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Report to NHS Employers Adjusting the General Medical Services Allocation Formula for the unavoidable effects of geographically-dispersed populations on practice sizes and locations March 2006

Contents

1. Introduction 1 1.1. Context of this work: Present Funding of General Medical Services 1 1.2. Objectives for the work described in this report 2 1.3. Scope of this report 3 1.4. Status of the material in this report 4 1.5. Structure of this report 4

2. Analytical framework adopted for this work 6 2.1. Examining what constitutes unavoidable costs 6 2.2. Defining criteria for assessing whether practices are “appropriately small”. 8 2.3. Analysis of the extent to which practice costs vary with size of Practice 8 2.4. Analysis of patient travel times an travel costs 10 2.5. An analytical model of the rurality adjustment 12 2.6. Exclusions from our analysis 13 2.7. Differences between the existing approach to allocating funds and the approach considered here 14

3. Data and Data Sources 16 3.1. GP Practice Cost Data 16 3.2. GP Practice Location Data 17 3.3. GP Practice Population Data 17 3.4. Matching Practice and locations data 18 3.5. Model Coverage 19 3.6. Geographical coverage 19

4. Modelling of economies of scale 21 4.1. Overview of the data with summary statistics and graphs 22 4.2. Variation in the data 24 4.3. Differences in average costs per patient with list size 25

4.3.1. Dispensing status 25 4.3.2. Potential magnitude of additional funding at small list sizes 26

4.4. Regression analysis 30 4.4.1. Single variable regression 31 4.4.2. Summary of results of single variable regression 31 4.4.3. Multivariate regression 35

4.5. Typical extra cost per patient 36 4.6. Comparison with the Carr-Hill analysis underlying the present formula 36 4.7. Conclusions 37 5.1. GIS Modelling Methodology 39

5.1.1. Travel Distances and Time 39 5.1.2. Travel Costs 39

5.2. Travel Distance Correlations 41

5.3. Travel Distances and Costs 42

6. Appropriately Small GP Practices 45 6.1. Unavoidable Travel Distances 45 6.2. Unavoidable Net Costs 49 6.3. The factors influencing net additional travel costs 51 6.4. Using distance to next nearest GP practice as a criterion for defining whether practices are appropriately small. 53 6.5. Prevalence of Unavoidably Small GP Practices 54 6.6. Conclusions 56

7. Unavoidable Cost Adjustment 57 7.1. Derivation of the Adjustment 57 7.2. Comparison with the Current Approach 58

8. Conclusions 62

9. Appendix 1 – List of Variables 65

10. Appendix 2 – Characteristics of GP Practices 66

11. Appendix 3 - Precedents on Access from competition authorities 67

12. Appendix 4 - Analytical solution to rurality adjustment of GMS 69

GMS Funding Formula Rurality Adjustment

Executive Summary

NHS Employers commissioned Deloitte, working in collaboration with SDG, to carry out research to estimate the unavoidable effect of geographically dispersed populations on the sizes and locations of practices providing General Medical Services (GMS). This report describes the results of this research, which was relatively small scale, comprising approximately 11 man-weeks of work.

Terms of reference and approach

The terms of reference for this research indicated that it is well established that there are diseconomies of scale for smaller practices. They required us to consider the extent to which such diseconomies of scale would lead to practices serving rural areas having unavoidably higher costs, and hence a requirement for increased funding, due to their smaller number of patients (i.e. smaller list sizes). The terms of reference also indicated that costs should be regarded as unavoidable if they would be present even with an optimal configuration of practices, but should not be regarded as unavoidable if they reflected sub-optimal configuration of practices.

In the light of these terms of reference we have interpreted the unavoidable costs of serving geographically dispersed populations as follows:

“The unavoidable costs of serving geographically dispersed populations are the additional costs that practices incur when they are “appropriately small” given their circumstances. A practice is “appropriately small” if the disadvantages to patients resulting from a configuration with larger practice sizes would outweigh the cost savings resulting from larger practice size.

Under this definition, practices in rural areas may be “appropriately small”. If they were larger, for example if they merged with neighbouring practices, access for many of their patients might become significantly more inconvenient and costly, outweighing any savings from larger scale. The additional costs arising from small size are thus appropriately incurred. In contrast urban practices are less likely to be appropriately small because it is less likely that the additional costs to patients of travelling to different sites would be larger than cost savings from merger.

This definition of when practices are appropriately small requires an assessment of the trade-off between cost savings in practices and additional travel burdens on patients. We have made this assessment by estimating the following.

How practice costs vary with size of practice, specifically how costs per patient vary with list size.

The additional travel costs that are incurred as a result of changes in practice configuration. The additional travel costs include both the value of patients travel time and the cash costs of travel they incur. These costs are used to represent the disadvantages to patients arising from the different travel burdens of different practice configurations.

When practices are appropriately small, the magnitude of the additional funding can be assessed based on the size of the practice. This approach is illustrated in the diagram below.

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Practice economies

of scale analysis

How large are potential practice

cost savings arising from increased Practice scale?

Are practice cost savings less than additional travel

costs?

How large are additional travel

costs when practice scale is increased?

Travel cost analysis

Is practice appropriately small?

How large are additional costs of appropriately small

practice?

Practice not appropriately small

so no additional funding required

No

Yes

Statistical analysis was undertaken to assess how costs varied with list size, and thus the extent of diseconomies of scale. This analysis was based on cost data for existing practices. Any assessment of whether costs of present practices are efficiently incurred is outside the scope of this work.

Additional travel costs that might be incurred by patients were modeled by estimating the effect of removing and merging each GP practice and measuring the marginal effects on patients’ travel costs of the new configuration. In carrying out this analysis we have assumed that if a GP practice were merged with another then its registered population at an Output Area (OA) level would be redistributed among other Practices in the same proportion in which residents from the same OA are currently registered. From this we calculated the effect of a change in practice configurations (from the pre-merger to the post- merger configuration) on patient travel distances and thus patient travel costs.

Results for the analysis of economies of scale

The variation in practice costs with list size is shown in the chart below. The chart shows both cost and expenses, that is with and without GP salaries.

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0

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0 2000 4000 6000 8000 10000 12000 14000

Average list size

£Cos

t/Exp

ense

s

Average cost per patient for bandAverage Expenses per patientMedian cost per patient for bandMedian Expenses per patient for band

Practices with list sizes below 1900 incur additional costs per patient compared with larger practices. This increase is statistically highly significant. However the precise magnitude of the additional costs at list sizes below 1900 is uncertain, for example because of variation in the data, lack of information on the dispensing costs of small practices and fewer instances of non-dispensing practices at small list sizes. This increase can be modelled by a 1/(list size) function. This functional form is be consistent with the data on both practice costs and expenses.

In contrast no robust evidence was found of continuing economies of scale as list sizes increased above 1900. There appears to be little, if any, evidence of economies of scale at such list sizes for non-dispensing practices. There is some tentative evidence of lower costs at larger list sizes for the dispensing practices. However, this may simply reflect additional dispensing costs rather than costs funded by the GMS formula.

These results are consistent with the hypothesis of a one-GP practice having largely fixed costs, with both the GP’s expenses and total cost, which includes their own salary, largely fixed. At list sizes of up to 1900 these fixed costs are spread over a larger number of patients. There are no such instances in urban areas. At list sizes of greater than 1900, which represents full capacity for a GP, costs cannot be spread over a larger number of patients. Consequently no further economies of scale are realised on non-dispensing costs.

Results of analysis of travel costs

The simulation work we have carried out shows that areas of low population density contain a number of instances where removing a practice would impose large additional travel costs on patients. Instances of removal of practices resulting in reduced travel costs are found in some cases because patients often are not registered with their nearest GP, especially in urban areas.

For many, but not all, practices in rural areas the costs to patients if the practice were not there would exceed the potential savings from economies of scale from larger practices. In many of these cases the practice is small, implying that additional funding is required. Such practices

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correspond to the definition of “appropriately small” set out above. There are few if any such instances in areas of high population density. The chart below is illustrates the average additional travel costs compared with the savings in GP costs for rural and urban areas.

-15

-10

-5

0

5

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15

20

25

Rural Urban

Pat

ient

/GP

Cos

ts (£

)

Patient Costs GP Costs

Factors influencing whether a practice is appropriately small

The likelihood that a practice is appropriately small, in that removing it would impose a large additional burden on patients, depends on:

the distance to the next nearest practice; and, to a lesser extent,

the density of the population in the area served.

Population density and distance to the next nearest GP are inversely related, although the relationship is not exact. Typically, in areas of low population density the distance to the nearest GP is greater than in areas of high population density. Although these two variables appear largely to be measuring the same underlying phenomenon, the rurality of a practice, regression results demonstrate that distance to the next nearest GP practice is a more robust indicator and as a result is the most appropriate variable to determine whether a practice is appropriately small.

Possible form of additional funding for appropriately small practices

The method for allocating additional funding to appropriately small practices could take a variety of forms. Some of the main types of funding adjustment that the review group is likely to wish to consider are shown in the table below.

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Decisions on whether a rurality adjustment should be granted for a practice

Variables driving decision on whether a rurality funding adjustment is required

Variables driving the decision of whether an adjustment is required could include:

Network distance to next nearest practice

Linear distance to next nearest practice

Average distance of population, which is used in the present formula

Density of population in area from which patients come

Variables involving distance to the next nearest practice could be modified to account for branch surgeries or other medical facilities

Whether decision is yes/no or probabilistic

A decision to make a funding adjustment could be binary (yes/no) or probabilistic, weighting the adjustment by the probability that a practice is appropriately small. This might, for example, take the form of an increasing weighting to the adjustment based on how far away the next nearest practice is, with those where the next nearest practice is very distant receiving more additional funding, other things being equal.

Varying the adjustment with list size

More demanding criteria (higher thresholds) could be required to justify additional funding for very small practices. As a purely illustrative example, some rurality adjustment might be granted to all small practices (list size less than 1900) more than 3km from the next nearest practice, but further rurality adjustment for very small practices (for example with list sizes below 1000) might only be granted in cases whether the practice is more than 8 km from the nearest practice. The rationale for this is that the smaller the higher costs of very small list sizes (e.g. 300 patients) may not be justified even in circumstances where small list sizes (e.g. 1500 patients) are justified by additional patient travel times.

Decisions on how large the adjustment should be

Degree of variation Adjustment could be:

Uniform for all small practices Banded according to list size Continuously variable as a function of list size

To what is it applied

The adjustment could apply to: Practice expenses per patient Total practice costs per patient

Basis of adjustments

Costs for non-dispensing practices Costs for all practices

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Number of practices affected and scale of funding adjustment

There are few practices which are both small and distant from the next nearest practice. The number of practices in our sample is shown by distance to the next nearest in the Table below. Out of our sample of 7461 practices only 267 both have a list size below 1900 and are more than 1km distant from the next nearest practice, and only 148 have a list size below 1900 and are more than 2km distant from the next nearest practice. These totals would be somewhat larger if the complete population were considered. However many of the practices not in our sample are in London, so would not be far from the next nearest GP. Consequently the total population is likely to contain even fewer practices proportionately than the sample shown here.

Number of large and small practice a certain distance from the next nearest GP

Next Nearest GP (network km)

Number of practices1,900+ <1,900 Total

1 3737 349 40862 1610 119 17293 316 15 3314 224 11 2355 167 15 1826 173 9 1827 154 6 1608 117 4 1219 107 8 115

10 68 4 7210+ 172 76 248

Total 6845 616 7461

Note: distances are maximum distance for the band, so a 2 in the left-hand column indicates that a practices are between 1 and 2 km from the next nearest.

The additional funding per patient can be significant compared with average costs per patient but because the total number of patients involved is small total costs remain small relative to the total funding for practices. On one illustrative classification and magnitude of additional funding total costs are approximately £4-6 million p.a., although this figure could vary significantly depending on the actual decision rule chosen.

This leads to a distribution of payments significantly different from that under the current adjustment. The charts below compare the distribution of the present rurality adjustment, which applies to all practices, with that from an illustrative instance of the type of funding adjustment that would follow from the methodology outlined in this report.

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Distribution of the Carr Hill adjustment

0

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600

0.88

0.

91 0.

95 0.

98 1.

01 1.

04 1.

07 1.

10 1.

13 1.

16 1.

20 1.

23 1.

26 1.

29 1.

32 1.

35

Carr Hill adjustment

Freq

uenc

y

Illustrative distribution of rurality adjustment under method shown in this report

0

10

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1.231.21.171.141.111.081.051.020.99

Adjustment factor

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ceiv

ing

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stm

ent

Conclusions

We conclude the following based on the analysis we have undertaken.

1. There is clear evidence of diseconomies of scale for practices with list sizes of below approximately 1900.

2. Our modelling results indicate that there are practices which are appropriately small because they serve a geographically dispersed population

3. Practices are most likely to be appropriately small if there are no alternative GPs nearby.

4. There is a range of possibilities for granting additional funding to appropriately small practices.

5. The number of practices that are appropriately small is likely to be only a small proportion of the total. Funding adjustments are likely to be a correspondingly small proportion of total funding.

We also note the following.

• There may be circumstances unconnected with geographical dispersion, such as low car ownership or poor provision of public transport of population in which practices may be appropriately small. Such instances are outside the scope of this report.

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• Adjustment of funding to reflect scale of rural practices may replace or be additional to

the present rurality adjustment. It is significantly different from the present rurality adjustment, creating significant changes for funding for many practices if used to replace the present formula.

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1. Introduction

NHS Employers commissioned Deloitte to carry out research to estimate the unavoidable effect of geographically dispersed populations on the sizes and locations of practices providing General Medical Services (GMS). The research is intended to help identify the unavoidable additional costs of providing General Medical Services to rural populations. It forms part of a range of work supporting the current review of the funding of GMS practices.

This report describes the results of Deloitte’s research. The report is in draft form at present and is intended for review and discussion with relevant individuals and organisations. There may be material changes in the final version of this report as a result of those discussions.

