Development of a resource allocation formula for substance misuse treatment

services

Andrew Jones 1, Karen P Hayhurst 2, Will Whittaker 3, Thomas Mason 3, Matt Sutton 3

Andrew Jones, Research Fellow: andrew.jones@manchester.ac.uk

Karen P Hayhurst, Research Fellow: karen.hayhurst@manchester.ac.uk

Will Whittaker, Lecturer in Health Economics: will.whittaker@manchester.ac.uk

Thomas Mason, Research Associate: thomas.mason@manchester.ac.uk

Matt Sutton, Professor of Health Economics: matt.sutton@manchester.ac.uk

1 Centre for Epidemiology, Division of Population Health, Health Services Research and Primary Care, School

of Health Sciences, University of Manchester, Manchester, M13 9PL, UK

2 Centre for Mental Health and Safety, Division of Psychology and Mental Health, School of Health Sciences,

University of Manchester, Manchester, M13 9PL, UK

3 Manchester Centre for Health Economics, Division of Population Health, Health Services Research and

Primary Care, School of Health Sciences, The University of Manchester, Manchester, M13 9PL, UK.

* Corresponding Author: Karen P Hayhurst, Centre for Mental Health and Safety, Division of Psychology and

Mental Health, University of Manchester, Manchester, M13 9PL, UK.

Email: karen.hayhurst@manchester.ac.uk Tel: +44 (0) 161 275 8365. Fax: +44 (0) 161 275 1668.

1

Development of a resource allocation formula for substance misuse treatment

services

Abstract

Background Funding for substance misuse services comprises one third of Public Health spend in England. The

current allocation formula contains adjustments for actual activity, performance and need, proxied by the

Standardised Mortality Ratio for under-75s (SMR<75). Additional measures, such as deprivation, may better

identify differential service need.

Methods We developed an age-standardised and an age-stratified model (over-18s, under-18s), with the

outcome of expected/actual cost at postal sector/Local Authority level. A third, person-based model

incorporated predictors of costs at the individual level. Each model incorporated both needs and supply

variables, with the relative effects of their inclusion assessed.

Results Mean estimated annual cost (2013/14) per English Local Authority area was £5,032,802 (sd 3,951,158).

Costs for drug misuse treatment represented the majority (83%) of costs. Models achieved adjusted R-squared

values of 0.522 (age-standardised), 0.533 (age-stratified over-18s), 0.232 (age-stratified under-18s) and 0.470

(person-based).

Conclusion Improvements can be made to the existing resource allocation formulae to better reflect population

need. The person-based model permits inclusion of a range of needs variables, in addition to strong predictors of

cost based on the receipt of treatment in the previous year. Adoption of this revised person-based formula for

substance misuse would shift resources towards more deprived areas.

2

Introduction

Where local public services are funded through central government taxation, the distribution of local allocations

presents a significant challenge.1 In England, the healthcare budget is split into sectors of care, each with a

resource allocation formula. In 2012, public health responsibilities were transferred to Local Authorities (LA);

regional bodies responsible for the delivery of a range of local services.2 There was no previous formula in place

for the allocation of public health funds; a preliminary formula was generated to allocate LA public health

budgets (£2.5bn in 2013-14; 2.6% of total health care expenditure).3,4 The Department of Health commissioned

research in 2014 to derive needs-based resource allocation formulae for drug and alcohol services (representing

31.5% of total public health expenditure), sexual health services (22.3%), and other public health services

(46.2%). This paper describes the approach taken to inform the formula for drug and alcohol services.

Most healthcare systems aim to provide services based on the need for care. Reducing inequality in access

and/or health has therefore become a key policy commitment.5 Distributing resources on the basis of need

maximises the efficiency of allocations.1,6 A key requirement of this approach is the ability to identify the need

for healthcare. Utilization of healthcare can be used as a proxy for need, but this can be problematic, as use of

services is influenced by issues of access (availability of services; patient acceptability of care; affordability).

Service use, alone, may not reflect underlying need.7,8

Resource allocation formulae have been used in healthcare in England since the 1970s. Originally, geographic

allocations were driven by historical expenditure. Carr-Hill and colleagues proposed utilization-based models,

with costed utilization modelled against a range of potential needs measures.9 The resulting needs estimates

informed needs indices, used to generate weighted population-based budget shares. Methodological advances

have addressed the extent to which utilization data reflect access to healthcare, rather than need for healthcare.

