Select Committee on Health Written Evidence


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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