In this introduction we summarise:

the background of the present funding of GMS;

the terms of reference for the work described in this report;

the status of the material in this report; and

the scope and structure of this report.

1.1. Context of this work: Present Funding of General Medical Services

In 2004/05, a new General Medical Services (GMS) contract was implemented for GMS primary care practices. Under this contract, payments to practices for essential and additional services are guided by the GMS Global Sum Allocation Formula. This report does not address funding of any service for which funding is not guided by this formula.

The Formula adjusts funding for practice circumstances. It does this by weighting practice populations for factors that influence the relative costs of delivering services to the population. Specifically, the Formula adjusts for the:

age and sex structure of the population, including patients in nursing and residential homes;

list turnover;

additional needs of the population, relating to morbidity and mortality; and

unavoidable costs of delivering services to the population, including a staff Market Forces Factor and rurality adjustment.

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The rurality adjustment in the formula is intended reflect the uncontrollable additional costs associated with the degree to which the area served is rural. The variables that determine the rurality adjustment are:

the population density of the area in which the Practice is located; and

the average distance of patients from the practice.

The formula does not adjust for other variables that might be associated with rurality, such as the size of practice or distance from other medical services.

1.2. Objectives for the work described in this report

The GMS Global Sum Allocation Formula is currently being reviewed. The review is intended to ensure that the Formula is based on the latest available evidence and promotes a fair distribution of practice payments. The review is being led by the Formula Review Group, which contains representatives of NHS Employers, the General Practitioners Committee, the Department of Health and the Devolved Administrations as well as academic experts. The role of the Group is to review the evidence base and methodology underpinning the current Formula and to identify potential improvements for 2007/08 payments.

As part of its work, the Review Group wishes to understand the additional costs that are unavoidably incurred as a result of the rurality of the area served by a practice. This will enable the Review to assess whether the present formula appropriately reflects these unavoidable additional costs and whether any modifications may be required to the formula. NHS Employers commissioned Deloitte on behalf of the Review Group to undertake a review of the unavoidable costs associated with the rurality of the area served.

In particular the Review Group has indicated that one criticism of the GMS Allocation Formula is that the adjustment for the extra costs of rurality does not take account of practice size. The analysis on which the adjustment is based separately accounts for the effect of size and shows it to be a significant driver of costs, but this factor is excluded from the funding formula. Instead, the formula provides payments for rurality based on analysis of the additional costs incurred by rural practices on the basis of analysis of population density and the average distance of patients from the practice. This may lead, among other things, to payments reflecting past funding rather than unavoidable additional loss.

It is regarded by the Review Group as well established that smaller practices involve higher average costs per patient because they do not benefit from economies of scale. The Review Group considers it may be appropriate to make a funding adjustment to reflect the loss of economies of scale. However, the Review Group is concerned that the GMS Allocation Formula should only adjust for any losses of scale associated with rurality that are unavoidable and not compensate practices for being small when the geographical dispersion of the population does not warrant this.

In this context the Review Group commissioned the work described in this report to assess how geographically-dispersed populations and other causes of higher travel costs affect optimal practice configuration. The optimal configuration will be influenced both by costs incurred by Practices, especially the extent of economies of scale, and costs incurred by patients in travelling to a Practice.

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In particular the research was intended to identify when practices are “appropriately small” as a result of the geographical dispersion of the population they serve. Such appropriately small practices may require additional funding.

The Review Group is considering the additional delivery costs associated with the geographical dispersion of population separately from the impact that rurality has on service demand. For example, the demographic make-up of the areas may differ systematically from those of urban areas, which may affect funding requirements. However, the Formula Review Group will consider the impact of rurality on service demand as part of the review of the additional needs of different populations, and, correspondingly, it is outside the scope of this report.

1.3. Scope of this report

This report describes the results of Deloitte’s research into the effect of geographically dispersed populations on the unavoidable costs of delivering care to practice populations. The report has been produced by Deloitte in collaboration with Steer Davis Gleave. The work has been relatively small in scale, representing a total of approximately 11 man-weeks of work. Additional work could lead to the conclusions being modified or refined.

A unified analysis was carried out for the whole of Great Britain. It was agreed with NHS Employers that Deloitte would not take account of variations in global practice costs or the value of time either between the countries of the UK or between regions within countries.

Consistent with the decision to carry out unified analysis for the whole country, it was agreed that data for Northern Ireland would be excluded from the work. Seeking to include this data would divert resources from other aspects of the analysis while adding only a small proportion of the total Practice population to the analysis. There did not appear to be any aspects of the geographical dispersion of population specific to Northern Ireland that would greatly influence the a national formula, as the range of population dispersion was captured by the countries in Great Britain for which data was included.

Given its subject, parts of the report are inevitably technical in nature. The Executive Summary and the Conclusions summarise the main points for those for whom the technical details are not relevant.

A number of matters were excluded from the terms of reference for the work described in this report. Among the items excluded were:

analysis of the form of any adjustment to funding resulting from rurality, including, for example, formulae or decision rules that might form part of the funding formula, which are matters for the review group;

testing of the implications of any suggested adjustment to the funding formula; and

financial modelling of effects on Practice finances of changes in funding.

Although this report provides some consideration of the implications for some of these issues of the research we have carried out, it does not contain detailed analysis of these issues and is not intended to imply any conclusions or recommendations in any of these areas.

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1.4. Status of the material in this report

The material contained in this report is subject to a number of qualifications regarding its status. These include the following.

This document and any related advice we give has been prepared for the sole purpose of assisting and advising NHS Employers in accordance with our engagement letter dated 5th August 2005.

The information we have used to prepare the report has either been provided to us by the NHS Employers, the DH, the parties named in this report, or is derived from our own research of publicly available sources. Our procedures have not included verification work and do not constitute an audit in accordance with auditing standards.

The scope of our work in connection with this report has been limited by the information made available to us. In the circumstances, you should not rely on our work as being comprehensive as we may not have become aware of all facts or information that you may regard as relevant. We have not verified the accuracy of the information provided to us.

This document is private and confidential as set out in the contract for this work. This document may not be relied upon, referred to, reproduced or quoted from, in whole or in part, for any other purpose than that set out in the contract, or by any other person, for any purpose whatsoever except, as specified in the contract.

We shall not under any circumstances whatsoever be under any liability to any party other than NHS Employers for whatever NHS Employers may or may not do in reliance on this document or any other information, opinions or advice given to NHS Employers by us.

This report is necessarily a summary and does not contain all matters relevant to a proper understanding of our findings.

1.5. Structure of this report

The remainder of this report is structured as follows.

Section 2 presents the analytical framework we have adopted for assessing the unavoidable costs of rurality, and compares it to the present funding approach.

Section 3 describes the data used to implement the analytical framework set out in Section 2.

Section 4 describes our analysis of economies of scale in GP practices.

Section 5 describes our analysis of travel costs incurred by patient.

Section 6 describes the implications of the modelling results for the assessment of the trade-off between economies of scale and additional travel costs. This allows us to identify the incidence of uncontrollable costs of rurality.

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Section 7 describes possible adjustments to the funding formula that might draw on the

research presented here, although it is beyond the scope of this report to analyse the potential adjustment options or their effect in detail.

Section 8 describes our conclusions.

Appendices provide the following:

Appendix 1 – List of variables

Appendix 2 – Precedents on access from Competition authorities

Appendix 3 – Analytical solution of rurality adjustment of GMS

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2. Analytical framework adopted for this work

In this Section, we outline the analytical framework adopted for this work. We describe the following.

The perspective we have adopted for examining what constitutes the unavoidable costs of serving geographically dispersed populations. We interpret unavoidable costs as being those costs which are incurred because Practices are “appropriately small” and so efficiently incur additional costs due to small size.

The criteria that might be adopted to define when practices are “appropriately small”. These criteria imply a need to analyse both practice costs and patients’ travel times and costs.

The approach we have adopted to examining the extent to which practice costs differ with size.

The approach we have adopted to assessing travel times and travel costs for patients and the implications for these of varying practice configurations

The possibility of deriving an analytical solution embodying this approach and the limitations of such a solution compared with the simulation modelling applied in the remained of this report.

Issues we have excluded from the analysis we have undertaken;

How the analysis presented here relates to the present funding approach.

2.1. Examining what constitutes unavoidable costs

As described in the Introduction to this report, the terms of reference for this research required us to consider the extent to which serving geographically dispersed populations might unavoidably lead to increased costs, and hence a requirement for increased funding, for some rural practices. The terms of reference also indicated that costs should be regarded as unavoidable if they would be present even with an optimal configuration of practices, but should not be regarded as unavoidable if they reflected sub-optimal configuration of practices.

In the light of these terms of reference we have interpreted the unavoidable costs of serving geographically dispersed populations as follows.

“The unavoidable costs of serving geographically dispersed poplulations are the additional costs that practices incur when they are “appropriately small” given their circumstances. A practice is “appropriately small” if the disadvantages to patients resulting from a configuration with larger practice sizes would outweigh the cost savings resulting from larger practice size.

Under this definition, practices in rural areas may be appropriately small because if they were larger, for example if they merged with neighbouring practices, access for many of their patients might become significantly more inconvenient and costly, outweighing any savings from larger scale. The additional costs arising from small size are thus appropriately incurred.

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In contrast, it is much less likely that practices in urban areas will be appropriately small. If practices gain scale by merger in urban areas, there will often be little increase in travel distances for patients because there will still be a practice nearby. Savings could therefore in principle be achieved by merger with other practices that would outweigh the additional costs to patients.

Considering whether practices are appropriately small thus requires an assessment of the trade-off between cost savings in practices and additional travel burdens on patients. The trade-off of practice costs and the burden on patients is illustrated schematically in Figure 2; which represents the burden on patients as travel costs. The trade off is illustrated as follows:

As the size of practice increases in any given area, practice costs per patient decrease, due to economies of scale This is indicated by the downward sloping line labelled practice costs.

However as size of practice increases, practices become fewer and travel costs per patients increase. This is indicated by the upward sloping line labelled travel costs.

Total costs consist of practice costs and patients’ travel costs. As practice size increases there are net gains as the benefits of economies of scale outweigh the additional costs to patients. However as the scale of practices continues to increase the increase in patients’ travel costs eventually outweighs the benefits of economies of scales. This is shown by the top line, which falls to a minimum before rising again.

There is an optimal size of practice which minimises the total of patients’ and GPs costs shown by the lowest point in the total cost line.

If this minimum point corresponds to small practice size then the practice is appropriate small.

The figure is illustrative of the structure of the trade-off only, so the positions of the lines should not be taken as representing the relative magnitudes of travel costs and practice costs.

Figure 1: Schematic illustration of the trade-off between practice size and total costs for urban and rural areas

Practice list size

S l f i

Cos

ts p

er p

atie

nt

Travel costs

Practice costs

Total costs

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2.2. Defining criteria for assessing whether practices are “appropriately small”.

The interpretation of practice costs as “unavoidable” when practices are “appropriately” small requires criteria to be defined that determine an optimal configuration the burden on patients arising from a given configuration. The definitions of the criteria will affect the estimation of optimum of practice size and thus the definition of which practices are appropriately small. For example the total costs may be minimised, as illustrated by the chart above, or a lowest cost solution may be sought subject to a constraint that a certain maximum travel time must not be exceeded for a certain proportion of patients.

No guidance has been made available to us from the DH or other bodies such as NICE on criteria for assessing the burden on patients caused by variations in practice configuration. We have therefore analysed the additional travel times and travel costs that will result from changes in practice configuration. This allows the implications of changes in configuration to be measured.

Guidance from other sources was also of limited relevance in setting criteria for assessing whether practices are appropriately located. We note that some relevant work on geographical definition of markets has been carried out the Competition Commission and the OFT. Some of this work specifies boundaries to markets in the form of maximum travel times, which reflect people’s willingness to travel, that is their implied travel costs. Examples of this work are briefly summarised in Annex 2 and briefly compared with the results of the modelling of travel times in this work. However, these market definitions are not used as assessment criteria for this work.

Although no firm criteria are available for determining optimum configurations of Practices it appears likely that analysis of the Practice and patient travel costs of different configurations will be relevant to assessing funding for most plausible criteria. For example, minimising total costs, setting maximum acceptable access times, or furthering equality of access would all require such analysis. We have therefore focussed on the assessment of the potential trade-off between practice costs and patients’ travel costs. We have done this by estimating:

how practice costs vary with size of practice, specifically how costs per patient vary with list size;

the additional travel distances that are imposed on patients as a result of changes in practice configuration that increase scale; and

the additional travel costs, including both the value of travel time and the cash costs of travel, that are incurred as a result of changes in practice configuration.

However in showing the results of the analysis we do not seek to make any judgement about the appropriateness of any particular criteria for assessing the relative suitability of different practice configurations which is a matter for the Formula Review Group and for DH.

2.3. Analysis of the extent to which practice costs vary with size of Practice

The variation of practice costs with scale is based on statistical analysis of recent cost data for practices. This analysis is described in Section 4 of this report.

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The analysis of practice costs serves two purposes:

it supports assessment of whether additional practice costs resulting from small scale exceed additional costs to patients and so whether practices are appropriately small; and

where practices are appropriately small, the extent of additional funding they may require given their scale.

This is illustrated in the chart below. The chart shows that the question of whether a practice is appropriately small requires consideration both of the magnitude of economies of scale and of the additional travel costs. If the additional travel costs are greater than economies of scale then the practice is appropriately small. If this is the case, the size of the required funding adjustment will also draw on the analysis of economies of scale.

Figure 2 Role of practice economies of scale in setting additional funding requirements

Practice economies

of scale analysis

How large are potential practice

cost savings arising from increased Practice scale?

Are practice cost savings less than additional travel

costs?

How large are additional travel

costs when practice scale is increased?

Travel cost analysis

Is practice appropriately small?