Later developments introduced regional-level indicators to control for differences in supply (access) and non-

need variables to control for differentially-met need (‘unmet need’).10 Subsequent refinements proposed one-

stage stratified models, allowing the effects of need variables to vary across age categories and for the effects of

age to be estimated, conditional on variation in supply.11 More recently, person-based allocation methods,

preferred where appropriate data are available, have been used for acute hospital12 and mental health services.13

The current substance misuse resource allocation formula3 is based on actual activity (76% weighting in 2014-

15), need (proxied by the Standardised Mortality Ratio (SMR) in under 75 year olds; 24% weighting), and

performance (20% weighting in 2013-14, 0% after). Treatment activity figures are partitioned into opiate and/or

crack cocaine users (OCU) and non-OCUs. This may be improved as: SMR is a narrow measure of need - other

factors, e.g. deprivation, may better identify need for drug and alcohol services; supply-side and unmet-need

biases were not accounted for; and analyses were conducted at an aggregate level. We aimed to develop needs-

based formulae for distributing resources for substance misuse services. This entailed:

(1) Expanding measures of need;

(2) Accounting for supply-side influences on service use;

(3) Estimating relative need using person-level data.

Methods

3

Data sources

Utilization data were sourced from the National Drug Treatment Monitoring System (NDTMS). NDTMS

routinely collects data on the use of structured community-based or residential treatment for drug or alcohol

misuse in England. The most recent available data (2013/14) were used, relating to c. 319,000 individuals

engaging in c. 413,000 treatment episodes. Area of residence was defined by the combination of postcode sector

and Local Authority (LA), creating the most granular area of residence available within this dataset (n=10 039

areas). Multiple areas were created where more than one sector was contained within a LA or where sector and

LA were not coterminous. Mid-year population estimates by age, sex and postcode were obtained from the

Office for National Statistics (ONS) and converted into the Post Sector/LA level areas.

A literature search informed potential needs variables. Drug treatment clients are characterised by male gender,

white ethnicity, involvement in crime, poor mental and physical health, unstable accommodation,

unemployment, receipt of welfare benefits and previous drug treatment episodes.14-16 Drug and alcohol misuse in

the community has been associated with additional factors, including population density,17 urbanicity,18

neighbourhood instability,19 homelessness,20 low socio-economic status,18 disadvantaged background,21 poor

school performance,21 teenage pregnancy22 and single parenting.18 These were sourced from area-level 2011

Census data, Index of Multiple Deprivation (IMD 2010) and Neighbourhood Statistics and included the

following rates: benefit claimants; lone parents; unemployment; 16+ population with no qualifications;

population turnover; under-18 conceptions; and homelessness, in addition to SMR, ethnicity, average household

size and indicators of population density. Data were required to be readily available, routinely updated and

statistically robust with coverage across England.

The needs of young people attending substance misuse services can differ from those of adult clients. In

particular, young people are more likely to present with problematic cannabis use than adult clients, which may

be associated with different predictors. Younger people are also less likely than adults to present with

problematic use of alcohol.23

Where data points were missing because of changes to geographical output areas, 2011 area data were

calculated using ONS best-fit lookup tables.24 Remaining missing data points were calculated using the mean

score of neighbouring areas. LSOA-, MSOA- (middle-layer super output area, n=6,791) and LA-level (n=151)

predictor variables were mapped into post sector/LA areas by weighting on postcode populations.

Supply variables (extracted from NDTMS) included mean waiting times, the distance (km) from post sector

centroid to postcode of the nearest drug treatment service, and the proportion of substitute prescribing accounted

for by GPs. As a source of prescribing not sourced via public health budgets, the latter measure acted as a proxy

of additional capacity and treatment choice.

Costs

Average costs per day of individual structured drug and alcohol interventions were obtained from Public Health

England (PHE). Costs were derived from a 2008/09 survey of treatment agencies (PHE unpublished data) to

4

which inflationary uplifts were applied. Total costs, accounted for by NDTMS-recorded interventions, in

2013/14 were £920 million.

Costs which could not be assigned to an area (5% of total), as client area of residence was not recorded, were

assigned geographically, according to the distribution of known cases. Where postcode sector was not recorded,

costs were redistributed within the LA, weighted by known treatment costs by age group within that LA. Where

LA was missing, costs were redistributed nationally, weighted by known treatment costs by age group

nationally.

Analysis

Our analytical approach was to replicate approaches that have been used previously for other elements of health

funding in England. Three approaches have been used: (i) age-standardised models, (ii) age stratified models,

and (iii) person-based models.

