Quantitative Techniques for Health Equity Analysis—Technical Note # 18
Catastrophic health care payments
Introduction
One conception of fairness in payments for health care is that households ought not be required to spend
more than a given fraction (say z) of their income on health care in any given period, and that spending in
excess of this threshold can be labelled “catastrophic”[1]. The “catastrophic” label mainly refers to the fact
that falling ill can induce often sizeable and unpredictable shocks a household’s living standards. Clearly,
the extent to which illness ‘shocks’ really result in catastrophic economic consequences for households
depends not only on medical care costs, but obviously also on any effects from reduced labor supply and
productivity, and on the extent to which households are able to ‘smooth’ their consumption over several
periods by borrowing and lending mechanisms [2]. Here we focus only on the medical care expenses
incurred and on the one period consequences (typically one year).
Catastrophic payments defined
The two key variables underlying the approach are: the health care payment variable whose catastrophic
impact one wishes to assess; and a variable capturing the living standards of the persons to whom the
payment applies. Other Technical Notes discuss the measurement of key health sector variables and the
measurement of household living standards. The data have to be at the household level (e.g. household
survey data), in which case one has, for each household, values of both the payments variable T and the
living standards variable. Living standards may be measured by total per capita (or equivalent) expenditure,
x, or alternatively in terms of a measure which more closely reflects ‘ability to pay’or discretionary
expenditure, y=x-D(x), where D(x) indicates necessary or non-discretionary expenditure on items such as
food. Catastrophic payments are then defined as those expenses for which the fraction T/x or T/y exceeds a
pre-specified threshold z. The appropriate level of z is, to some extent, arbitrary and would clearly depend
on whether living standards were measured by x or y. A health spending fraction of 20% of all expenditure
may be considered catastrophic if the denominator refers to total expenditure but it may not be regarded as
catastrophic if the denominator only includes the discretionary (e.g. non-food) component of all
expenditure.
Measuring incidence and intensity of catastrophic impact
One straightforward way to summarize the extent to which a given sample of individuals has been
exposed to catastrophic expenses is the number (or fraction) of individuals whose health care costs as a
proportion of income exceed the threshold. The horizontal axis in Figure 1 shows the cumulative share of
the sample, ordered by the ratio T/x, beginning with individuals with the largest ratio. Reading off this
parade at the threshold z, one obtains the fraction H of the sample whose expenditures as a proportion of
their income exceed the threshold z. This is the catastrophic payment headcount. Define an indicator E,
which equals 1 if Ti/xi>z and zero otherwise. Then the headcount is given by:
(1)
H=
1
N
∑
N
i =1
Ei ,
where N is the sample size.
This measure does not reflect the amount by which households exceed the threshold. Another
measure, the catastrophic payment gap (or excess), captures the average degree by which payments (as a
proportion of income) exceed the threshold z. Define the excess or ‘overshoot’ as Oi = Ei ((Ti / xi ) − z ) , i.e.
the amount by which the payment fraction Ti/xi exceeds the catastrophic threshold z . Then the gap is
simply the average overshoot given by
Catastrophic payments
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Quantitative Techniques for Health Equity Analysis—Technical Note # 18
(2)
G =
1
N
∑
N
i =1
Oi ,
In Figure 1, G indicates the area under the payment share curve but above the threshold level. It
is clear that while H only captures the incidence of any catastrophes occurring, G also captures the intensity
of the occurrence. They are related through the mean positive gap which is defined as
G
.
H
Because this implies G = H . MPG, it means that the overall mean catastrophic ‘gap’ equals the
fraction with catastrophic payments times the mean positive gap. Obviously, all of the above measures can
be computed using either x or y as denominator.
(3)
MPG =
Payments as share of income
Figure 1: Catastrophic payments as share of pre-payment income,
by cumulative % of population, ranked by decreasing payment fraction
T ota l catastrop hic
‘ex cess’ G
P rop ortion H exceedin g
thresh old
z
0%
10 0%
C u m % of p op , ran ked b y d ecrea sing pa y m en t fractio n
The various measures are illustrated using data taken from the 1993 Vietnamese Level of Living
Survey in Box 1.