How large are additional costs of appropriately small

practice?

Practice not appropriately small

so no additional funding required

No

Yes

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2.4. Analysis of patient travel times an travel costs

In estimating when practices are appropriately small it has been necessary to consider alternative configurations of practices. Alternative configurations allow changes in both practice costs and patients’ travel costs from those incurred in the present configuration to be estimated.

In considering these alternative configurations we have examined variations from the present configuration of practices rather than seeking to define a theoretical optimal configuration of practices for the following reasons.

It is computationally difficult to determine the optimum distribution and GPs across the UK because of the infinite range of potential configurations and large number of facilities (more than 10,000).

Even if such an optimal configuration were determined it would be unlikely to be practical to reach it from the present practice configuration Consequently, there would be no practical way of realising any theoretical savings in net costs that might be identified. It would thus be of limited relevance to assessing to what extent existing practice costs are unavoidable.

We have therefore concentrated on simulating the effect of iteratively removing and merging each GP practice and measuring the marginal effects on Practice costs and travel costs of the new configuration. In carrying out this analysis we have assumed that if a GP practice were ‘merged’ then its registered population at an Output Area (OA) level would be redistributed among other Practices in the same proportion in which residents from the same OA are currently registered. From this we calculated the effect of a change in practice configurations (from the pre-merger to and post- merger configuration) on patient travel distances and thus patient travel costs.

This is illustrated in the Figure below. Travel times are calculated from Output Area (OA) to the Practices with which patients are currently registered (GP1 to GP6). One of these practices (GP2) is assumed to be merged with another (GP1). Patients in the Output Area who can no longer go to GP2 (because is has merged) are redistributed among GP1, GP3, GP4, GP5 and GP6 in the same proportions as the patients who went to each practice pre-merger. For example if 25% of those patients in OA (excluding those going to GP2) went to GP3 pre-merger, 25% of all patients from OA (including 25% previously going to GP2) would go to GP3 post merger.

Modelled travel distances and time were derived from a GIS network model. Distances were converted into costs using assumptions regarding the value of time and the cost of transportation. This approach is described in more detail in Sections 5 and 6.

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Figure 3. Modeling change in practice configuration.

GP1

GP2

GP3

GP4

GP5

GP6

OA

Post Merger Practice Configuration

Pre Merger Practice Configuration

GP1+

GP3+

GP4+

GP5+

GP6+

OA

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2.5. An analytical model of the rurality adjustment

Simplifying assumptions can be adopted to give optimal size of practice for a given population density and thus provide indications of when a practice is appropriately small. If these simplifying assumptions are adopted the optimal size of practice can be derived analytically. The analytical solution implies that optimal practice size is given by the following formula.

Figure 4 - Analytical solution to optimal scale of practice

s = (p/c) (1/(p+0.5)). d (1/(2p+1))

s is optimum list size

p is the economies of scale factor, usually 0<p<1,

c is a constant related to unit travel costs

d is population (needs weighted) density measured in

(needs weighted) patients per sq. km.

Population density (d)

Opt

imal

list

siz

e (s

)

Optimal practice costs

This implies that optimal practice size slightly more than doubles for a ten fold increase in population density of the area served, as shown in the accompanying chart, which allows the optimal practice costs then to be derived. The derivation of this result is given in Annex 3. The analysis can readily be adapted to define threshold travel times or distances which in turn define catchment areas.

This result rests on a number of assumptions, among which the most important are the following:

travel costs vary with linear distance from a practice;

practices serve areas of uniform population density;

patients are served by their nearest practice; and

travel times are proportional to distance.

Of these the least well supported by analysis of actual data are the assumptions that:

practices serve areas of uniform population density; and

patients travel to their nearest practice (although this is better supported in rural areas).

The solution takes no account of the existing configuration of practices. As such it does not relate directly to whether particular practices in the present configuration may be appropriately small, which is the subject of the numerical modelling described in the remainder of this report.

However the analytical result serves as a cross check on the results from the numerical modelling in indicating the likely maximum travel distances with optimal configurations. The analytical solution also provides an indication that at moderate or high population densities the variation in costs close to the minimum is small, implying that varying practice size within certain bounds may only vary costs relatively little. This suggests that for many practices there would be modest

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gains or losses from varying over a wide range of configurations. This is consistent with the numerical modelling results reported in Section 6.

2.6. Exclusions from our analysis

The structure of analysis described excludes various issues that are outside the agreed scope of this report but may be relevant to setting the appropriate funding adjustment for rurality. These include the following.

We have based the estimate of diseconomies of scale on data on present costs. It is possible that present costs are above an efficient level and that cost savings are possible without damaging service to patients. Equally it is possible that in some respects existing funding levels may be below optimal levels, for example causing difficulties with maintaining service levels. Consequently additional funding required by appropriately small practices may be more or less than indicated by our analysis.

We have not assessed whether the overall scale of GP funding is optimal. The results of this study do not identify whether additional funding for appropriately small rural practices should optimally come from reductions in funding to other practices or from a general increase in funding.

We have focussed on the unavoidable costs of existing practices. We have not sought to identify locations at which it would be desirable to create additional practices.

Modelling of the public transport network was excluded from this work. Modelling the network would be time-consuming and complex as data on the network is scarce. Furthermore results would not be robust over time as public transport networks are subject to change. In practice provision of public transport may affect levels of access, although the implications of this for additional funding are unclear.

In considering the travel costs to patients of the merger of practices we have excluded any analysis of the other costs of merging practices. We would expect there to be additional costs associated with merger. This may affect the threshold at which additional funding is judged to be appropriate. However hypothetical merger costs would not affect the scale of the additional funding required, as this is based on continuing costs.

Lack of available data has precluded branch surgeries from our analysis. It is possible that thresholds for whether practices are appropriately small could be adjusted to take account of the presence of branch surgeries.

We have not sought to identify the effect of practice configuration on other possible policy objectives, such as enhancing opening hours of practices or patient choice.

We return to some of these issues in the conclusions to this report.

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2.7. Differences between the existing approach to allocating funds and the approach considered here

The approach to funding implied by this paper differs fundamentally from the present approach; raising important questions about the extent to which the two approaches are complementary and to which they are mutually exclusive.

The present approach

The present approach uses differences in existing costs of urban and rural practices to derive the funding formula adjustment. The formula defines funding for practices based on empirical examination of historical unit cost data of the present costs of practices with similar characteristics.

As such the present approach takes existing configurations or practices as given. In effect the present formula sets funding based on examining the question: “How much funding does a practice in these circumstances need?” through examination of present costs.

The research underlying the present formula, which was carried out by Professor Roy Carr-Hill, used regression methods to analyse how practice costs varied in response to various drivers. Funding is presently adjusted for the two rurality variables included in the analysis, but not for list size, although the Carr-Hill regression analysis on which the funding formula is based showed list size to be a significant driver of costs. This implied that the rurality effect was separate from the effect of size.

Updating the Carr-Hill analysis is outside the scope of this work. However, we note that multiple regression analysis of costs carried out as part of the analysis of economies of scale showed the rurality variables continue to be significant separate drivers of costs in themselves.

Approach adopted in the analysis described in this report

In contrast to the analysis underlying the present approach, the analysis described in this report in effect analyses the question: “Should a practice in these circumstances be at this scale?” We have examined when the existing practice configuration is justified by population dispersion and thus when practices have “appropriately small” list sizes. In contrast to the analysis underlying the existing formula configuration is not taken as given.

The approach adopted here examines how rurality (as measured by population dispersion) affects the configuration of practices given travel times. List size and distances, which are inputs to the present funding formula, are outputs to be optimised by variations in configuration of practices. Funding is then influenced by practice size, which depends on rurality. This difference in approach is illustrated on the chart below.

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Chart 2.1 - Approach adopted in the analysis described in this report

Existing funding approach Approach analysed in this study

Existing practice configuration

Practice size

Funding

Existing practice configuration

New practice configuration

Practice size

Travel times

Population served

Distance toPractice

PopulationDensity Economies of scale

Additionality of present funding adjustment and adjustment analysed in this report

It is possible that the present rurality variables are capturing additional costs of serving geographically dispersed populations that do not relate to scale. This may include factors not captured by the analysis but associated with rurality such as dispensing costs, which we understand were included in the Carr-Hill analysis, or increased average length of consultation, perhaps reflecting time taken on home visits. However, it is beyond the scope of this work to investigate such effects on demand for services.

Alternatively the significance of the rurality adjustment in the previous regression analysis may simply reflect higher historic funding and not be related to additional costs arising from demand drivers. Previous funding formulae tended to allocate additional resources to rural areas. This has the potential to reinforce existing inefficiencies due to the circular nature of the allocation. A practice may be allocated an allowance for being rural, it then appears to have high unit costs and is allocated additional funding via a capitation formula.

In such cases it may not be appropriate to reimburse such costs.

The uncertainty about what is being captured by the analysis underlying the present adjustment raises the question of whether any adjustment for the costs of smaller scale should:

replace the present rurality adjustment;

be used to modify but not replace the present rurality adjustments; or

be added to the present rurality adjustment. We expect the Formula Review Group will wish to consider this matter in its decision making process.

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3. Data and Data Sources

In this section we describe the main data sources made available to us for this and discuss the limitations imposed on our analysis of restrictions on data availability. The data included:

GP Practice cost data;

data on the location of GP practices;

data on the locations of populations served by each GP practice;

data on the road network through which patients need to travel; and

travel cost parameters, such as the value of time.

The data on GP practice costs, locations of GP, and locations of populations and road network coverage is reviewed in this section and issues arising in combining the various data sets discussed. Calculations of travel costs are described in Section 5.

All data on Practices and Practice populations used in this report were provided by NHS Employers or other interested parties, including the Department of Health. The scope of work be undertaken by Deloitte and SDG did not include any review of data sources, data gathering, or data research by Deloitte or SDG. Any data which was not provided to us was excluded from the scope of our analysis. Furthermore, the scope of the analysis agreed with NHS Employers excluded any analysis of Northern Ireland, so no data for Northern Ireland was included from our work.

Data on road networks came from SDG’s internal databases. Some additional data, for example on the value of time, was gathered from public sources such as the Department for Transport.

3.1. GP Practice Cost Data

In order to estimate the effect of economies of scale we were provided access to Her Majesty’s Revenue and Customs (HMRC) data from 2002/3 (2002-03 Schedule D data being the latest available). We were provided information on a sample of over 6,000 Practices in Great Britain. The HMRC data provided information on the cost and expenses amalgamated to the Practice level. The data included:

Practice total cost per patient; and

Practice total expenses per patient.

The dataset contained information on the list size of each Practice. The information was anonymised. Exact list size was not available for reasons of confidentiality. Instead practices were grouped within list size bands; for example list sizes from 1900-2000.

Additional analysis was facilitated by the availability of data on other Practice characteristics including the dispensing status of the Practice, population density and age and sex structure of the population served. In particular, our dataset includes the Practices for which information on all the following variables was available:

Total cost per patient

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Total expenses per patient (total cost less doctors’ salaries)

Total premise costs per patient

List size

Age-sex profile weighting on practice workload

Dispensing status

Number of GPs in practice

Long term illness rate

Staff market forces factor

Average distance of patients from practice

Patients per hectare

These variables comprise the majority of the Carr-Hill variables. There was no data available for the remaining variables which include contract status and three further socio-economic indicators.

The dataset was limited due to incomplete information on all GPs. In cases where data was not available for a particular GP, the entire Practice was excluded.

Due to confidentiality constraints our access to this data set was limited. Some of our analysis during visits to the HMRC offices in London.

3.2. GP Practice Location Data

In order to calculate travel distances from each OA to GP practice we required information on the geographical location of each GP practice in England, Scotland and Wales. These data sets were made available by the Department of Health, the Scottish Executive Health Department and the National Assembly for Wales. They provided us with information on the location of 9,533 GP practices in England, 1068 in Scotland and 565 in Wales.

3.3. GP Practice Population Data

In order to estimate patient travel times to their GP we were provided information on the location of patients registered with each GP practice. Due to the confidential nature of GP list size information, clearance was required from three separate organisations: the Department of Health, the Scottish Executive Health Department and the National Assembly for Wales.

Patient location data was provided by Census Output Area (OA) which is the smallest geographical grouping of population used within the 2001 Census1. This data came from two main data sources:

the attribution data set provided information on the Census Output Area and GP practice for all registered patients in England and Wales in 2004 (Department of Health);

1 The average population in an OA is 120 in Scotland and 300 in England and Wales

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the Community Health Index (CHI) dataset provided similar information for Scotland for

2003/04 (National Assembly for Wales).

These datasets were extremely large with 2.2m GP to OA pairings in England, 0.4m in Scotland and 0.1m in Wales.

3.4. Matching Practice and locations data

It was difficult to match the GP practice population data with the GP practice location data using the data provided for a number of reasons.

There were slight differences in the time periods during which the data available was gathered. During the periods for which the data sets differed GP practices could have been created or merged.

The GP practice location data provided did not contain valid postcode information.

In England there was no unique GP practice identifier on the GP location dataset provided by the Department of Health and as such it was difficult to match these data points to data on practice populations. The matching process involved matching practice names and the use of algorithms matching based on similar geocodes. The lack of a consistent matched dataset in England created significant additional difficulties for our analysis and as a result we have lower confidence in the quality of the GP practice location data in England compared with that in Scotland and Wales.

Table 3.1 sets out the number of GP practices identified within the population dataset and the percentage of these matched to GP locations.

Table 3.1 Matching of GP Population and Location Data

GP Practices Matched Locations Country Population

Data Location

Data Number %

Patients England 9,533 9,800 8,896 96% Scotland 1,037 1,068 990 n/a Wales 510 565 494 n/a Total 11080 11433 10380 n/a

Source: Steer Davis Gleave

Branch surgeries were not included in our analysis. There was no information on the location of branch surgeries in England and Wales. We were therefore unable to examine the impact of branch surgeries on patient travel distances in England and Wales. Data on locations of branch surgeries was available in Scotland, but no data was available on their opening hours so it was not possible to assess the extent to which they improved patient access to services. The implications of the exclusion of branch surgeries are discussed further in our conclusions.