A series of models used both needs and supply variables to predict area-level cost of substance misuse service

provision. The inclusion of supply measures reduces confounding on the needs estimates where correlations

exist between the supply and needs measures, and supply and costed use.

A series of stepwise regressions determined inclusion of needs variables in the final models with the order of

inclusion determined by the relative coefficient size of associations between covariate z-scores and the

dependent variable. Covariates with a high degree of collinearity with other variables (VIF > 5) were removed.

The resulting covariate set was entered into linear regression models, accounting for Upper Tier Local Authority

(UTLA), the administrative area responsible for commissioning drug and alcohol treatment provision.

The coefficients of the needs variables were used to generate the needs index. This adds needs-specific

“weights” to areas at the commissioning level (UTLA). The inclusion of supply measures in the regression

analysis but exclusion in the needs index serves to ‘sterilise’ the formula from reflecting supply-side access bias

due to the removal of observable supply-side confounding on the needs estimates.25

Analyses used SPSS version 20 and STATA version 13.

Model 1: age-standardised model

A model was developed to examine predictors of small-area variation in the age-standardised ratio of actual cost

to expected cost (1-year period). This was the approach used prior to the CARAN (Combining Age Related and

Additional Needs) review.9 Areas with a small population size (n < 30, 7%, n=673) were excluded to avoid

undue leverage on the model by extreme cost ratio values. Expected cost was obtained by calculating national

cost per capita for eight age bands (<15, 15-19, 20-24, 25-29, 30-44, 60-64, 65+) and applying these costs to

each area, using age-specific 2011 population data. Analyses were weighted by expected costs for each area.

Since the need for drug services and alcohol services may differ we estimated three models: all service use, drug

services only, and alcohol services only.

Model 2: age-stratified model

Model 1 assumes the effects of the needs measures are the same across all age groups. Model 2 relaxes this

assumption by analysing predictors of small-area variation in the ratio of actual to expected cost separately for

5

different age groups. This was the econometric approach taken in both the CARAN and the RAMP (Resource

Allocation for Mental health and Prescribing) review.26 Younger clients in treatment may differ from over-18s.

Separate analyses were therefore performed for over-18s and under-18s. Areas with small (n < 30) adult (18+)

populations (n=760) and under-18 populations (n=1333) were excluded.

Model 3: person-based model

A model was developed to investigate predictors of costs at individual level using previous year supply-

independent risk markers to predict costs in the current year. This was the approach used in the PRAM (Person-

based Resource Allocation formula for Mental Health) review.13 Measures of past-year treatment utilization

(days of treatment received, whether treatment was completed and receipt of substitute prescribing) were

incorporated into the model and used to predict 2013/14 expenditure at the individual level. We also included

area-level needs variables stratified by age group. Cases with known receipt of treatment but unknown area of

residence were excluded. Non-users of services were included with zero costs, with cases aggregated by age

group and area. The model was weighted by area population, set to one for individual case data.

Results

Mean recorded annual (2013/14) cost of treatment per LA area was £5,032,802 (sd 3,951,158). Drug misuse

costs comprised the majority (83%) of substance misuse treatment costs (mean £4,107,650, sd 3,398,499) with

costs of alcohol misuse treatment considerably lower (mean £108,042, sd 694,558). Costs for under-18s

represented 2% of total costs.

Model 1: age-standardised model

Figure 1 shows the age specific per-capita costs used to calculate area-level expected costs for drug and alcohol

misuse treatment. Costs peaked within the 30-44 age group; more sharply for drug services. The age-

standardised model for combined drug and alcohol misuse costs had an adjusted R-squared of 0.522 (see Table

1). Significant predictors of the ratio of actual to expected cost were SMR, the IMD domains of Crime,

Environment, Income, population turnover, proportion male and proportion white British. Significant supply

variables were the proportion of GP prescribing and distance to nearest service. The inclusion of needs

variables (in addition to SMR) reduced the coefficient associated with SMR by 40% and increased the adjusted

R-squared substantively (from 0.470 to 0.517). Despite significant associations, the addition of supply variables

made little difference to the overall explanatory power of the model, increasing the R-squared from 0.517 to

0.522.