Catastrophic payments
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Quantitative Techniques for Health Equity Analysis—Technical Note # 18
Box 1:
Out-of-pocket payment shares for Vietnam, 1993
Table 1 presents some results on the catastrophic impact of out-of-pocket payments for health care in
Vietnam in 1993 and illustrates its sensitivity to the choice of expenditure variable in the denominator and
to different threshold level. Raising the level from 5 to 15% makes the proportion of the population with
catastrophic payments drop from over 38% to below 10%, while the mean gap drops from just below 3% of
expenditure to under 1%. Obviously, both the incidence and intensity is larger when catastrophe is defined
as a share of discretionary, non-food expenditure per capita. This is also illustrated graphically in Figure 2,
which shows the oop share curves for both definitions. Obviously, ‘catastrophic’ shares are more prevalent
when the narrower definition of (discretionary) expenditure is used. For instance, 20% of all Vietnamese
households spent almost a quarter of their non-food spending on health, but just 10% of their total
spending.
Table 1: Catastrophic impact of out-of-pocket payments, Vietnam, 1993, various thresholds
threshold level
Out-of-pocket health expenditure
z
5%
10%
15%
25%
Headcount (H)
38.19%
18.40%
9.26%
-
Mean gap (G)
2.85%
1.51%
0.84%
-
Mean positive gap (MPG)
7.47%
8.21%
9.06%
-
Headcount (H)
67.17%
46.52%
33.25%
17.88%
Mean gap (G)
9.95%
7.14%
5.17%
2.70%
Mean positive gap (MPG)
14.81%
15.36%
15.55%
15.11%
as % of total expenditure per cap
as % of non-food expenditure per cap
Figure 2: Catastrophic payments as share of total and non-food expenditure
oop as % of spending
1
0.8
0.6
0.4
0.2
0
0%
20%
40%
60%
80%
100%
cum % of pop, ranked by decreasing oop share
oop as % of tot exp
Catastrophic payments
oop as % of non-food exp
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Quantitative Techniques for Health Equity Analysis—Technical Note # 18
Making catastrophic impact sensitive to income rank
The approach thus far is insensitive to whether it is the poor or the better-off individuals who
exceed the threshold. It seems likely that most societies will care more if it is an individual in the lowest
decile whose spending (as a share of its income) exceeds the threshold than if it is one in the top decile.
One way of registering the location of the incidence and intensity of the impact across the income
distribution is to compute a concentration index for Ei and Oi , which we could define as CE and CO. [See
Technical Notes 5 and 6 for the definition of a concentration curve and index]. A positive value of CE
indicates a greater tendency for the better-off to exceed the payment threshold, while a negative value
indicates that the worse-off are more likely to exceed the threshold. Similarly, a positive value of CO
indicates a greater intensity of overshoots amongst the better-off, whilst a negative value will indicate a
greater intensity amongst the worse-off.
But because the level measures (i.e. Η and G) and the distribution measures (i.e. CE and CO) of the
catastrophic impact could vary in the same or in opposite directions, it is useful to have an index trading off
the two dimensions. This can be achieved by constructing weighted versions of the level measures which
take into account whether the excesses are concentrated mostly amongst the poor or the better-off. One
way of doing this is by weighting the excess indicator variable, Ei, by the individual's rank in the income
distribution. One particular weighting scheme (proposed in [1]) attaches to the person with the lowest
standard of living a weight equal to 2, and then the weight declines linearly with rank so that the person
with the highest level of living receives a weight of zero. This leads to a (rank-dependent) weighted index
W E defined as [1]:
(5)
(
)
W E = H ⋅ 1 − CE .