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3.5. Model Coverage

The model covered most of the road network. However, there were some omissions. In particular, the model was unable to calculate travel times from some of the Scottish Islands to the mainland, although, this represented a tiny proportion of calculations and the registration data may well be erroneous.

A more significant issue was the difficulty of matching all census Output Areas in England to the transport network, especially OAs in Central London given the data provided to us. As a result a high proportion of OAs in London were not connected to the network and hence most London GP practices were not covered by the analysis2. Whilst this reduced the sample size for further analysis we considered unlikely it would impact the results as no GP practice in London would be eligible for the rurality adjustment under any likely criteria.

Table 3.2 illustrate the total number of GP practices for which we have full model coverage and were able to calculate patient travel times. In total our analysis included data on 8,480 GP practices across Great Britain accounting for just over 75% of all practices. Coverage was significantly higher in Scotland and Wales at over 95%. As noted above, most of the missing observations relate to GP practices in London.

Table 3.2 - Total GP Practice Sample

Matched Locations Country Number of Practices Total Sample Size

England 9,533 6,996 Scotland 1,037 990 Wales 510 494 Total 11,080 8,480


3.6. Geographical coverage

We have not identified any cases in where incomplete data seems likely to affect our results significantly; though it is possible that incomplete data biases the results in some way. However we have not been able to verify the sensitivity of results to additional data as no additional data has been provided to us.

We note the following possible effects.

We have been advised that the Review Group considers the sample of GP costs provided by DH from HMRC databases to be reasonably representative. We understand from DH that the Data covers England and Scotland in approximate proportion to the number of

2 This was also partially due to difficulties of obtaining ‘clean’ data on GP locations in England which significantly delayed the progress of the project.

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practices.3 Consequently while some sample bias is possible, members of the review group do not consider it likely to have a major effect on the results.

The excluded points in London potentially create a biased sample . However the scale of the issue is known and any percentages of practices can be adjusted to reflect this bias. Furthermore, none of the excluded Practices is likely to be shown to be appropriately small by the analysis as they are not serving geographically dispersed populations.

The information of practice locations and populations includes both very rural areas and very urban areas. As such it covers the range of circumstances likely to be found in Northern Ireland, which in any case only accounts for a small proportion of practice population (less than 2%). As such we do not expect the results to be inapplicable to Northern Ireland for any reason related to the type of geography covered.

3 e-mail from Mike Vickermann, 30th November 2005.

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4. Modelling of economies of scale

This section describes the analysis of the extent to which economies of scale are found in Practices. In the context of this study, economies of scale are defined as lower cost per patient for larger Practice list sizes.

The analysis of relationships between Practice costs and list sizes for this work consists of the application of statistical techniques to existing data. In carrying out analysis of existing costs to identify economies of scale we have not attempted to carry out fundamental analysis of the cost drivers of small practices to confirm whether higher costs per patient are efficiently incurred. Such analysis is outside the scope of this report but may be useful in providing additional input into the formula review.

The following categories of data were included in the analysis.

Practice cost and Practice expenses (that is Practice costs with and without GP salaries). Where we use the term Practice costs in this report it refers to both practice expenses and practice costs.

Practices with and without dispensing status were analysed both separately and as a single population.

Practices above and below a list size of 1900 were analysed both separately and a single population.

This section includes the following.

An overview of the data with summary statistics such as means and variances.

A description of the amount of variation in the data.

An initial assessment of the extent to which average cost per patient varies with list size.

An initial assessment of the magnitude of additional costs that are incurred on average at smaller list sizes.

Regression analysis of the relationship between costs per patient and list sizes. Analysis of costs is carried out against list size alone (univariate regression) and against list size and other variables (multivariate regression). The regression analysis includes testing a variety of hypothesised functional forms and examining a range of statistical diagnostics to check for the robustness of the results, including tests for discontinuities and trend breaks.

Analysis of uncertainties in the magnitudes of economies of scale at different list sizes identified by this analysis.

Comparison of the results of this analysis with those of the Carr-Hill analysis underlying the present funding formula.

Conclusions from the analysis of economies of scale.

Further details of the analysis are provided in the Annexes.

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4.1. Overview of the data with summary statistics and graphs

The sample with which we were provided included a total of 6092 practices. Statistics of the data are summarised in the following tables. Distinctions have been made between:

Cost and expenses per patient. We note that cost is influenced by the present funding formula. This is different in Scotland (where the Arbuthnott formula rather than the Carr-Hill formula is used), and there may be distortions to the Scottish data as a result of this. However these are not shown separately in the data set with which we were provided so it has not been possible to analyse this effect separately.

Practices with and without dispensing status. This is because the costs of dispensing medicines to patients increases the cost per patient; and the data does not allow us to quantify the costs of dispensing alone (see Section 1.2.2). There are some practices for which the dispensing status is not reported.

Practices with list sizes of below 1900 and above 1900, since the cost per patient begins to increase rapidly at list sizes below approximately 1900. This has a clear rationale as the average number of patients on an individual GPs list is just under 19004. This implies that list sizes below 1900, costs which may be largely invariant with the number of patients, such premises costs for a single GP, as a GP’s salary and the receptionists salary, are spread over fewer patients.

We have not within the scope of this work attempted to derive separate cost functions for rural and urban populations. This is consistent with the Carr-Hill analysis, which controlled for practice scale effects independently of rurality. However we note that there are many possible sources of differences in practice costs, including regional differences of variations between urban and suburban practices. One such source of possible systematic differences in cost structure is rurality, and this might imply some variation in the cost adjustment.

4 The average list size for the sample is 1867. The is based on the mid-point of the band, actual practice sizes being unavailable. Practices with less than 1900 patients were excluded from the calculation of the average as the intention was to assess the average number of patients on a full GP list, which would not include those below 1900.

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Table 4.1 - Summary statistics for costs data

Below 1900 Dispensing Non dispensing All

Number of practices

105

349

533

Cost per patient

Mean 292 101 146

Median 252 90 101 σ 188 52 131 Expenses per patient

Mean 208 60 92

Median 171 54 62 σ 186 34 88

Above 1900 Dispensing Non dispensing All

Number of practices

654

3884

5559

Cost per patient

Mean 170 85 99


Mean 118 50 61

Median 111 49 52 σ 51 16 34

Total sample Dispensing Non dispensing All

Number of practices

759

4233

6092

Cost per patient

Mean 187 86 103


Mean 131 51 63

Median 115 49 53 σ 90 19 42

Note: The column for all practices includes those for which dispensing status is not known and therefore the number of practices is greater than the sum of those in the dispensing and non-dispensing columns.

As noted, the list size data we were provided with was banded. For our analysis we have assumed the list size for each individual surgery to be the mid point for the band. The average cost and expenses per patient for each practice were obtained by dividing total cost and expenses by list size.

The statistics show that cost and expenses per patient are higher for dispensing practices and for practices of list size below 1900. There is also more variation in cost/expenses for such practices.

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4.2. Variation in the data

The variation in costs is also shown in figure 4.1, which shows the cost per patient data for each Practice (within each list size band). In addition, the mean practice costs for each band have also been plotted to indicate the overall trend. There is a great deal of variation in costs at each practice size which would be expected given the wide variation in other parameter values shown by the data. There may also be reporting errors.

Figure 4.1 - Variation in the data

Cost per patient by list size band

0

50

100

150

200

250

300

300 1850 2250 2650 3150 3750 4450 5350 6250 7350 8650 10250 14750

Average list size

Cos

t per

pat

ient

(£)

Cost per patient by practiceAverage cost per patient (for list size band)

The variation in the data appears to have an asymmetric skew. There is with a larger proportion of the data showing unusually high costs than unusually low costs. Furthermore, the higher cost practices show a larger difference from the average than low cost practices, as low costs are bounded at zero and high costs have no similar upper bound. This increases the mean and may be a particular issue for regression analysis, where extreme values potentially distort results5. This effect will tend be reduced but not necessarily eliminated by the use of log variables, which are applied in some of the analysis. The problem can also be addressed by the use of median rather than mean values for cost per patient in each band.

We considered excluding some data points as outliers. Outliers might arise from misreporting or from exceptional circumstances and so are not representative of general patterns. However this was not practical as no reliable criterion for excluding data points given the available data. Only one Practice was excluded from our analysis as it appeared to be a clear outlier with an cost per patient of £1,973.

5 Extreme values have a particular influence on the position of the regression line because the line is computed to minimise mean square deviation from the line. Squaring the deviation increases the influences of points further from the line.

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4.3. Differences in average costs per patient with list size

The following graph shows mean and median costs and with average expenses per patient. The mean and median they show similar trends as list size increases. Costs per patient fall rapidly as list size increases to approximately 1900. As list size continues to increase beyond this point costs appear to remain approximately constant, with mean values showing a small apparent decrease and median values showing no such trend.

Figure 4.2: Full dataset costs and expenses against average list size

0

50

100

150

200

250

300

0 2000 4000 6000 8000 10000 12000 14000

Average list size

£Cos

t/Exp

ense

s

Average cost per patient for bandAverage Expenses per patientMedian cost per patient for bandMedian Expenses per patient for band

4.3.1. Dispensing status

The sample was separated into dispensing and non-dispensing Practices in order to gain additional insight into any trends. As noted previously, when a practice dispenses medicines to patients, the cost per patient increases on average because the costs of the dispensing function are included in the total cost/expense per patient and cannot be separated out in the data provided.

The following graph shows mean cost per patient separately for dispensing and non-dispensing Practices, and those for which the status is not reported. The pattern is similar for expenses, as is shown in the Annexes. This indicates that practices without dispensing status have higher cost per patient at smaller sizes. This may account for the slight downward trend apparent in the mean cost per patient for the whole sample, as no such trend is evident with the non-dispensing practices.

There are various possible explanations for higher cost of dispensing practices at smaller list sizes. For example it is possible that smaller practices undertake proportionately more dispensing, increasing their apparent cost and expenses per patient. It could also reflect the fee

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structure for dispensing which includes both fixed and variable components. However it has not been possible to assess whether this is the reason on the basis of the data provided.

Figure 4.3: Mean costs and expenses per patient by list size dispensing and non dispensing

0

50

100

150

200

250

300

0 2000 4000 6000 8000 10000 12000 14000

Average list size

£Cos

t/Exp

ense

s

Average cost per patient for band- NondispensingAverage cost per patient for band- Dispensing

Average Expenses per patient for band-DispensingAverage Expenses per patient for band- Nondispensing

There are many more non dispensing than dispensing practices in the known dataset. If the set for which status is unknown is distributed in the same way, mean costs per patient in the dataset for which status is unknown would be closer to those for dispensing than for non-dispensing practices. This is what is found in the analysis, consistent with the practices for which status is not know containing a mix of dispensing and non-dispensing practices that is similar to those for which status is known.

In view of the differences in cost levels and behaviour, regression analysis was carried out separately for the whole population of practices, and for dispensing and non-dispensing practices.

4.3.2. Potential magnitude of additional funding at small list sizes

As noted, the behaviour of costs and expenses appears to change as list sizes move beyond approximately 1900. Looking at cost per patient (for clarity), and showing the moving average, it is evident that that costs fall as list sizes increases to 1900 but that the rate of fall greatly reduces at larger list sizes, perhaps to zero.

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Figure 4.4 - Data plot with trendline

Cost per Patient by List Size

40

90

140

190

240

290

0 2000 4000 6000 8000 10000 12000 14000

Average list size

£ A

vera

ge c

ost p

er p

atie

nt fo

r ban

d

Average cost per patient for bandMoving average per 5 data points

BAND 1 BAND 2 BAND 3

In order to assess the magnitude of any differences, and thus the potential additional funding, we have analysed the differences in the means and the total practice population in three bands.

Band 1: List sizes up to 1,900

Band 2: List sizes between 1,901 and 6,750

Band 3: List sizes above 6,750

The breakpoint at 6750 is based on informal inspection of the moving average in order to give an indication of the difference between ‘medium’ and ‘large’ practices.

The bands were identified as having statistically different means by use of t-tests. The weighted average cost and expenses for each band are summarised in the following table. The additional costs of Band 2 relative to Band 3 appear to be due to the presence of dispensing practices and thus may not reflect costs covered by the funding formula.

Table 4.2 – Mean costs and expenses per patient for each band

Dispensing

Band 1 Band 2 Band 3Costs 287 183 143Expenses 210 129 96

Mean £ per patient

Non Dispensing

Band 1 Band 2 Band 3Costs 137 85 87Expenses 75 51 50

Mean £ per patient

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These separate bands can be used to give an overall approximation of the magnitude of savings if each surgery was to move into the next band, as would be the case if surgeries were merged into units. This also indicates the additional funding that might be required if practices remain small rather than all becoming larger.

The additional cost per patient for changing in size such that they move from Band 1 to 2 and Band 2 to 3 was calculated and applied to the sample population in each band. In each case the mean for the band was used, with no allowance for variations in cost within the band. The total was scaled using the ratio between the total list size of all the Practices in the sample and the UK population to give an estimate of the total possible additional costs for the UK as a whole. The analysis shows that, as an estimate of theoretical gross savings, there are £130m-£140m available from merging surgeries in order to move them to the next higher band.

Table 4.3 - Total costs saving estimates

Band 1 to 2 Band 2 to 3 TotalCosts 37m 90m 127mExpenses 26m 111m 137m

Band 1 to 2 Band 2 to 3 TotalCosts 14m 120m 134mExpenses 13m 97m 110m

Band 1 to 2 Band 2 to 3 TotalCosts 11m (25m) (14m)Expenses 7m 11m 19m

Total Savings (£) - Dispensing

Total Savings (£) - Non Dispensing

Total Savings (£) - All practices

The difference between the mean costs of Band 2 and Band 3 is small but applies to a large number of practices. This is illustrated in the chart below. The saving on moving from Band 2 to Band 3 is thus greater than on moving from Band 1 to Band 2. However, as noted, these apparent savings may be an artefact of the inclusion of dispensing costs in the sample data.