Predictors common to both the drugs misuse and the alcohol misuse model were SMR, IMD Crime, IMD

Environment, population turnover, proportion male and proportion white British. A significant predictor in the

drugs model but not the alcohol model was IMD Income. The final alcohol model contained the IMD mood and

anxiety indicator; not a significant predictor in the drugs model. The final models achieved an adjusted R-

squared of 0.513 for the drugs cost ratio but performed less well for the alcohol cost ratio (adjusted R-squared =

0.334).

6

Model 2: age-stratified model

Table 1 also shows the age-stratified model, applied separately to young people (under-18s) and adults (18+).

The removal of the under-18s from the all-age group increased the adjusted R-squared statistic from 0.522 to

0.533. The model performed less well in the under-18s group (adjusted R-squared = 0.232. Variables which

were significant predictors of the over-18s group were not significant in the under-18s (IMD Income, IMD

Environment, proportion male, proportion GP prescribing and distance to nearest service). Mean waiting time

was not significant in the over-18s but was in the under-18s. Additional potential predictor variables, such as

proportion in full-time education, were explored to determine whether a better-performing model could be

obtained for the under-18s but an adjusted R-squared of higher than 0.232 could not be achieved.

Within a drugs-only model a higher adjusted R-squared (0.526) was achieved for over-18s but was decreased (to

0.169) for under-18s. Within an alcohol-only model, a lower adjusted R-squared was achieved for both over-18s

(0.327) and under-18s (0.160).

Model 3: person-based model

Table 2 presents the results of the person-based model for drug and alcohol misuse combined. The best-

performing predictors in the model were: received prescribing in the past year; days treated in the past year; and

whether treatment was completed in the previous year. These three variables together (plus age dummy

variables) explained 46.9% of the variance in expenditure. The addition of other needs variables (SMR,

population turnover and proportion male) and supply variables did not add substantially to the final adjusted R-

squared statistic (0.470). When aggregated to area level for the purposes of comparison with other models, an R-

squared statistic of 0.560 was achieved.

Separate person-based models for drug and alcohol misuse services were considered. As with the combined

model, the three best explanatory variables in both the drugs misuse and the alcohol misuse models were:

received prescribing in the past year; days treated in the past year; and whether treatment was completed in the

previous year. An adjusted R-squared of 0.490 was obtained in the drug misuse model and a much lower

statistic (0.021) in the alcohol misuse model.

Impact of adoption of revised formula on target share

Figure 2 summarises the impact that adoption of the revised person-based formula for substance misuse would

have on existing target share. This shows the size of the impact plotted against a measure of overall deprivation

(IMD 2010) and the proportion of young adults (18-30 year olds) for each LA. Adoption of the revised formula

would have a net effect of redistributing more resources towards more deprived areas (higher IMD 2010 score).

There is no corresponding shift in resources toward areas with a higher or lower proportion of young people.27

Discussion

We developed age-standardised, age-stratified and person-based models of substance misuse treatment costs by

Local Authority in England, incorporating both need and supply variables to predict area-level variation in the

costs of service provision. These were designed to better inform the allocation of substance misuse-specific

public health budgets.

7

Main findings of this study

The age-standardised model performed well in predicting variation in the ratio of expected to actual cost by area

(R-squared=0.522). A separate model for alcohol misuse performed less well than that for drug misuse. The

age-stratified model performed well for over-18s (R-squared=0.533) but poorly for under-18s (R-

squared=0.232). The person-based model permits the use of a wider range of predictor variables, in particular,

very strong predictors based on past-year treatment history. Predictive power was high for a model based on

individual-level data (R-squared=0.470) and conversion to area-level data for comparison purposes identified

this model as the strongest of the three. For these reasons, we prefer the use of a person-based model of drug

and alcohol misuse services.

What is already known on this topic

Resource allocation formulae have been used in healthcare in England since the 1970s. Needs estimates were

generally amalgamated into a needs index, used to generate weighted populations to inform budget share.

Developments introduced regional-level indicators to control for differences in supply (access) and non-need

variables to control for differentially-met need.10 Subsequent refinements incorporated age-stratification. More

recently, person-based models have been developed where individual-level data are available. The existing

substance misuse allocation formula3 is based on actual activity, need (SMR<75), and performance. However,

SMR is a narrow measure of need, supply-side and unmet-need biases were not accounted for and analyses were

conducted at an aggregate level.

What this study adds

We aimed to develop a needs-based formula for distributing resources for substance misuse services that:

expands the measures of need over that used currently; accounts for supply-side influences on the use of

services; and estimates relative need using individual-level data.

