealth, etc.

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!

Comparing too many concentration

curves is bad for your eyes!

0%

20%

40%

60%

80%

100%

0% 20% 40% 60% 80% 100%

cumul % live births,

ranked by equiv consumption

cu

mu

l %

un

de

r-5

de

ath

s

Equality

Brazil

Cote d'Ivoire

Ghana

Nepal

Nicaragua

Pakistan

Cebu

S Africa

Vietnam

Brazil is most unequal,

but how do the rest

compare?

The concentration index

is a useful tie-breaker

Poorest 50% of population

75% of

disease

burden

Cu

mu

lati

ve p

rop

ort

ion

of

illn

ess

Concentration index (CI) = 2 x shaded area

CI lies in range (-1,1)

CI < 0 because variableis “concentrated” among the poor

The case where inequalities in illness

favor the poor

Poorest 50% of population

25% of

disease

burden

Cu

mu

lati

ve p

rop

ort

ion

of

illn

ess

Here inequality

favors the poor:

they bear a smaller

share of illness

than their share in

the population

Concentration index (=2 x shaded area, as before) is positive in this case because variable is “concentrated” among the better off

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.

0%

25%

50%

75%

100%

0% 25% 50% 75% 100%

cum. % population ranked by income

cum

. %

of

hea

lth

va

ria

ble

C = 2 x area between 450 line and concentration curve

= 2A=2(0.5 - B) = 1 - 2B

C>0 (<0) if health variable is disproportionately concentrated on rich (poor)

C=0 if distribution is proportionate(unless crossing diagonal)

C lies in range (-1,1)

C=1 if richest person has all of the health variableC=-1 of poorest person has all of the health variable

Concentration index defined

A

B( )h

L p

Some formulae for the concentration index

( )1

0

1 2 hC L p dp= − ∫

1

2 11

n

i i

i

C h rn nµ =

= − −∑

If the living standards variable is discrete:

where n is sample size, h the

health variable, μ its mean and

r the fractional rank by income

( )2

cov ,C h rµ

=

For computation, this is more convenient:

Properties of the concentration index

• depend on the measurement characteristics of the health variable of interest.

• Strictly, requires ratio scaled, non-negative variable

• Invariant to multiplication by scalar

• But not to any linear transformation

• So, not appropriate for interval scaled variable with arbitrary mean

• This can be problematic for measures of health that are often ordinal

• If variable is dichotomous, C lies in the interval (μ-1, 1-μ) (Wagstaff, 2005):

– So interval shrinks as mean rises.

– Normalise by dividing C by 1-μ

Erreygers’ (2009) has normalized the

concentration index for bounded variables

• This satisfies the following axioms:

– Level independence: E(h*)=E(h), h*=k+h

– Cardinal consistency: E(h*)=E(h), h*=k+gH, k>0, g>0

– Mirror: E(h)=-E(s), s=bh-h

– Monotonicity

– Transfer

( ) ( )4h h

E h C hb a

µ=

−

Where bh and ah are the max and min

of the health variable (h), and μ is the mean

Total inequality in health and

socioeconomic-related health inequality

0%

20%

40%

60%

80%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

cum % of pop, ranked by health or income

cu

m %

of

he

alt

h

diagonal Lorenz curve Conc curve

By definition, the

health Lorenz curve

must lie below the

concentration curve.

That is, total health

inequality is greater

than income-related

health inequality.

Total inequality in health is larger than

socioeconomic-related health inequalityGini index of total health inequality

Then

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

µ=

2cov( , )

hG h r

= ≥cov( , )

1cov( , )

hh rG

C h r

rh is rank in health distribution

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”

– Where the fractional rank (r) is calculated as follows if there are weights (w)

– OLS estimate of β is the estimate of the concentration index

22 ir i i

hrσ α β ε

µ

= + +

1

0

0

, 02

ii

i j

j

wr w w

−

=

= + =∑

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 re-

ranking of individuals is correlated with health

(Wagstaff & Watanabe, 2003)

22 i

r i i

hrσ α γ ε

µ∆

= + ∆ +

1 2ˆC C γ− =

From OLS estimate of

where is the re-ranking and 1 2i i i

r r r∆ = − 2

rσ ∆ its variance,

the difference in concentration indices is

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

Consumption Asset index

Difference

CIC – CIAI

t-value for

differenceCI t-value CI t-value

Hospital visits 0.166 8.72 0.231 12.94 -0.065 -3.35

Health center visits 0.066 3.85 -0.136 -8.49 0.202 9.99

Complete immunizations 0.059 8.35 0.194 34.69 -0.135 -19.1

Delivery control 0.063 11.86 0.154 35.01 -0.091 -15.27

Institutional delivery 0.089 11.31 0.266 43.26 -0.176 -20.06

Concentration indices for U5MR

25

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

Vie

tnam

1982-9

3

Pakis

tan 1

981-9

0

Ghana 1

978-8

9

Cote

d’Ivoire 1

978-8

9

Nepal 1985-9

6

South

Afr

ica 1

985-8

9

Phillipin

es (

Cebu)

1981-9

1

Nic

ara

gua 1

983-8

8

Bra

zil (

NE &

SE)

1987-

92

C a

nd 9

5%

conf in

terv

al

Changes in CIs of stunting

Taking account of the level and the

distribution of healthIf there is concern for the level of health, and not only socioeconomic-

related 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:

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 traded-off against increases in its concentration on the poor.

( )( )

( )( )ν

ν ν µ ν−

== − = −∑

1

1

1( ) 1 1

n

i iiI h r C

n

Mean and inequality-weighted mean in

under-five mortality

Mean and inequality-weighted

mean of medically attended birthsDeliveries by a medically-trained person

0

10

20

30

40

50

60

70

80

90

100

Guate

mala

Haiti

Peru

Boliv

ia

Nicara

gua

Colo

mbia

Bra

zil

Dom

inican

Rep.

% b

abie

s deliv

ere

d b

y a

medically

-tra

ined p

ers

on

Mean

Achievement

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