Figure 4.5 - Proportion of patients within bandings

Proportion of sample population in each band

Band 12%

Band 243%Band 3

55%

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Proportion of sample practices in each band

Band 261%

Band 330%

Band 19%

The savings on moving from Band 1 to Band 2 are smaller but are likely to reflect in large part diseconomies of scale unrelated to dispensing status, as higher costs are observed at small scale in both dispensing and non-dispensing practices. The savings are £42m on cost and £31m if expenses only are considered.

This estimate puts and upper bound on the likely additional funding required for small practices, as it represents the costs that could be avoided if all small practices were merged. In practice any rurality adjustment designed to compensate for small size is unlikely to require such large additional funding, provided that the adjustment is limited to practices in Band 1 (below 1900 list size), because many small practices are in urban areas. The actual size of the required adjustment is considered further in Section 7.

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Exclusion of merger costs

Note that this analysis estimates the gross theoretical savings available in moving from one size of practice to another, ignoring the extra costs associated with this. The estimate of total savings is useful as it allows us to quantify the total savings that would be possible in the extreme scenario where all practices below list size of 6,750 were merged.

Such savings are unlikely to be achievable from the merger of practice in reality. The reasons for this are:

1. The saving is gross and does not include the additional travel costs to patients from having fewer GP surgeries. This constitutes the other part of our analysis (see next section).

2. The estimate excludes the transactions costs involved with merging GP practices, which may, for example, include the following.

property costs;

administrative costs of changing address (moving, informing patients);

loss of goodwill from patients;

purchase of new equipment or furniture for new premises;

extra travel times for the GPs and staff; and

extra travel times for GPs on home visits.

Conversely, we note that there could be intangible benefits resulting from the merger such as:

increased flexibility (in terms of doctors’ working times);

opportunity to move to more modern, refurbished surgeries; and

potentially greater ease for patients in finding an appointment, as there will be a larger number of GPs who may have a spare slot at a particular time.

Analysis of any such costs and intangible benefits is outside the scope of this work.

4.4. Regression analysis

As noted earlier in this section, the plots of the data shows that there is potentially different behaviour for:

total cost and expenses;

dispensing vs. non dispensing practices; and

practices of list size greater than and less than 1900

Separate regression analysis was undertaken for each of these different subsets. Simple and multiple regressions were carried out using various functional forms.

All the models seek to reflect the different cost behaviour for small practices; either in a single function, or splitting the regression into two separate relationships prevailing above and below 1900.

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4.4.1. Single variable regression

We used several model specifications to quantify the relationship between practice list size and average cost or expenses per patient. The majority of our regressions were on the raw data, however we also performed the analysis on the median cost or expenses for each list size band in order to attempt to remove bias potentially caused by a small number of high costs practices.

The following specifications were modelled:

Model 1: Combined Linear, the simplest relationship

Model 2: Log function, the functional form adopted in the Carr-Hill analysis

Model 3: Log with constant, a modification to the Carr-Hill analysis.

Model 4: 1/x function for the entire dataset;

Model 5 (two variants)

1/x function for list sizes below 1900 and linear list sizes greater than or equal to 1900

Medians: similarly but with median costs for each list size banding rather than the raw data, to eliminate the effects of outliers

Model 6: 1/x function for all practices greater than or equal to 750 list size; to ensure that the very small practices do not distort the results

All models show a trend in which costs fall rapidly at small list sizes and then only marginally (if at all) as list sizes increase further.

Models 1 and 5 explicitly contain a pre-defined break point at list sizes of 1,900. As noted earlier in this section the rationale for this point is the fact that 1,867 is the sample average patients on a single GP’s list (excluding small practices).

Note that Model 3 is based on the assumption that there is a minimum cost (or expense) per patient to which we would expect each practice to converge. To reflect this we have used the log of ‘cost – 80’ as the dependent variable. 80 represents this minimum value, determined with consideration of the band average graphs (See figure 4.3). Consistently with this approach, we believed it would be appropriate to exclude the practices with costs/expenses below this level as, on the assumption that these practices either face a set of particular circumstances that help them to keep the costs to a level below the minimum value that we have set, or in some cases could have failed to record their data correctly. Therefore caution must be exercised interpreting this model since it applies to a smaller dataset.

4.4.2. Summary of results of single variable regression

The results of the regressions are summarised in Table 4.4 for costs and Table 4.5 for expenses per patient. The main points from the results can be summarised as follows.

All results show that there is there exists statistically significant negative coefficients on list size for small (Band 1) practices, indicating costs falling with scale.

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Running Model 5 on a median cost per patient basis improves the fit of the regression in

Band 1, though it makes little difference to Band 2 results.

The list size coefficient is significant even following the exclusion of the smallest list size (highest cost) practices from the 1/x regression, though the gradient is lower without these points.

There does not appear to be a significant scale effect at list sizes greater than 1900, except for the dispensing practices.

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Table 4.4 - Regression results: Cost per patient analysis


Table 4.5 - Regression results: Expenses per patient

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Regression diagnostics

In summary, the regression diagnostics show that:

The log function passes the specification test only for dispensing practices. Model 2 only passes for the dispensing expenses data; whereas Model 3 passes for both dispensing cost and expenses data.

For costs, 1/x passes the specification test for list sizes below 1900 (Model 5 raw data) for the full data sample, and dispensing practices, with a narrow fail for non-dispensing. For expenses, the specification test is passed for the dispensing and non-dispensing samples, with a narrow fail for the full dataset. For the specifications that narrowly failed, the test constituted an improvement on log or linear functions for band 1. 1/x in Model 5 (medians) passes the specification test for the full sample and dispensing practices, failing for non-dispensing. This is the case for both costs and expenses.

1/x does not pass the specification test when list sizes greater than 1900 are included, (Model 4), for costs and expenses.

The linear function (Model 1) passes the specification test for Band 2 regressions on the full sample and non dispensing practices.

The residuals from the 1/x functions (Models 4 and 5) are not normally distributed, though they do seem broadly independent.

4.4.3. Multivariate regression

The corresponding multivariate analysis was also carried out using the variable listed in Section 3.1 to verify that the list size effect remains statistically significant when analysed together with other determinants of cost.

Correlation between the independent variables was also assessed. Three of the variables were found to be significantly correlated with each other; however, even after their removal from the analysis, a highly significant scale effect was present.

The following table summarises the regressions carried out at the Inland Revenue on cost data for the full sample only. We did not examine all models as the purpose was mainly to show the robustness of the conclusion of economies of scale in band 1 to the inclusion of other data points.

Table 4.6 - Multivariate Regressions

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4.5. Typical extra cost per patient

Using the function that shows the best fit with the data (1/x in Band 1) we can calculate the estimated additional costs incurred due to practices being small, together with corresponding confidence intervals.

The confidence intervals have been calculated on the coefficient only as it is the change in the cost/expense that we are examining.

The following tables set out the extra costs or expenses (with corresponding confidence intervals) moving from a base list size value of 1900 to 1000 and 500; and from 1000 to 500 in turn, for dispensing and non dispensing practices.

Table 4.7 Additional costs per patient

Additional costs (£ per patient)

Dispensing Non DispensingCosts Costs

1900 1000 500 1900 1000 500

1900 065

33 to 97202

103 to 301 1900 039

19 to 59121

58 to 184

1000 n/a 0137

70 to 204 1000 n/a 082

39 to 125

500 n/a n/a 0 500 n/a n/a 0

To list size

From

list

siz

e

from list size

From

list

siz

e

Additional Expenses (£ per patient)

Dispensing Non Dispensing

1900 1000 500 1900 1000 500

1900 029

9 to 4991

29 to 153 1900 016

9 to 2351

29 to 73

1000 n/a 062

20 to 104 1000 n/a 035

20 to 50

500 n/a n/a 0 500 n/a n/a 0

To list size

From

list

siz

e

from list size

From

list

siz

e

These results show that there are significant extra costs associated with operating at small list size, though our regression analysis indicates wide confidence intervals. These may be wider still if other including multivariate were considered.

There is a significant difference between the additional costs for dispensing and non-dispensing practices. However it has not been possible to separate out dispensing costs on the basis of the data provided, so it is not possible to say if this additional cost is only due to costs associated with dispensing or also includes other costs which are systematically higher for dispensing practices.

4.6. Comparison with the Carr-Hill analysis underlying the present formula

The regression analysis underlying the present formula found a significant economies of scale effect. The analysis showed a significant and relatively stable negative coefficient on the list size variable, when costs per patient was analysed. This was the case at GP and practice level, and for total cost per head as well as total expenses per head. The list size co-efficient was much larger in the GP level model than the practice level model. This is shown in the table below.

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Table 4.8 - Summary of Key Results for the Models

GP, list size

continuous Practice, List size continuous

GP, list size dummies

Log Density -0.01 (-3.92) -0.06 (-8.5) -0.02 (-6.49) Log Average Distance 0.04 (5.38) 0.05 (3.21) 0.03 (3.75) Log List Size -0.74 (-114) -0.34 (-17.11) List Size Dummies, 100-999

1.12 (86.15)

100-1499 0.54 (47.41) 1500-1999 0.33 (34.62) 2000-2499 0.18 (19.68) Adjusted R-Square 0.566 0.49 0.492

For the practice level results the results indicate that:

Log (Expenditure per patient) = -0.34 log (Practice list size) or -0.74 (GP list size).

Or:

Expenditure per patient = list size-0.34

This implies that increasing the list size by a factor of 5 reduces costs to 58% of the value with a smaller practice and conversely decreasing list size by a factor of 5 increases costs by a factor of 1.7.

It is not clear from the analysis that we have carried out that the log formulation across the sample size adopted by Carr-Hill is robust. However, in the absence of additional diagnostic statistics for the Carr-Hill analysis it is difficult to comment in detail. We nevertheless note that the conclusion of economies of scale at small list sizes is supported by the analysis.

4.7. Conclusions

Based on the analysis reported in this chapter we conclude the following:

Economies of scale for list sizes below 1900

Our analysis shows the additional costs per patient below 1900 to be statistically significant. This conclusion is robust to a wide range of tests. However the precise magnitude of the additional costs at list sizes below 1900 is uncertain, for example because of “noise” in the data, lack of information on the dispensing costs of small practices and fewer instances of non-dispensing practices at these list sizes.

A change in behaviour with economies of scale at 1900 has a clear rationale corresponding to the average list size per GP across the sample. If the costs of a practice with a single GP are largely fixed at list sizes below approximately 1900 costs per patient would be expected to decrease rapidly as list size increases.

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This increase can be modelled by a 1/x function. This functional form is found to be consistent with the data on both practice costs and cost.

This result is robust to the removal of practices with list sizes below 500 and whether a median or the whole data set is considered. However testing for these sensitivities affects the parameters estimated by the regression.

Uncertainties in the magnitude of economies of scale

The analysis indicates additional cost of £39 per patient for non-dispensing practices at a list size of 1000 and £121 per patient at a list size of 500. However, the magnitude of the additional costs at list sizes below 1900 is uncertain, for example because of:

variation in the data, and an issue with asymmetry (more of the variation appears to be higher costs, which pulls the average up);

differences between dispensing and non-dispensing practices, with no data available to allow dispensing costs to be separated; and

smaller sample size caused by excluding those practices with dispensing status and lack of data on proportion of dispensing costs.

Limited evidence of economies of scale above 1900

We have not found a robust model for list sizes greater than 1900. There appear to be little, if any economies of scale at such list sizes for non-dispensing practices. There is some tentative evidence of a downward trend for the dispensing practices. However, this may, as noted, simply reflect additional dispensing costs rather than costs funded by the GMS formula.

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5. Patient Travel Distances and Costs

In this section we outline our approach to estimating patient travel distances to their GP and the associated cost of journeys. We describe the methods used to model patient travel journeys and present some summary statistics indicating the level of patient access to GP services and the relative isolation of GP practices across Great Britain.

We note that, in line with the terms of reference for this work, the modelling does not address access issues other than those arising from the geographical dispersion of the population. For example there may be issues with access for those with mobility difficulties or other restrictions. However consideration of such limitations on access is outside the scope of this work.

5.1. GIS Modelling Methodology

5.1.1. Travel Distances and Time

Patient travel distances and travel times to their GP were calculated on the estimated travel distance from the OA of the patient to the GP at which they are registered. We used the TransCAD transit modelling Geographic Information System (GIS) application to establish a complete road network accessibility model based on Ordnance Survey digital mapping data. This software application incorporated both the topological network modelling and standard GIS functionality which allowed us to use a detailed, geographically accurate road network as the base for calculating travel times. This approach allowed us to calculate three variables for each OA to GP pairing:

total travel distance based on the road network;

estimated walking time; and

estimated drive time which takes into account the quality of the road network, for example, drive times are longer in urban areas because average road speeds are lower.

As noted in Section 2, we did not take into account the public transport network when calculating travel distances, times or costs since it would be impractical to develop a complete model to derive public transport travel costs, particularly within the scope of this project.

5.1.2. Travel Costs

Travel distances and times estimated using the GIS modelling were then converted into travel costs using a number of assumptions including:

patients would walk to the practice if it was within a 10 minute walking distance, otherwise they would drive;

travel time was valued in line with Department of Transport guidance;

patients would visit the doctor on average six times per year (based on data from the 2002 General Household Survey).

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Table 5.1 - Parameters for Estimating Value of Time

The main parameters for the cost modelling are summarised in the table below.