The weighting results in an attractive and simple summary measure defined as the catastrophic
payment headcount multiplied by the complement of the concentration index. If those who exceed the
threshold tend to be poorer, the concentration index CE will be negative, and this will make W E greater
than Η. Thus the catastrophic payment problem is worse than it appears simply by looking at the fraction
of the population exceeding the threshold, since it overlooks the fact that it tends to be the poor who exceed
the threshold. By contrast, if it is the better-off individuals who tend to exceed the threshold, CE will be
positive, and Η will overstate the problem of the catastrophic payments as measured by W E .
The same weighting approach can be used for the catastrophic payment excess to define:
(6)
(
)
W G = G ⋅ 1 − CO .
As above, the difference between the unweighted G and the rank-weighted WG depends on the
distribution of the overshoots: W G will be larger than G to the extent that a greater share of the overshoots
occurs amongst the poorer population groups (i.e. if CO is negative).
Box 2:
Rank-sensitive measures of catastrophic impact
Table 2 presents the concentration indices and the rank-weighted headcount and gap measures for the same
example of Vietnam. Again, using a different denominator makes a substantial difference. Not only looks
the catastrophic impact much larger when oop payments are expressed as a fraction of discretionary
expenditure, also the distribution by income is quite different. For shares of total expenditure, the
concentration indices of headcounts and gaps are are mostly positive, indicating greater incidence and
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Quantitative Techniques for Health Equity Analysis—Technical Note # 18
intensity among the better-off. As a result, the rank-weighted measures are smaller than the unweighted
measures in Table 1. The opposite is true for the shares of discretionary expenditure: (generally) negative
concentration indices suggest catastrophic impact is more prevalent and more intense among poorer
Vietnamese households, and the rank-weighted measures therefore tend to be larger than the unweighted
ones.
Table 2:
Rank-weighted incidence (headcount) and intensity (or gap) of
catastrophic out-of-pocket payments in Vietnam, 1993
threshold level z
Out-of-pocket health expenditure
5%
10%
15%
25%
-0.0115
0.0154
0.0502
-
Rank-weighted headcount ( W )
38.57%
18.46%
9.30%
-
Conc index of intensity (CO)
0.0396
0.0722
0.1020
-
2.85%
1.51%
0.84%
-
-0.0645
-0.0833
-0.0753
-0.0617
Rank-weighted headcount ( W )
71.50%
50.40%
35.75%
18.98%
Conc index of intensity (CO)
-0.0539
-0.0441
-0.0297
0.0066
10.49%
7.46%
5.32%
2.68%
as % of total expenditure per cap
Conc index of incidence (CE)
E
O
Rank-weighted headcount ( W )
as % of non-food expenditure per cap
Conc index of incidence (CE)
E
O
Rank-weighted headcount ( W )
Computing catastrophic impact measures from micro data
When micro-level data on household payments and living standards are available, the measures
outlined above can be computed fairly straightforwardly using routine statistical packages such as SPSS or
Stata.
SPSS syntax
The first step is to generate a fraction variable indicating health care payments as a proportion of the living
standards (or ability to pay) variable. In the example below, based on data from the 1993 Vietnam Living
Standards Survey (VLSS), this variable oopshare is computed as per capita out-of-pocket health
payments, pcoop, divided by per capita household consumption, pcexp. This is the variable for the yaxis in the payment fraction chart. [Remember to use the WEIGHT command if the sample is not selfweighting]
compute oopshre = pcoop/pcexp.
compute ceiling = 0.2.
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Quantitative Techniques for Health Equity Analysis—Technical Note # 18
[Obviously, the procedure is identical if instead of pcexp a variable like non-food expenditure (e.g.
pcnfexp) is used.] We then identify those facing catastrophic expenditure are identified by catcount
and the extent to which this is the case by catgap, and compute their means.
compute catcount = 0.
compute catgap = 0.
if (oopshre > ceiling) catcount = 1.
If (oopshre > ceiling) catgap = oopshre - ceiling.
Descriptives variables= catcount, catgap, oopshre
/statistics = mean stddev min max.
execute.