We expanded on current measures of previous year service use data (incorporating days treated, treatment

completion, receipt of prescription) and these were found to be strong predictors of current service use.

Expanded measures of need, including population turnover and proportion male were also significant predictors

of cost. The R-squared statistic achieved by our person-based model (0.470) was higher than that seen in similar

work (0.123) to develop formulae to allocate resources for hospital care.12

Our analysis has shown that it is possible to generate statistical models that predict the costs of substance misuse

services using measures of population need and supply characteristics. This included approaches to reduce

confounding due to observed supply-side provision differences. A range of needs measures were consistently

found to predict service use: SMR, the proportion of males in an area, age, and population turnover. The ability

to identify previous service use substantially improves explanatory power.

These models can be used to generate budgets that reflect variations in need across areas and therefore direct

limited resources where they are needed most. Internationally, public health policies have the central aim of

tackling inequalities in health. 5 Socioeconomic factors, such as income and education, together with physical

and social environmental factors, such as crime, are the main determinants of health inequalities. 5 Of note, three

IMD domains of deprivation, Income (models 1 and 2), Environment (models 1 and 2) and Crime (model 1)

8

were important predictors of the ratio of actual to expected cost in our models, demonstrating the pivotal role of

deprivation in describing the need for drug and alcohol misuse services. Adoption of our revised person-based

formula for substance misuse would shift resources toward more deprived areas, thereby tackling health

inequalities. At the time of writing, these models had not been adopted by the English Department of Health.

Limitations of this study

The available geographic level of analysis (postcode sector/ LA combination) did not directly match that of

available socio-demographic data, requiring the use of weighted population estimates.

Separate tariffs for alcohol or young people’s services were not available; costs were estimated based on adult

drug service estimates. Explanatory power was lower for alcohol and young people’s models. There may be

other predictors of these services that are not routinely collected. Although the alcohol model was not as strong,

the best alcohol misuse model was highly correlated with the drug misuse model (r = 0.994); a combined model

for drug and alcohol misuse was therefore recommended.

Whilst we were able to model observed confounding, there remains the possibility of unobserved confounding

due to excluded supply-side factors that are correlated with our needs variables. There may also be measures of

need that we have failed to source but that are valid and strong predictors of service use.

There are limitations of the existing approaches. First, the age-standardised approach may lead to biased age

estimates – should these be correlated with the additional needs measures they could over- or under-represent

the effects of age. In addition, such models impose a restriction that the additional needs measures have the

same proportionate effect for all age groups. Age stratified models alleviate this issue to an extent, enabling

additional needs measures and their estimated effects to vary across age groups. The recent transition towards a

person-based approach enabled historic risk information for each individual captured in prior diagnoses to be

factored into the formula. There is a concern that this information may contain non-need influences, such as

supply factors that influence the probability of diagnosis. As a consequence, it is recommended to include a rich

set of supply variables and include risk markers that are as independent as possible from unmeasured supply

factors.28

In common with previous approaches to estimating resource allocation formulae for health care services in

England, we have analysed variations in cost-weighted utilisation and assumed that, once the effects of supply

variables have been controlled for, the effects of population characteristics reflect differences in need. If there is

systematic unmet need for some population groups, or differences in quality and effectiveness across population

groups, this assumption is not met. The adoption of utilisation to measure equity has been disputed for many

years, 29,30 but remains the preferred practical compromise in the absence of less imperfect, comprehensive

measures of the need for resources.31

9

Disclosure of potential conflicts of interest

None

Funding

This work was supported by the UK Department of Health (DH) Policy Research Programme (grant number

085/0010). The views expressed are the sole responsibility of the authors and do not necessarily represent those

of TAG, ACRA or the Department of Health.

Acknowledgements

We are grateful to members of the DH Technical Advisory Group (TAG) and the DH Advisory Committee on

Resource Allocation (ACRA) for advice and comments and specifically would like to thank Michael Chaplin,

Stephen Lorrimer and Keith Derbyshire from the Department of Health and Virginia Musto of Public Health

England for their guidance and advice.

Disclaimer

This report relates to independent research commissioned and funded by the Department of Health Policy

Research Programme.The views expressed in this publication are those of the author(s) and not necessarily

those of the Department of Health, ‘arms’ length bodies and other government departments.

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Fig. 1 Mean annual costs per capita for drug and alcohol misuse treatment by age group (2013-14 data).