Walk Speed 4.8 kmph

Max walk distance 0.8 km

Max walk time 10 mins

Car parking time 10 mins

Value of Time £4.46 per hour

Vehicle Operating Costs £0.50 per km

Walk Weight 2

Note: The value of time is at 2002 prices for consistency with HMRC cost data used in the analysis of economies of scale. ‘Walk weight’ is the weighting on time caused by the preference for people to drive rather than walk, time being equal.

The resulting travel cost function is illustrated in the chart below, which for the purposes of illustration assumes uniform travel speed for the road network. The travel costs shown are for a single one-way journey. The simulation modelling takes account of variations in travel speeds.

Figure 5.1 - Travel Cost vs Distance (uniform speed)

0 1 2 3 4 5 6 7 8 9

10

0 400 800 1,200 1,600 2,0002,4002,8003,2003,6004,0004,4004,800

Distance m

Cost (£) Drive CostWalk CostComposite Cost

As noted in the introductions to this report, NHS Employers requested that that analysis be carried out on a unified basis for the whole of Great Britain. There was thus no variation assumed in the value of peoples’ time.

A single value for the cost of time was also applied to all classes of patient, for example with no variation between the value of time for those retired and those of working age. This appears

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consistent with the principle of equal access to care under the NHS, endorsed by NICE and other bodies. Valuing the time of individual groups differently, for example according to age or cost, would tend to weight optimal provision towards those with a higher value of time, and therefore higher travel costs.

5.2. Travel Distance Correlations

As noted in Section 5.1 we have used travel distances based on ‘network’ distances rather than straight line distances in this report. This is because it provides a more accurate measure of travel cost. This is especially relevant in remote areas and coastal districts where the relationship between straight line distances and travel distances can vary more markedly due to local topography.

We assessed the relationship between straight line and network distances. On average network distances were just over 20% longer than straight line distances although we also found a very strong correlation between both metrics as illustrated in Figure 4.4.

Figure 5.2 - Correlation between Network and Straight Line Distances to GP practies

Source: Deloitte

0

10

20

30

40

50

0 10 20 30 40 50Network Distance (km)

Stra

ight

Lin

e D

ista

nce

(km

)

r=0.99 (p=0.000)

The strong correlation (r=0.99) between the two distance measures indicates that straight line distances multiplied by 1.22 can be used as a good proxy for network distances in most circumstances, although differences remain.

This may have important implications for setting funding adjustments in practice. Whether a practice is appropriately small due to the geographical dispersion of its population will depend on network travel distances. Network travel distances are difficult to measure without a detailed modelling exercise of the type undertaken for this work. It may therefore be difficult to apply network distances within any funding formula. However geographical distances are easier to obtain and indeed are used in the present rurality adjustment. The analysis shown here indicates

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that these are a good proxy for network distances and so may be used instead to set funding adjustments.

5.3. Travel Distances and Costs

Figures 5.3 and 5.4 show average travel distances to a GP by country and by a measure of rurality (the population density profile of the practice sample population divided into quintiles). We have also presented travel distance to the nearest GP practice which is substantially lower than actual travel distances because people are often not registered with their nearest GP. Across Great Britain patients on average travel 3.3km to their GP practice, although, on average a patient’s nearest GP practice is only 1.9km away. In urban areas only a third of patients visit their nearest GP practice whilst in rural areas this increases to 50%. This may reflect patient preferences, a desire for continuity with a GP practice after moving within an area, or supply constraints. It indicates that any analysis which assumed patients do visit their nearest GP practice would underestimate travel distances, especially in urban areas.

In rural areas, represented in these charts as the 20% of practices in the sample (i.e. excluding many practices in London) with the lowest population density, average travel times to the GP increase substantially. Figure 5.4 illustrates that in the 20% most rural areas patients travel on average 5.5km to their GP, whilst in urban areas this falls to 2.4km.

The range of alternative GP practices to patients living in rural areas is also substantially lower relative to those living in urban areas. On average patients from a single census Output Area are registered with 11 different GP practices, in rural areas it is only 8 and in urban areas 14.

We note that average travel distances appear broadly consistent (or somewhat smaller than) the typical travel distances used in calculating isochrones (times of equal travel) of the type found in the market definition used by the Competition Commission (see Annexes). As such they do not seem to imply unrealistically high travel distances.

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Figure 5.3 - Network Distance to a GP Practice by Country6

Source: Deloitte

Figure 5.4 - Network Distance to a GP Practice by Population Density Quintile

Source: Deloitte

4.1

3.13.3

2.5

2.11.8

0

1

2

3

4

5

Wales Scotland England

Net

wor

k D

ista

nce

(km

)

Average Closest

0

1

3

6

Rural Urban

Net

wor

k D

ista

nce

(km

)

2

4

5

Average Closest

We have also estimated that for an average patient to visit their GP in any one year costs £32. This is of comparable order of magnitude to the additional costs incurred by small practices,

6 data for England excludes GP practices in London

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suggesting that there will not be an unambiguous trade-off but that the trade-off is likely to vary with circumstances. Figure 4.8 illustrates that travel costs are 50% higher in rural areas relative to urban areas.

Figure 5.5 - Patient Travel Costs by Population Density Quintile

Source: Deloitte

£46

£30 £31 £29£27

£0

£10

£20

£30

£40

£50

Rural Urban

Pat

ient

Tra

vel C

osts

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6. Appropriately Small GP Practices

In this section we examine the circumstances in which a practice may be appropriately small due to the geographical dispersion of the population it serves. This section includes the following.

Analysis of the additional travel distances, and hence travel costs, that would be incurred by patients if practices were merged.

Analysis of the net costs to patients after any savings from merger (due to economies of scale) have been deducted from patients’ additional travel costs. If there is a net cost due to the merger of a practice (after deducting savings from merger) then a practice may be regarded as “appropriately small”, subject to certain caveats related to noise in the data.

An analysis of the factors influencing whether there are net additional travel costs for patients and thus whether practices are appropriately small. In particular we consider the extent to which whether practices are appropriately small is due to:

geographical dispersion of the population they serve, which is measured by population density; and

the extent to which they are isolated from other medical services, which is measured by distance to the next nearest practice.

Further examination of the effectiveness of distance to the next nearest GP practice as a criterion for defining whether practices are appropriately small.

The prevalence of appropriately small GP practices and the consequent scale of the additional funding that might be required.

The conclusions arising from this analysis.

6.1. Unavoidable Travel Distances

Figures 6.1 illustrates the geographical dispersion of GP practices in Scotland. It shows that some small GPs are in urban areas. These would not qualify for additional funding based on the geographical dispersion of the population they serve. In contrast, some small GPs in rural areas might qualify for such funding. These may include, for example, those around the Scottish coast. England and Wales show similar patterns, but with fewer rural practices, corresponding to their less rural geography.

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Figure 6.1 - Distribution of GP Practices in England


We have assessed which of these small practices is “appropriately small” using simulation modelling techniques to estimate the effect on patients’ travel distances and times, and hence costs to patients, of changes in practice configuration. The approach examines the additional costs that would arise if there were no practice at a current location by examining the effect of it being removed or merged, as described in Section 2. If a practice is not in a certain location and it results in a substantial increase in patient travel distance then it will tend to be appropriately located.

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Figure 6.2 illustrates the results of this simulation modelling. It illustrates the average net increase in patient travel distance per patient for a single one-way trip to the GP practice resulting from a practice merger. Each bar represents the average value for quintiles of the sample ranked by population density. These results illustrate that in practices in the sample serving areas with the lowest 20% population density if a GP practice were removed or merged then patients would face an average increase in travel distance of 3.2km7. There is relatively little change in travel distances in other areas.

Figure 6.2 - Additional Patient Travel Resulting from Practice Mergers

3.2

1.1

0.6 0.50.3

0

1

2

3

4

Rural Urban

Pat

ient

Tra

vel D

ista

nce

(km

)

Source: Deloitte

However, not all patients in rural areas would face significant additional travel distances if their local GP practice were removed. Based on the results of our modelling a significant proportion of patients would face no additional travel distance or may even travel a shorter distance. These results occur when there is an alternative GP practice close by, or even nearer to the current population (which can occur due by patients not registering with their nearest GP practice). Figures 6.3 illustrates the results of simulation modelling at a GP practice level for all practices.

7 The sample excludes many practices in the London area, as described in Section 5. The 20% lowest population densities in the sample therefore are likely to represent appropriately 16% of the lowest density within the total population, as the omitted practices in London serve areas of high population density.

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At lower population densities additional travel distances tend to increase following a practice merger, although there is a large amount of variation between individual practices in the data set, as would be expected from the wide variety of situations in which practices find themselves. Figure 6.3 illustrates that following a merger there would be some practices in more rural areas for which there would be a significant increase in travel distances. In contrast, there would be relatively little effect on travel distances for the majority of practices, including many in rural areas.

Figure 6.3 - Unavoidable Additional Patient Travel from Practice Mergers (Most rural areas)

-10

-5

0

5

10

15

20

25

0 25 50 75

Population Density

100

tient

Tra

vel D

ie

m)

stan

cP

a (k

Source: Deloitte

Note some points above 100 not shown for clarity. Population density is weighted average in people per hectare across OAs served by the practice. Unweighted averages of the areas served by the practice show much lower density in people per hectare.

The causes of changes in travel distances are specific to each set of circumstances and therefore every point is different. In many cases there are complex interactions between locations of patients and GPs. GPs can often serve as many as 300 OAs and patients in those OAs can often go to several other premises. However to illustrate the type of behaviour found we now outline the circumstances of a small rural GP and a small urban GP. The examples have been anonymised to protect confidentiality.

Example 1: A Small Rural Practice

For one small GP practice in Scotland we estimated that patient’s would have to travel in excess of 20km further than they currently do if the practice was ‘removed’. This practice currently has 550 registered patients on its list spread across 10 Census Output Areas (OAs). The weighted

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average population density of these OAs is 1.3 people per hectare8 and each OA is classified as very remote on the Scottish Executive Urban Rural classification.

Approximately 400 patients live within 5km of the GP practice (of which about 150 live within 0.5km and 120 within 1.3km), the remaining 150 patients live between 13 and 25km from the GP practice. The next nearest GP practice is over 21km away. We estimate that if the GP practice were removed then the average increase in travel distance would be approximately 20km. This additional travel distance is almost as long as the distance to the next nearest GP. This is due to the closeness of many of the patients to the current practice and the configuration of the road network, allowing few alternative routes.

Example 2: Small Urban Practice

For one small GP practice in England we estimated that patients would actually have shorter journey times if the practice was ‘removed’. This practice has a registered population of only 170 patients split across over 60 Census OAs. The average travel distance to the GP practice is 4.8km whilst the next nearest GP practice is only 1.4km away. The practice covers an area of higher population density (14 people per hectare) and is classified as covering an urban settlement.

Only a small number of patients for the practice live in each OA and the residents of each OA have significant choice in terms of their GP practice (residents are registered with 10-15 alternative GPs per OA). After running the simulation model it was found that if the GP practice was removed and patients visited alternative practices in proportion to the current GP-OA pairing distribution then travel distances would on average fall by 2.6km.

6.2. Unavoidable Net Costs

As described in Section 2, our approach to this project has been to examine the net effect of patient travel costs and potential GP practice savings from merger scenarios. The effect of merging a GP practice increases patient travel distances (and therefore costs) in more rural areas, However, there are larger potential savings in practice cost because GP practices in rural areas are slightly smaller.

Figure 6.5 illustrates the effect of merger scenarios on patient travel costs and GP practice costs. The top line indicates the change in patient travel costs (the value of time and the cost of travel) following a practice merger. In the 20% most rural practices in the sample, on average per capita patient travel costs would increase by just over £20. The bottom line indicates the potential savings in terms of GP expenses from merging GP practices (based on 1/x as an economies of scale adjustment) as described in Section 4. In these most rural areas modelled per capita savings are in the region of £10, substantially less than the increase in patient travel costs.

8 The OAs cover an area of over 100,000 hectares with a population of just under 1,000. However, not everyone from these OAs go to this GP practice and the people per hectare figure is a population weighted average.

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Figure 6.5 - Changes in Cost Associated with Practice Mergers (per capita)

Source: Deloitte

This analysis implies that in general there will be little difference in total costs between different configurations and location of GP practices within urban areas. This is because potential premise savings and additional patient travel costs would be small and in opposite directions, leading to an even smaller net effect. This finding is reinforced by the finding set out in Section 4 that it is not well established that there are any significant savings from merging larger practices. It is also consistent with the finding set out in Section 5 that the majority of patients are not registered with their nearest GP in urban areas, which indicates that any additional travel costs from changes in configuration are likely to be small.

In contrast, if GP practices were merged in rural areas the increase in patient travel costs would more than outweigh savings, although there remains significant variation between individual cases.

From this analysis we conclude that:

-15

-10

-5

0

5

10

15

20

25

Rural Urban

nt/G

P C

)P

atie

osts

(£

Patient Costs GP Costs

only in rural areas (lowest density practice quintile) do we find that patient travel costs exceed potential practice savings on average;

in other areas that there is only limited scope for GP practice savings, and that these are approximately equal to any increase in patient travel costs9.

However, these results are averages, and, as illustrated by figures 6.3 and 6.5 there are wide variations in individual practice. It is necessary to understand what determines whether a practice in a rural area is “appropriately small” and it is this that we now examine.

9 The functional form used in this analysis includes savings for larger practices. As noted these are not well-established. This is unlikely to affect estimated funding adjustments, as such practices would not be available for additional finding because they fall above the defined size threshold. Nevertheless, analysis may overstate the savings available in urban areas.

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6.3. The factors influencing net additional travel costs

As illustrated above, it is more likely that a small GP practice in a rural area is valuably located, that is removing it would lead to additional costs that outweigh savings from merger and thus is “appropriately small”. In order to analyse which characteristics determine whether a practice is valuably located we used regression techniques.

