Evidence submitted by Mrs Jane Galbraith,
University College London (Def 06)
1. Mervyn Stone and I are statisticians
(emeritus professor and honorary research fellow) at University
College London. We have studied the derivation of the Department
of Health's funding formula which is partly based on selected
recommendations in RARP 26, a report to the Department of Health
entitled "Allocation of Resources to English Areas"
(reference 1). Our refereed article in the Journal of the Royal
Statistical Society, Series A (Stone and Galbraith, 2006, reference
2) gives a critique of the methodology developed in RARP 26 (reference
1) and refutes any claim that the selected socio-economic and
health related variables provide a valid and reliable measure
of need for health care expenditure.
2. The methodology of RARP 26 (reference
1) is extremely complicated partly because the underlying theory
is unclear and inadequate (see paragraph 3 below) and partly because
numerous subjective decisions are required such as which variables
to include, what scales of measurement to use, what units of analysis
to use, and whether the formula should be additive or multiplicative
or a mixture. These decisions will affect the funds allocated
to individual Primary Care Trusts. For example, the decision to
use within-Health-Authority regression coefficients but not the
Health Authority intercepts in the Acute and Maternity Index will
favour Trusts in previously low spending Health Authority areas.
Further complexity arises when the formulae recommended in RARP
26 are combined to produce the "unified weighted population"
on which the target allocation of funds is based.
3. (a) Because a direct measure of need
for health care expenditure is not available, RARP 26 (reference
1) tries to obtain an indirect measure. Their formula expresses
the actual expenditure as the sum of three parts. The intention
is that the first part should depend on need, the second part
should depend on supply factors (such as waiting lists or distance
from a hospital), and the third is a residual or unexplained part.
If the "supply" and unexplained parts were unrelated
to true need and if the "need" part were a good measure
of true need then the "need" part could provide an appropriate
guide for the allocation of funds. But these conditions do not
hold.
(b) An article in Health Economics by the
same authors, Gravelle et al (reference 3), attempts to
explain and to illustrate their methodology for identifying the
"need" part by considering the multiple regression of
age-adjusted expenditure for acute hospital episodes on a selection
of socio-economic and health related variables (proxies for need)
together with selected variables chosen as proxies for supply
and some "other" variables. The (over-optimistic) theory
is that the partial regression coefficients for the "need"
variables will be the correct coefficients for relating them to
need-based expenditure. Gravelle et al (reference 3) conditions
on the chosen "supply" variables and "other"
variables by setting them at their national averages (which fixes
the constant term) and uses the resulting partial regression equation
to estimate the needs-based part of the age-adjusted expenditure
for each unit (electoral ward or Primary Care Trust).
(c) There are some problems which undermine
this theory and remove any justification for the methodology of
RARP 26 and Gravelle et al (references 1 and 3). These
include:
(i) Some of the socio-economic and health
related variables used to measure need are not pure measures of
need but are also partial measures of supply. An extreme example
is PEN, the proportion of non-whites in the population, which
is thought to be positively associated with need but which had
a negative coefficient in the multiple regression. Because the
sign was counter-intuitive Gravelle et al (reference 3)
could identify that there was a problem and try to resolve it.
Similar but less extreme problems with other "need"
variables might not be identified because, although their coefficients
might be affected by their supply content, this might not result
in counter-intuitive signs.
(ii) Conversely the "supply"
variables may be partial measures of need, which would make conditioning
on them inappropriate. RARP 26 (reference 1) and Gravelle et
al (reference 3) discuss the related problem of endogeneity.
Their proposed solutions side-step rather than solve the problem.
(iii) The choice of national averages
for the "supply" and "other" variables is
arbitrary and results in the constant term of the partial regression
being small. The relative sizes of the constant and the partial
regression coefficients determine how strongly the formula responds
to differences in the variables which are proxies for need. Although
it is desirable that the formula should respond appropriately
to true need, the response should not be excessive (I may have
slightly greater need than you but that would not justify me in
having hugely greater resources). Also the "need" variables
used are only proxies which may not be good measures of true need.
(iv) Some of the unexplained variation
may be due to aspects of need that have not been covered by the
selected "need" variables, in which case, using the
partial regression equation to estimate needs-based expenditure
will be unreliable.
4. Need for health care is related to age
in a non-linear fashion (the very young and the very old are more
expensive). The Department of Health funding formula attempts
to separate the effects of age from those of the selected proxy
variables for need. The resulting formula for the "unified
weighted population" has the effect of giving more emphasis
to differences in the socio-economic variables which are proxies
for need than to differences in age profile. Primary Care Trusts
with an elderly population might feel discriminated against.
5. The Department of Health uses the "unified
weighted populaton" to obtain a target allocation for each
Primary Care Trust. If we define the Target Index to be the ratio
of the "unified weighted population" to the (estimated)
population of a Trust, then the Department of Health's aim is
that the Target Index should give the relative cost per capita
of providing the same level of health care in different Primary
Care Trusts. If the Target Index varied a lot between Trusts it
would give some Trusts much more per capita than others. Compared
with the previous formula (Carr-Hill et al, 1994, reference
4) the current formula gives a much wider spread of per capita
funding. The Target Index would allocate up to twice as much per
capita to some Trusts than to others. Is this sensible? If the
formula is wrong it has potential to do harm. We have no reason
to suppose that it is right.
6. I would favour the development of direct
measures of need, met and unmet, possibly though a combination
of medical records (for met need) and sample surveys (for both
met and unmet need). Initially these could be used to validate
any funding formula based on proxy variables but ultimately it
might be possible to estimate need for health care expenditure
directly. Since funds are limited, such an approach would require
explicit value judgements giving some needs greater weight than
others.
7. In order to examine why some PCTs have
deficits, it might be informative to compare the funding they
receive now with what they would have received were the same total
expenditure distributed under the previous formula. Whether or
not one formula is fairer than the other it seems likely that
the transition would create difficulties (even though the new
formula is being phased in slowly).
8. My colleague, Mervyn Stone, is making
a separate written submission which gives more detail on some
of the above points as well as making some different points.
9. The views expressed above are my own
and this evidence is submitted on an individual basis. My work
in this area is unpaid and my concern is for the correct use of
statistics and for the efficient and equitable use of resources
for the National Health Service.
10. I would be happy to give verbal evidence
or to answer questions in writing if that were useful to the Committee.
REFERENCES
1. Sutton, M, Gravelle, H, Morris, S, Leyland,
A, Windmeijer, F, Dibben, C and Muirhead, M (2002), Allocation
of resources to English areas: individual and small area determinants
of morbidity and use of healthcare resources. Report to the Department
of Health (RARP 26). Information and Statistics Division, Edinburgh.
2. Stone, M, and Galbraith, J (2006), How not
to fund hospital and community health services in England. J Roy
Statist Soc A (Statistics in Society) vol 169, pages 143-164.
3. Gravelle, H, Sutton, M, Morris, S, Windmeijer,
F, Leyland, A, Dibben, C, and Muirhead, M (2003), Modelling supply
and demand influences on the use of health care: implications
for deriving a needs-based capitation formula. Health Economics
vol 12, pages 985-1004.
4. Carr-Hill, R A, Hardman, G, Martin, S, Peacock,
S, Sheldon, T A and Smith, P (1994), A formula for distributing
NHS revenues based on small area use of hospital beds. Centre
for Health Economics, University of York.
Janie I Galbraith
Department of Statistical Science, UCL
22 May 2006
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