Table 1 Age-standardised and age-stratified models, drug and alcohol misuse, 2013/14 data

Variable All ages (standardised) 18+ yrs only Under 18 yrs only

SMRa 0.025** 0.015** 0.015** 0.017** 0.006**

[0.001] [0.001] [0.001] [0.001] [0.001]

IMD Crime 0.414** 0.389** 0.451** 0.261**

[0.024] [0.024] [0.027] [0.037]

Population turnover b 0.006** 0.006** 0.005** 0.005**

[0.001] [0.001] [0.001] [0.001]

Proportion white British 0.790** 0.829** 0.535** 1.177**

[0.093] [0.093] [0.111] [0.160]

Proportion male 4.174** 4.189** 6.339** 1.661

[0.861] [0.862] [1.020] [1.151]

IMD Income 0.632** 0.631** 0.731** -0.020

[0.120] [0.119] [0.138] [0.216]

IMD Environment 0.003** 0.003** 0.004** 0.002

[0.001] [0.001] [0.001] [0.001]

Proportion of GP prescribing -0.571** -0.630** 0.148

[0.051] [0.059] [0.107]

Distance to nearest service c -0.01** -0.01** -0.006

[0.002] [0.002] [0.004]

Mean waiting time -0.002 -0.002 -0.008**

[0.001] [0.001] [0.002]

Adj. R-squared 0.470 0.517 0.522 0.533 0.232

Notes: * p < 0.05. ** p < 0.01. a Standardised Mortality Ratio. b Outflow rate all ages: rate per 1000 (2009-10). c Distance (km) from post sector centroid to post code of the nearest treatment service. The dependent variable is the indirectly-standardised cost ratio. Unit of observation is the postcode sector/local authority combination (n=9,366). Robust standard errors in [ ]. All models include indicators for each Upper Tier Local Authority.

Table 2 Person-based model, all ages, 2013/14 costs of drug and alcohol misuse treatment.

i ii iii ivAge

Age (15-19 years) 3.09** 1.06** 0.96** 0.99**

[0.167] [0.101] [0.108] [0.113]

Age (20-24) 7.01** 1.11** 0.59** 0.64**

[0.243] [0.135] [0.141] [0.146]

Age (25-29) 22.31** 4.30** 3.95** 4.04**

[0.421] [0.187] [0.191] [0.197]

Age (30-44) 42.17** 8.14** 8.12** 8.37**

[0.598] [0.165] [0.169] [0.177]

Age (45-59) 16.81** 2.36** 2.55** 2.64**

[0.287] [0.114] [0.119] [0.125]

Age (60-64) 2.93** -0.21* 0.09 0.11

[0.177] [0.103] [0.108] [0.114]

Age (65+) -0.11 -0.65** -0.33** -0.34**

[0.149] [0.077] [0.083] [0.088]

Individual treatment history

Days of treatment previous year 10.31** 10.31** 10.32**

[0.042] [0.042] [0.042]

Completed treatment previous year -1640.84** -1641.03** -1644.97**

[6.475] [6.474] [6.527]

Received prescribing previous year 1316.24** 1315.91** 1319.25**

[13.569] [13.569] [13.658]

Area characteristics

SMR a 0.05** 0.05**

[0.003] [0.003]

Population turnover b 0.03** 0.03**

[0.002] [0.003]

Proportion male 25.92** 30.05**

[3.856] [4.257]

Supply variables

Proportion of GP prescribing -8.55**

[0.351]

Distance to nearest service c -0.06**

[0.012]

Mean waiting time -0.01

[0.009]

Adjusted R-squared 0.025 0.469 0.469 0.470Notes: * p < 0.05. ** p < 0.01. Reference category is age group 1 (under 15). a Standardised Mortality Ratio. b Outflow rate all ages: rate per 1000 (2009-10). c Distance (km) from post sector centroid to post code of the nearest treatment service. The dependent variable is drug and alcohol misuse expenditure for 2013/14. Unit of observation is the individual (n=53,085,707). Robust standard errors in [ ]. All models account for UTLA.

Fig. 2 The impact of changing the substance misuse formula on LA target shares.

Notes: solid circles indicate an increased target share, open circles a reduced target share, with the area of the circle proportional to the impact (London in solid red / bold, other in solid blue / faint). Figure reproduced with permission from: Advisory Committee on Resource Allocation (ACRA) and the Department of Health, London (2015) Public health grant: proposed target allocation formula for 2016/17, https://www.gov.uk/government/consultations/public-health-formula-for-local-authorities-from-april-2016