We used regression analysis to explain variations in additional costs for patients using a series of explanatory variables including population density and the distance to the nearest alternative GP practice10. Table 6.1 illustrates that distance to the nearest GP explains a high proportion of the variation in the additional travel distance for patients resulting from the merger of a practice (just over 46%). Model 1 indicates that a 1km increase in distance to the nearest GP would on average increase patient travel distances by 0.55km. Population density variables are not significantly related to additional travel distance after controlling for the distance to the nearest GP (low t-scores). Distance bands also explain a high proportion of the variation in excess travel distances but this functional form fails the RESET specification test (Model 3).

Table 6.1 - Determinants of ‘Appropriately’ Located GP Practices

Additional Travel Distance (km)

Model 1 Model 2 Model 3 Variable

Coefficient t-score Coefficient t-score Coefficient t-score 10% lowest density -0.250 -1.668 20% lowest density 0.095 0.933 Nearest GP (km) 0.549 37.964 0.556 29.214 Nearest GP 1-3km 0.528 12.623 Nearest GP 3-5km 1.634 18.295 Nearest GP 5-10km 3.453 30.129 Nearest GP 10>km 7.796 24.212 Observations 7977 7977 7977 R2 0.466 0.467 0.404 RESET 0.200 0.199 0.000

Source: Deloitte

1 population density (population per hectare) based on the weighted average characteristics of the GP practice catchment population 2 based on network distances

10 Outlier observations were truncated from the analysis as they mainly related to small practices which were unduly influenced by one or two unusual GP to OA pairings.

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A single variable regression using population density as the explanatory variable ( but excluding distance to the next nearest practice) shows that this variable is also a significant explanatory variable, but has less explanatory power than the distance to the next nearest practice (r-squared is 18%).

The figure below shows the relationship between the two sets of explanatory variables, distance to nearest GP and population density. This shows distance to nearest practice to be inversely related to population density, although there is a wide range of outcomes, again illustrating the wide variation in individual circumstances. In view of this correlation the results of regression analysis using both variables should be treated with caution.11

From this analysis it appears that the two variables of distance to nearest practice and population density are to some extent measuring the same thing, which we interpret as rurality. If population is more dispersed there will, other things being equal, be further to travel to the next nearest practice.

As noted, distance to next nearest practice is at better predictor or high additional travel costs than population density and models which use both should be treated with caution. For these reasons we focus on distance to nearest practice as an explanatory variable of whether practices are “appropriately small” in the remainder of this section.

11 Among the assumptions underlying standard regression analysis is that two explanatory variables are independent.

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Figure 6.2 - Relationship between Population Density and Distance to next Nearest GP

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6.4. Using distance to next nearest GP practice as a criterion for defining whether practices are appropriately small.

If a practice is closed some patients will need to travel the full additional distance to the next nearest practice. However others will have smaller additional travel distances, for example when they are located part way between one practice and another, and some may have not further to travel at all. None will have a greater additional travel time than the distance to the next nearest GP, as they could travel to one location then on to the other. The average additional travel distance for patients will therefore be less than the distance to the next nearest GP.

The relationship between change in travel distance and distance to next nearest GP is shown in the chart below, which indicates that the additional travel distance for patients is typically about half of the distance to the next nearest GP. Thus, if the next nearest practice is 5km away the chart below shows that the average increase in travel distance will be about 2.5 km, consistent with the results of the regression analysis shown in Table 6-1 above. In some cases it will be more than this, and in some cases less. One instance of additional travel distance being greater than half the distance to the next nearest GP is the illustrative case of the small rural GP described above, where a GP 21 km away is removed and average travel distance increases by 20km. Indeed, as illustrated by the table above, in 31% of cases where the next nearest GP is 5 to 10km away the travel distance is over 5km, which implies that in these cases the additional travel distance is more than half the distance to the next nearest GP.

Chart 6.1 - Mean travel distance vs. mean distance to next nearest GP

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(mean) nt_min

(mean) change_d Fitted values

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The table below shows the additional annual travel cost for patients for specified additional travel distances based on the travel cost function reported in the previous section. This shows that an additional travel distance of 2.5km (equivalent typically to the next nearest practice being 5km distant) will result in additional travel costs per patient of approximately £31 p.a. based on an average number of 6 visits per annum. This additional cost per patient will be sufficient to outweigh the savings on merger for all except the smallest practices, as the economies of scale analysis show that additional costs per patient are as large as £31 only, on average, for practices with less than approximately 800 patients12. This accounts for less than one fifth of small practices and correspondingly less than 1% of the total practice population. Except in these cases it is therefore highly probable that additional patient travel costs will predominate if the next nearest practice is over 5km away.

Table 6.4 - Additional travel costs arising from additional travel distances.

Additional travel distance per one-way journey (km)

Additional travel cost per one-way journey (£ per patient)

Additional travel cost p.a. based on 6 two-way journeys (£per patient)

1.5 1.83 22 2.5 2.55 31 3.5 3.27 39

6.5. Prevalence of Unavoidably Small GP Practices

A lower distance cut off would increase the number of ‘eligible’ practices, a higher cut-off would increase the number of eligible practices. As noted these thresholds are inevitably arbitrary as

12 Based on analysis of non-dispensing practices.

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there is no single break-point covering all practices at which additional travel costs exceed savings from economies of scale.

However we note that in any case only a small proportion of practices are both small and distant from the next nearest practice. The number of practices in our sample is shown by distance to the next nearest in Table 6.5 below. Out of our sample of 7461 practices only 267 both have a list size below 1900 and are more than 1km distant from the next nearest practice, and only 148 have a list size below 1900 and are more than 2km distant from the next nearest practice. These totals would be somewhat larger if the complete population were considered. However many of the practices not in our sample are in London, so would not be far from the next nearest GP. Consequently the total population is likely to contain even fewer practices proportionately than the sample shown here.

Table 6.5 Number of large and small practice a certain distance from the next nearest GP

Next Nearest GP (network km)

Number of practices1,900+ <1,900 Total

1 3737 349 40862 1610 119 17293 316 15 3314 224 11 2355 167 15 1826 173 9 1827 154 6 1608 117 4 1219 107 8 115

10 68 4 7210+ 172 76 248

Total 6845 616 7461

Note: distances are maximum distance for the band, so a 2 in the left-hand column indicates that a practices are between 1 and 2 km from the next nearest.

As expected given the topography of Scotland there are a relatively high number of unavoidably small GP practices whilst the number of GP practices meeting this definition is smaller in both England and Wales. Because these GP practices have small list sizes they account for just under 0.3% of all registered patients in Great Britain.

When using a decision rule, such as awarding additional funding based on the distance to the next nearest practice, there are a inevitably number of practices that are identified as isolated when in reality they are not, that is the test produces some ‘false positives’. There will also be a number of isolated practices not identified using the decision rule i.e. ‘false negatives’. Correspondingly any decision rules for determining whether a GP practice is ‘appropriately’ located is likely to result in imperfect prediction. The smaller the distance to the next nearest practice the smaller the number of false negatives (that is practices that should receive additional funding but do not) and the larger the number of false positives (that is practices that should not receive additional funding but do).

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Instances of false positives and false negatives from predictive algorithms are inevitable, because such rules are always incomplete representations of individual practices situations. Such instances are common to all decision rules. We note that the regression analysis underlying the present formula only explains around half the variations in costs despite taking into account a wide range of variables. However the alternative of modelling each practice individually would imply a decision making process fundamentally different from that presently applied.

6.6. Conclusions

The analysis in this section indicates that:

For many, but not all, practices in rural areas the costs to patients if the practice were not there would exceed the savings.

In many of these cases the practice is small, implying that additional funding is required. Such practices correspond to the definition of “appropriately small” set out in Section 2 of this report.

The distance to the next nearest GP is a significant predictor of whether practices are appropriately small, and appears to be a better predictor than population density.

However there are few of these practices (only at most a few hundred in Great Britain) The total additional funding requirement is therefore likely to be small. This is discussed in more detail in the next section.

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7. Unavoidable Cost Adjustment

As noted in the introduction to this report, this work was intended to assess the effect of geographically dispersed populations on practice configuration. It was not intended to define the adjustment to the funding formula, which is a matter for the Review Group. However, in this section we describe how our analysis might be applied to developing an adjustment to represent unavoidable cost for small and isolated GP practices in order to aid consideration of these issues by the Review Group. This is intended to

illustrate the various forms in which the analysis might be applied;

provide an indication of the potential scale of any funding adjustments; and

illustrate the potential effects for certain ‘types’ of GP practice compared with the current Carr-Hill rurality adjustment and.

None of the material in this section, or elsewhere in the report is intended to recommend that any particular option or type of option be adopted. Any assessment of the appropriate means of implementing the formula is outside the scope of this study and would require further analysis and guidance from the Review Group.

7.1. Derivation of the Adjustment

There are many possible ways of setting a formula adjustment that reflects the additional costs of serving rural areas. These are illustrated in Table 7-1 below, which considers:

whether a rurality adjustment should be granted for a practice; and

how large that should be.

Table 7.1 – Required rurality adjustment

Decisions on whether a rurality adjustment should be granted for a practice

Variables driving decision on whether a rurality funding adjustment is required

Variables driving the decision of whether an adjustment is required could include:

Network distance to next nearest practice

Linear distance to next nearest practice

Average distance of population, which is used in the present formula

Density of population in area from which patients come

Variables involving distance to the next nearest practice could be modified to account for branch surgeries or other medical facilities

Whether decision is yes/no or probabilistic

A decision to make a funding adjustment could be binary (yes/no) or probabilistic, weighting the adjustment by the probability that a practice is appropriately small. This might, for example, take the form of an increasing weighting to the adjustment based on how far away the next nearest practice is, with those where the next nearest practice is very

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distant receiving more additional funding, other things being equal.

Varying the adjustment with list size

More demanding criteria (higher thresholds) could be required to justify additional funding for very small practices. As a purely illustrative example, some rurality adjustment might be granted to all small practices (list size less than 1900) more than 3km from the next nearest practice, but further rurality adjustment for very small practices (for example with list sizes below 1000) might only be granted in cases whether the practice is more than 8 km from the nearest practice. The rationale for this is that the smaller the higher costs of very small list sizes (e.g. 300 patients) may not be justified even in circumstances where small list sizes (e.g. 1500 patients) are justified by additional patient travel times.

Decisions on how large the adjustment should be

Degree of variation Adjustment could be:

Uniform for all small practices Banded according to list size Continuously variable as a function of list size

To what is it applied

The adjustment could apply to: Practice expenses per patient Total practice costs per patient

Basis of adjustments

Costs for non-dispensing practices Costs for all practices Whether the cost adjustment is based on all practices, or only

rural practices

We now briefly discuss examples of the type of rule set out in the table above to illustrate further the type of adjustment that might be implemented. We assume for the purposes of illustration that only small and isolated GP practices would be eligible for any additional funding. Any such adjustment would be likely to affect GP practices in isolated areas and would have no impact on the vast majority of practices.

We have based the illustration on a size adjustment derived form analysis of all practices. We note that there is substantial uncertainty in the estimate due to the amount of noise in the data. We have not separately analysed economies of scale in rural practices only. Rurality is one of many variable potentially affecting the size of any diseconomies of scale, and we would not expect any analysis for rural practices to lie outside the range of adjustments estimated based on data for all practices.

7.2. Comparison with the Current Approach

There are two main differences between the current approach and the approach we are proposing:

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GP practices which do not receive the unavoidable cost adjustment are given small

rurality adjustment constant across all practices and intended to find the higher costs of rural practices. In the current formula as GP practices become progressively more urban they continue to lose resources although at a decreasing marginal rate;

not all GP practices in rural areas receive an unavoidable cost adjustment, only practices which are isolated and small receive the adjustment.

Table 7.2 compares the effect of the current approach with the approach developed in this report for different types of GP practice.

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Table 7.2- Comparison of Rurality Adjustments

Illustrative Unavoidable Cost Adjustment Factor Type of GP Practice Current Deloitte

Urban: Small 0.960 0.995 Urban: Large 0.960 0.995 Rural: Large 1.100 0.995 Rural: Large and Isolated 1.100 0.995 Rural: Small 1.100 0.995 Rural: Small and Isolated 1.100 1.100

Source: Deloitte

The new approach would substantially reduce the coverage of the rurality and remoteness factor in the current GMS formula. This is further illustrated in the charts below. The first shows the distribution under the present funding formula, showing a wide range of variation with the majority practices receiving adjustments of more than 1% and many receiving adjustments of up to 10% in both directions. The second shows an illustrative distribution of adjustments under the funding adjustment assessed in this report. This shows a marked contrast to the present rule, with approximately 95% of practices receiving a small decrease in funding (approximately 0.5%) with the remaining 5% of practices (towards the top end of the likely range for the number of practices receiving additional funding) receiving additional funding ranging from 1% to approximately 20%. The case shown assumes adjustments to be based on the additional expenses for non-dispensing patients, with approximately half of small practices unavoidably small. The size of the adjustments and the number of practices receiving any given size of adjustment would, of course, depend on the actual decision rules and economies of scale factors chosen, the possibilities for which were summarised earlier in this chapter.

In addition to restricting the coverage of the rurality and remoteness adjustment the new approach would also break the automatic link between being in a rural area and gaining additional resources. Figures 7.1 and 7.2 overleaf illustrate the size and shape of the adjustment by population density. It demonstrates that under the Carr Hill approach practices in areas of low population density always gain under the adjustment (indices above 1.0 in low density areas) whilst only selected practices do under the new approach.

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Figure 7.1 – Distribution of the Carr Hill adjustment

Distribution of the Carr Hill adjustment

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Figure 7.2 – Illustrative distribution of Rurality Adjustment under method shown in this report

Illustrative distribution of rurality adjustment under method shown in this report

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8. Conclusions

This section summarises the conclusions from our work. These conclusions are subject to the caveats set out described in report and Annexes. Our main conclusions are as follows.

Conclusion 1. There is clear evidence of diseconomies of scale for practices with list sizes of below approximately 1900.

