Introduction

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The 1990s saw an increase in managed care in the United States and western Europe. ^{1 2} This change was partly in response to growing awareness of the inescapable scarcity of healthcare resources in almost all countries in the Organisation for Economic Cooperation and Development.³ Various market style approaches to reforming health care have also been tried to help contain costs. ^{4 5} At the same time many countries have been trying to improve funding mechanisms so that the whole population has equal access to carefor example, Canada, ^{6 7} Germany,⁸ the Netherlands,⁹ the United Kingdom,¹⁰ and the United States.¹¹

Methods for adjusting funding according to need (risk adjustment) have probably been most carefully studied in the United Kingdom. Equity of funding has been a recurring preoccupation of NHS policymakers and analysts for at least 20 years. There has been periodic and sometimes acrimonious debate¹² about how best to use available morbidity and socioeconomic data to reflect healthcare needs once demographic differences have been accounted for.

The original English Resource Allocation Working Party report in 1974 recommended using standardised mortality ratio as a default proxy for morbidity and ultimately need for health care.¹³ During the 1980s it became increasingly recognised that any risk adjustment formula should include measures of social deprivation as well as health and that the effects of supply of facilities needed to be disentangled from their use so that the relative effects of social deprivation and morbidity could properly be estimated.

Availability of data across the United Kingdom has improved greatly in recent years, and methods to adjust for the confounding of need and supply have been developed. ^{14 15} However, previous methods have relied on census data, which are often out of date and include only proxy measures of household income such as car ownership. We describe a study of the determinants of use of inpatient services undertaken as part of a review of the expenditure needs of the four health and social services boards in Northern Ireland. As part of this study we investigated the potential contribution of social security data as direct measures of poverty.

	Methods

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We assembled large quantities of data on broad population healthcare needs (both health and socioeconomic); use of inpatient services; and supply of hospital and community services. We aggregated data on needs and use to electoral ward level (average population 3200) and attached grid references to the supply variables for use in the spatial interactive modelling (see below). When electoral wards were small, we amalgamated neighbouring electoral wards to ensure a minimum population size of 2000.

Needs
The health variables included mortality (in the form of standardised mortality ratios), limiting long standing illness and permanent sickness (from the 1991 census), and low birth weight (<2500 g,¹⁶ from the boards' child health systems for July 1990 to June 1996). There were 34 socioeconomic needs variables, which were mainly drawn from the census. These included religious denomination, which is recognised to be an important social indicator in Northern Ireland.¹⁷ We also included ward data from the end of 1996 on recipients of income support and family credit. Recipients of income support were divided into two broad age groups: 18-64 years and 65.

Use of services
We used routinely available hospital data for 1994-5 and 1995-6 to derive numbers of discharges and bed days for inpatients and day cases by specialty. Non-residents and private patients were excluded. The use and estimated specialty cost data were used to produce a measure of intensity of use at ward level (estimated cost divided by expected cost). We adjusted for the size and the age and sex distribution of the population within each ward by indirect standardisation using the overall Northern Ireland rates.¹⁸

Supply of health services
We used spatial interactive modelling methods to reflect the influence of supply on usage.¹⁹ These provide a means of reconciling the proximity of each ward to all possible facilities and the attractiveness (usually size) of each facility. We estimated travel times to hospital and used these to calibrate the acute specialty models.

Modelling methods
Because of the high degree of intercorrelation among the needs variables, we used correlation, cluster, and regression analysis to aid data reduction. In modelling hospital use, we concentrated on disentangling the feedback loop caused by simultaneous supply of, and demand for, health care (endogeneity). This arises because although the physical supply of beds at ward level is responsive to historical demand, historical supply itself may have stimulated use and could also be influenced by factors such as the characteristics of the local area and the general practitioners working within it.

We modelled use of hospital services as a function of supply and need by two stage least squares. We then excluded those needs drivers that were found to affect use only through supply, along with the supply variables themselves. The second stage of the regression was concerned with estimating coefficients for the surviving drivers, which were taken to directly affect use. This provided an adjustment for the influence of supply on use. The health and social needs variables entered into the regression models as both explanatory and instrumental variables are available on bmj.com.

	Results

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A model with five variables retained most of the explanatory power of the full model with both supply and needs variables (adjusted R2=52%, table 1 ). This risk adjustment model has been adopted for use in conjunction with an age-sex cost curve for acute hospital services in Northern Ireland to distribute funds for acute hospital services to the health and social services boards.

Table 2 shows the model obtained when the income support and family credit variables were excluded from the candidate set. This model contains seven variables, none of which is related to poverty, although many of the census based socioeconomic indicators are surrogate measures of income and material disadvantage.

Table 3 shows the results of applying the two models to a notional sum of £500m, which is roughly the amount spent on acute services in Northern Ireland annually. The allocations produced using the crude and effective (age weighted) populations are also shown for comparative purposes. Because the size of a population has by far the greatest influence on its need for health care size, any formula of this kind will have only a marginal (though important) effect on financial allocations. Apart from population size, the other two drivers are age structure and the needs factors used. Table 3 shows that the effect of age structure is less than 0.5% and that of the needs factors is up to 5%. The two risk adjustment models result in very different distributions of resources, particularly in the case of the largest board (Eastern). Model 1 gives that board £1.25m less than its age weighted population share, whereas model 2 gives it over £1.5m more.

	Discussion

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This study represents a considerable advance on previous work on risk adjustment ^{14 15} because we used direct measures of poverty at small area level rather than indirect census based proxies. It is widely acknowledged that understanding of the association between socioeconomic standing, health status, and the need for health services would be enhanced if data directly reflecting income levels were more readily available.²⁰ In addition, four of the five variables in our model (including household income) can be updated between censuses. This is clearly important for a formula used to allocate resources on an annual or three yearly basis. Our work is also an improvement on the current formula used in England in the following respects: more precise cost data were available; there was accurate and current measurement of access to private beds in health service hospitals; and the effect of distance from acute beds was empirically estimated by specialty.

The previous British government's decision to damp down the effect of the "York formula" on allocations in the English NHS caused some controversy.²¹ This decision limited the extent of transfer of resources from the shire counties to metropolitan districts. It is notable, therefore, that the main effect of our formula that included social security benefits was to move resources from the board centred on Belfast to those serving primarily rural parts of Northern Ireland.

	Acknowledgments

We thank Stephanie Harcourt, Karen Campbell, David Marshall, Stephen Donnelly, and Sandy Fitzpatrick for providing the data and helpful advice.

Contributors: See bmj.com

	Footnotes

Funding: Northern Ireland Department of Health and Social Services.

Competing interests: JQJ has received research funds for a member of staff from the Northern Health and Social Services Board. RC-H is self financing and carrying out the study meant that there were sufficient funds to pay his salary.

The full version of this article appears on bmj.com

	References

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(Accepted 26 September 2001)