The means of catcount and catgap directly give us estimates of H and G, while their covariances
with the fractional rank can be used to generate the concentration indices using the convenient covariance
or regression approach given in TN#7. Covariances can be generated with the usual commands outlined in
Technical Note #7.
rank
variables=pcexp (A) /rank /rfraction /print=yes /ties=mean .
rename variables rfr001 = frpcexp.
correlations
/variables=catcount catgap frpcexp /statistics xprod/ missing =
pairwise.
execute.
Probably the best option to generate the graphs is to copy the oopshre variable(s) into an Excel
spreadsheet, to sort in descending order of oopshre, to generate a new rank variable (rfoopsh) and then
do a scatterplot of oopshre versus rfoopsh. The result can be seen in Figure 2.
Alternatively, such graphs can also be done in SPSS using the following graph command.
rank
variables=oopshre (D) /rank /rfraction /print=yes
/ties=mean .
rename variables rfr001 = rfoopsh.
Variable labels oopshre “out-of-pocket exp as % of income”
variable labels rfoopsh "cum prop of oop share".
graph
/scatterplot(bivar)= rfoopsh with oopshre
/missing = listwise.
Double clicking on the resultant graph will allow it to be edited. On the axis options, title the axes, set the
ranges, check the grid box and edit the legends. The smallest possible marker needs to be selected. Some
of the options can be saved in a chart template. Fig 3 shows the SPSS chart obtained with the 1993
Vietnam data.
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Quantitative Techniques for Health Equity Analysis—Technical Note # 18
Fig3: Out-of-pocket payment share curve, Vietnam 1993 (SPSS)
1.0
out-of-pocket exp as % of income
.8
.6
.4
.2
0.0
0.0
.2
.4
.6
.8
1.0
cum prop of oop share
Stata syntax
First we need to generate the relevant catcount and catgap variables.
gen zcat = .10
gen oopshre = pcoop / pcexp
gen catgap = oopshre - zcat
replace catgap = 0 if catgap < 0
gen catcount = (catgap>0)
[Obviously, the procedure is identical if instead of pcexp a variable like non-food expenditure (e.g.
pcnfexp) is used.] Then we can compute the concentration indices for both measures using the familiar
(cf Techn Note #7) methods. I.e. use the glcurve command to generate the fractional rank of the pcexp
variable and then obtain the relevant means and covariances for the convenient covariance formula of a
concentration index. [Remember to add [fw=wt] in these commands if data are weighted.]
glcurve pcexp, pvar (exprank)
cor exprank catcount catgap , c m
All headcount and gap measures can then be obtained from these results.
Alternatively, the relevant variables can be copied into an Excel spreadsheet for the generation of charts
with more chart editing options Again, graphs can be produced in Excel by copying the relevant variables
The glcurve and graph commands allow an oop share curve diagram to be constructed as shown in Fig
3.
* generate the fractional rank variable p in descending order of oopshre
gen recshre = 1 - oopshre
glcurve oopshre , gl(glshre) pvar(p) sortvar(recshre)
* graph the sharecurve
gr oopshre p, border psize(10) xlab(0(0.1)1) l1 ("cumul pop prop")
l2 ("oops as shre of expend")
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Quantitative Techniques for Health Equity Analysis—Technical Note # 18
When copying and pasting the graph, make sure to save it with a white background. This is done by
selecting General preferences, Result Colors, Color Scheme: white background to obtain the result in
Figure 4.
Fig 4: Out-of-pocket payment share curves, Vietnam 1993 (Stata)
cumul pop prop
oops as shre of atp
.901724
0
0
.2
.4
.6
Cum. Pop. Prop.
.8
1
Useful links
Technical Note #7 on the concentration index in this series provides full computational details for weighted
and unweighted samples.
Bibliography
1.
2.
Wagstaff, A. and E. van Doorslaer, Catastrophe and Impoverishment in Paying for Health Care:
With Applications to Vietnam 1993-98. Health Economics 2003 (forthcoming).
Gertler, P. and J. Gruber, Insuring consumption against illness, American Economic Review, 2002,
51-70.
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