As list sizes fall below approximately 1900, practices show increases in costs per patient. Both expenses per patient and total costs per patient increase in a similar way. The increases conform to a model in which costs per patient are proportional to the reciprocal of list size (i.e. costs per patient are proportional to 1/list size). These increases are statistically significant, although a good deal of variation in the data is not accounted for by list size, as would be expected given the widely differing circumstances of small practices.

At list sizes of greater than 1900 no economies of scale are found for non-dispensing GPs. There is some evidence of economies of scale are found for dispensing GPs. It is not clear why there is this difference in behaviour but there are a number of possible reasons. Among the possible reasons is that dispensing costs, which are not shown separately in the data, account for a larger proportion of costs in smaller dispensing practices.

1900 is the approximate number of patients per GP across all practices in the sample. These results are consistent with the hypothesis of a single GP practice having largely fixed costs. At list sizes of up to 1900 these fixed costs are spread over a larger number of patients. At list sizes of greater than 1900, which represents full capacity for a GP, costs cannot be spread over a larger number of patients. Consequently no further economies of scale are realised.

The result of significant diseconomies of scale for smaller practices is broadly consistent with the Carr-Hill regression analysis which was used in setting the present formula. This analysis found significant diseconomies of scale for smaller list sizes.

We note that this conclusion is based on statistical analysis of existing cost and expenses. Our work did not include any analysis of whether such costs are efficiently incurred.

Conclusion 2. Our modelling results indicate that there are practices which are appropriately small because they serve a geographically dispersed population

The simulation work we have carried out shows that areas of low population density contain a number of instances where removing a practice would impose large additional travel costs on patients. These additional travel costs outweigh the potential economies of scale from larger practices. There are few, if any, such instances in areas of high population density.

Conclusion 3. Practices are most likely to be appropriately small if there are no alternative GPs nearby.

The likelihood that a practice is appropriately small, in that removing it would impose a large additional burden on patients, depends on:

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the distance to the next nearest practice; and

the density of the population in the area served.

Population density and distance to the next nearest GP are inversely related, although the relationship is not exact. In areas of low population density the distance to the nearest GP tends to be greater than in areas of high population density. These two variables thus appear largely to be measuring the same underlying phenomenon, the rurality of a practice. The regression results demonstrate that distance to the next nearest GP practice is a more reliable indicator than population density of whether a practice is appropriately small.

Conclusion 4. There is a range of possibilities for setting additional funding to appropriately small practices.

The approach described in this report implies a two stage process in awarding additional funding to small scale practices serving geographically dispersed populations:

deciding whether the practice is appropriately small; and

determining the scale of the additional funding required.

There are a number of approaches to deciding whether practices are appropriately small. Conclusion 1 indicates that small is likely to be defined as a list size of less that 1900. Conclusion 3 indicates that the decision on whether the practice is appropriately small may take account of its rurality, which may be measured by distance to nearest practice or, potentially, population density.

It is possible to estimate which practices are “appropriately small” using a simple algorithm which identifies rural and small GP practices, although there are significant numbers of mis-identifications compared with detailed simulations based on actual data. An algorithm could be modified to take account of branch surgeries or the availability of other medical services.

The magnitude of the additional funding required is provided by the analysis of diseconomies of scale, although the amount of variation in the data means that there is considerable and inevitable uncertainty about the magnitude of any adjustment. There are a number of different approaches to determining the magnitude of additional funding, as described in Section 7 of this report

Conclusion 5. The number of practices that are appropriately small is likely to be only a small proportion of the total. Additional funding is likely to be a small proportion of total funding.

Of approximately 10,000 practices in Great Britain only approximately 1000 (9%) have list sizes below 1900. Many of these are not likely to be classified as appropriately small because they are in urban areas. Thus, at most, between approximately 200 and 400 hundred practices are likely to be classified as appropriately small.

The additional funding per patient can be significant compared with average costs per patient but because the total number of patients involved is small total costs remain small relative to the total funding for practices. On one illustrative classification, total costs are £4-6 million p.a., although this figure could vary significantly depending on the actual decision rule chosen.

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Conclusion 6. There may be circumstances unconnected with geographical dispersion of population in which practices may be appropriately small.

There may be reasons for which practices are appropriately small for reasons unconnected with the geographical dispersion of population that is the subject of the analysis described in this report. For example, it is possible that small practices are necessary to maintain adequate access to services for example in urban areas of low car ownership and poor public transport provision. Study of such cases is beyond the scope of this report but raises issues which the Review Group may wish to consider.

Conclusion 7. Adjustment of funding to reflect scale of rural practices may replace or be additional to the present rurality adjustment. It is significantly different from the present rurality adjustment, creating significant changes for funding for many practices if used to replace the present formula.

The research described in this report was intended to identify the effects of geographical dispersion scale. The regression analysis on which the present funding is based also included an adjustment for scale in addition to the rurality variables included in the current adjustment which, by implication, were associated with increased costs for reasons other than their effect on scale. The effect of the rurality adjustment in the present formula is thus in principle distinct from scale, although may simply reflect previous funding patterns.

It would be possible to use the type of adjustment identified in this report in addition to the current rurality adjustment, or as a replacement, or to combine the two.

The type of adjustment described in this report would lead to significant changes in funding if it were to replace the present formula. This is because many practices receive funding adjustments of under the rurality formula adjustment, which can be positive or negative, typically by a few percent. Under the new formula most practices (in excess of 95%) would receive only a small reduction in funding to pay for the additional funding for the small number of practices receiving the new rurality adjustment.

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9. Appendix 1 – List of Variables

Variable

Obs Mean Std. Dev Min Max

Dependent Variables Distance > 5km 8176 0.076 0.264 0 1 Net Cost > £20 8176 0.101 0.301 0 1 Explanatory Variables 10% lowest density 8176 0.122 0.327 0 1 20% lowest density 8176 0.210 0.407 0 1 Nearest GP (km) 8129 2.299 3.775 0 67.42 Nearest GP 0-1km 8129 0.503 0.500 0 1 Nearest GP 1-3km 8129 0.295 0.456 0 1 Nearest GP 3-5km 8129 0.070 0.255 0 1 Nearest GP 5-10km 8129 0.093 0.291 0 1 Nearest GP 10>km 8129 0.039 0.194 0 1 Dependent Variables (truncated*) Distance > 5km 8012 0.067 0.250 0 1 Net Cost > £20 8012 0.092 0.290 0 1 Explanatory Variables (truncated*) 10% lowest density 8012 0.118 0.323 0 1 20% lowest density 8012 0.206 0.405 0 1 Nearest GP (km) 7977 2.194 3.287 0 41.03 Nearest GP 0-1km 7977 0.505 0.500 0 1 Nearest GP 1-3km 7977 0.297 0.457 0 1 Nearest GP 3-5km 7977 0.070 0.255 0 1 Nearest GP 5-10km 7977 0.092 0.289 0 1 Nearest GP 10>km 7977 0.036 0.187 0 1

* excluding GP practices with a population under 100 (n=285) and the 1st and 99th percentiles (n=164)

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10. Appendix 2 – Characteristics of GP Practices

Table 10.1 Average Characteristics of Unavoidably Small GP Practices

Isolated and Small (<1,900) Isolated and Relatively Small Metric No Yes No Yes

Population Density 45.12 9.17 46.39 13.55 Distance to GP (km) 3.26 6.97 3.16 5.81 Distance Alternative GP (km) 0.98 9.79 0.84 4.69 Urban Rural Category1 2.07 5.78 1.85 5.06 Morphology Score2 1.25 2.71 1.20 2.64

Source: Deloitte

1 urban rural category apply to Scottish data (1 urban 6 rural)

2 morphology scores apply to England and Wales (on a 1 to 4 scale)

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11. Appendix 3 - Precedents on Access from competition authorities

Access times are widely used for defining relevant geographical markets. Such market definition is often necessary in the assessment of the competition implications of mergers and acquisitions. We have referred to reports prepared by the Competition Commission and the OFT, which define the geographical markets of particular businesses as the areas within which the majority of customers are willing to travel.

To the extent that such travel times are considered reasonable for a particular business (or service), we can apply similar thresholds to our assessment of optimal GP configurations.

The reports considered relate to supermarkets, cinemas and betting shops.

Supermarkets Safeway plc Inquiry (Competition Commission 2003) Somerfield plc and Wm Morrison Supermarkets plc (Competition Commission 2005) The 2003 Safeway merger report defines local areas by drawing 10 to 15 minute drive times around each individual store, to create sets of ‘isochrones’ (lines joining points of equal travel time). The accuracy of the isochrones produced depends on the detail in the digitised road network software used in the analysis; more detail allows a better simulation of actual travel times.

Drive times of 10 minutes were used for urban areas and 15 minutes for rural areas (for these purposes, urban areas were defined as having a minimum population of 10,000). These times were decided based on empirical evidence suggesting that 80% of stores’ revenues are derived from these isochrones in each type of area.

Note that significant percentages of customers walk to supermarkets, particularly in rural areas. Therefore the distances walked were converted to drive times in order to more accurately capture the areas from which 80% of revenues are derived.

Such isochrones have been generally accepted and used in subsequent market investigations, including the 2005 Somerfield acquisition by Morrison.

The 10 and 15 minute times have been applied to ‘one-stop shops’ (stores at which customers can carry out their entire weekly shop); other access definitions were given to mid-range and convenience stores. For our purposes, however, a GP surgery may be compared to the ‘one-stop shop’, as there are no smaller-scale alternatives to which patients could go to receive equivalent medical care.

Cinemas

Acquisition by Terra Firma Investments of United Cinemas International and Cinema International Corporation (OFT 2005)

In assessing the local markets of cinemas (for the purposes of the acquisition of two rivals by Terra Firma Investments), the OFT has followed a similar method as the Competition Commission supermarket reports. Isochrones, based on drive times were developed with the assumption that the typical catchment area for a cinema is a drive time of 20 minutes.

This greater drive time for cinemas appears reasonable given that cinemas are more of a destination than a convenience; and people generally go to the cinema less often than the supermarket.

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Note that the report states that it is not appropriate to model Central London using this approach, due to the prevalence of other modes of transport and diverse audiences.

Betting shops Acquisition by William Hill plc of the licensed betting office business of Stanley plc (OFT 2005) The isochrones for betting shops tend to be formed on the basis of walking. Per the OFT, there is evidence to suggest that customers are not prepared to travel far to place bets. Isochrones of 400m are considered an appropriate measure by most parties; though it is argued that 400m applies better to urban areas with high population density; and that 800m should be used for less dense towns with fewer betting shops.

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12. Appendix 4 - Analytical solution to rurality adjustment of GMS

We define the problem as minimisation of total costs per patient as a function of the scale of practice (as measured by list size). Total costs comprise practice costs and travel costs incurred by patients, so the requirement is to minimise: C = P(s) + T(s) With respect to s, where: s = list size C = total cost per patient P = practice costs per patient T = travel costs per patient Practice costs are assumed to be of the form: P(s) = Fs-p + V Where: F = Fixed costs V = variable costs p is the economies of scale factor, usually 0<p<1, with 1 representing the case where costs represented by F are completely invariant with scale (as measured by number of patients) and 0 representing the case where all costs are variable, so costs per patient do not vary with scale of practice. This functional form is consistent with the assumptions for list size effects in the Carr Hill analysis, which found a value for p of 0.34 at the practice level and 0.76 at the GP level.

Travel costs are assumed to be of the form: T(s) = c.s0.5 .d-0.5

Where: c is a constant related to unit travel costs d is population (needs weighted) density measured in (needs weighted) patients per sq. km. The rationale for this formula and the assumptions on which it is based are described further below. Combining these functions gives: C = Fs-p + V + c.s0.5 .d-0.5

Differentiating with respect to s and setting equal to zero to get First Order Conditions, then rearranging gives: s = (p/c) (1/(p+0.5)). d (1/(2p+1))

In the case of p =1, that is costs are either completely fixed or variable, this equation shows that optimum list size varies with the population density to the power 1/3. The case of p = 0.34 from the Carr hill

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analysis it shows optimum practice size to vary with population density to the power 0.6, with the constant also varying with p. Basis for travel cost function The travel cost function is based on the following main assumptions

population density is uniform within the area served; and travel costs are proportional to geometric distance from the practice.

Neither of these assumptions is likely to hold in consistently practice, and the extent of divergence is examined as part of our modelling work. In particular travel costs will often not be a linear function of geometric distance, although this variable is used as an indicator of rurality in the present formula. Despite these simplifying assumptions, the function give a useful indication of the form of the relationship between optimal scale and rurality as measured by population density. It can be modified to deal with non-linear relationships between travel costs and geometric distance if required. Relationship of travel costs to population density. Travel costs increases with the square root of the reciprocal of population density. For example, if the same number of people is spread over four times the areas density decreases by a factor of four while linear distances double. This is illustrated in the figure below.

x 2x

Linear travel distances double, density decreases by a factor of 4 Similarly,if spread over nine times the area travel costs triple. This implies a relationship of the form: T(s) = k /d 0.5 for a given list size.

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Relationship of travel costs to practice configuration. Consider moving from a four practice configuration to a one practice configuration, as illustrated below.

List size increases by a factor of four, but travel costs only double. Again it is a square root relationship so: T(s) = k .s0.5 for a given density. Combining the results for population density and list size indicates that: T(s) = c.s0.5 .d-0.5

As a sense check of this formula we note the following. If practice configuration remains unchanged and the number of people in the area served increases by a factor q then both list size, s, and population density, d, increase by a factor q. However is these people are spread evenly, in line with the assumption of uniform population density, travel times are unchanged. This implies that the ration of list size to population density is invariant with q, i.e.: c.f(s)/f(d) = c.f(qs)/f(qd). In practice this is likely to mean that the functions for s and d have the same exponent but of the opposite sign. This is consistent with the modelled result of exponents of 0.5 and -0.5.

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