Approach
An economic model was constructed to synthesise clinical and economic data to
estimate the incremental cost per unit of outcome gained by diversion and
aftercare interventions. The perspective taken was that of the CJS, NHS and
social care providers and offenders. These comprise the key components of a
societal perspective. The consequences of offending behaviour for victims are
included indirectly by including the costs to victims in the cost estimates of
offences.
Current practice varies in the diversion and aftercare packages and sequence of
treatment and support interventions used. In the UK, the main approach is the
DIP. However, this varies in the intensity and range of approaches used to
identify, assess and refer substance using offenders to treatment and aftercare.
For the primary analysis, the diversion and aftercare intervention was broadly
defined to cover the variety of interventions provided in the UK. Sensitivity
analyses were used to explore the impact of varying the intensity and scope of
the DIP on the probability of reoffending, costs and outcomes.
The comparator for the primary analysis is no formal identification and
assessment process to refer substance-using offenders into treatment and
aftercare. The model includes the fact that a proportion of offenders will
already be in contact with treatment services at the time of arrest or will
engage with treatment and aftercare services. This may be by informal referral
or advice from the CJS or by another route. This applies to both the
intervention and comparator arms of the model.
The measures of health benefit for the economic analysis were the
quality-adjusted life-year (QALY) for the primary analysis and life-years gained
for the sensitivity analysis. In addition, proxy measures of outcome were used
in the sensitivity analysis to estimate the incremental cost per person
reoffending and incremental cost per person using class A drugs.
The time horizon for the primary analysis is the 12 months following the index
contact with the CJS. The evidence about the relative long-term benefits (in
terms of reoffending, drug use and health status) of diversion and aftercare is
limited and uncertain. It is also confounded by the type and effectiveness of
treatment and aftercare interventions used. In addition, the use of a time frame
longer than 1 year for the analysis, with a high level of uncertainty about
these outcomes of treatment, may mask the costs, outcomes and uncertainty
resulting from the use of the alternative diversion and aftercare packages. The
long-term impact (5 and 10 years) is explored in sensitivity analyses (see
Sensitivity analysis and key assumptions) and discounted at
3.5% as recommended by the National Institute for Health and Care Excellence
(NICE).102
Data sources
The economic model was intended to synthesise clinical and economic data from the
systematic reviews carried out as part of the project, together with that
obtained from available databases of observed data. It was anticipated that
insufficient data would be obtained from the existing published literature to
fully populate the economic model with data on the probabilities of events,
UK-specific cost data or with final health-related measures of outcome such as
QALYs. Relevant data on outcomes, costs and events were therefore extracted from
a range of sources (detailed below) to populate the economic model for the
primary analyses. Data from the effectiveness review were used to estimate
probabilities of reoffending for the sensitivity analyses to explore the impact
of different types of diversion programme.
The Drug Data Warehouse (DDW)103
is a case-linked collection of national data sets relating to substance users in
England and Wales between 1 April 2005 and 31 March 2009. It includes data from
prison and probation services, criminal justice referral and/or drug testing on
arrest schemes, and drug treatment services (England only), with additional
linkage to criminal records data from the PNC. The DTORS26,50,104 was a
longitudinal, observational, multisite cohort study, recruiting from 342
agencies within 94 Drug Action Teams in England during 2006/7. A
cost-effectiveness analysis was carried out alongside DTORS.42 Additional data sources included
UK Home Office reports.105–107 These
were supplemented with unit costs of CJS estimated by the Home Office
specifically for the DTORS analysis.42 Cost data were adjusted to reflect 2012 prices using the annual
percentage increase in the Retail Price Index, as recommended by The
Green Book. Appraisal and Evaluation in Central Government,108 and accessed via the Office for
National Statistics (ONS).109
Economic model
Population
The population for the model is opiate- and/or crack-using offenders who come
into contact with the CJS. Offenders who are already in contact with
treatment and aftercare services are included in this population since a
proportion will have a new referral via the diversion service. The model for
the primary analysis focuses on people who will receive a community-based
sentence. This implies that the type of sentence is known before the
decision to refer a person via the DIP. The rationale for this is based on
the following factors:
The majority of substance users report offences that would typically
attract a community rather than custodial sentence, such as
shoplifting, buying and selling stolen goods, other stealing.
26In the UK, there is no formal link between involvement with DIP and
those sentencing options determined by the court, although having
sought treatment may impact on the court’s decision.
There is a paucity of data with which to estimate the proportions who
would receive a community, custodial or no sentence with and without
DIP.
However, the Drug Interventions Programme Operational
Handbook39 is
clear that the decision to use DIP should be made when a person is
identified as a substance user at the point of arrest and before the
sentence for the offences associated with the index arrest is known. In
addition, for a proportion of people committing minor offences, the volume
of repeat offending may lead to a custodial sentence. The relative
cost-effectiveness of DIP for the broader population of substance user
arrestees is explored in the sensitivity analysis. This broader population
incorporates the possibility of a prison sentence or no sentence for the
offences associated with the index arrest.
Model structure
The cost-effectiveness of diverting drug-misusing offenders into appropriate
treatment at arrest, was compared with the usual pathway of such offenders
through the CJS was assessed using a decision analytic model. The structure
and design of the model was agreed with the wider project group which
included experts in offending and drug use research and forensic
practitioners.
The model for the primary analysis (community-based sentences) starts with a
simple decision tree. This represents the sequence of possible events
following an index arrest and decision to manage an offender suspected of
substance use by DIP with or without a drug test over a 1-year time horizon.
A simplified version of the decision tree is shown diagrammatically in
(DIP and treatment pathways) and (subsequent offending pathways) for the 1-year
time horizon used in the primary analysis. Appendix 10 presents the full decision
tree in tabular format. For the longer time horizons in the sensitivity
analyses, subsequent cycles are included using a Markov approach.
Decision tree, year 1. a, DIP and treatment pathways; and b,
subsequent offending pathways.
Decision tree, year 1 (continued): subsequent offending pathway.
The tree begins with a square decision node, where a choice is made between
the alternative strategies of DIP with or without a drug test or no DIP with
or without a drug test. Circular chance nodes indicate a point where a
number of subsequent events are possible; these events are assigned a
likelihood that they will occur (probability). The design of the tree sets
out possible progression through a number of chance nodes from the starting
point of an index arrest to the end point of further offence/no offence
(within a 1-year time horizon). This design leads to 112 mutually exclusive
sequences of events, or pathways (see Appendix 10). Each pathway probability
reflects a joint probability, estimated by multiplying probabilities along
the pathway.110 The model
does not explicitly include whether or not those entering treatment, or not,
achieve abstinence or complete treatment, or not. This is because of a lack
of clear indicators of what constitutes a completed treatment episode or
what constitutes abstinence or a successful treatment outcome. However,
there is evidence that longer times in treatment are associated with reduced
substance use, lower levels of offending, lower overall costs and improved
health status. Accordingly, the model explicitly includes the impact of
treatment entry on new recorded offences. The model also includes time in
treatment for the different branches of the pathway for those receiving
treatment. The time in treatment is used to estimate the costs of treatment
and the health status utilities associated with the different treatment
pathways.
For the longer time horizons in the sensitivity analyses, at the start of the
second and subsequent cycles, people can be in one of two states: alive or
dead. Those alive will fall into one the following categories ():
Markov states in subsequent cycles for longer time horizons.
The series of events that occur within a cycle for people with a recorded
offence include a chance that the person will be subject to DIP with or
without a drug test, or not, and then incur the costs and QALYs associated
with the treatment and reoffence pathways in the initial decision tree (see
and ).
Variable estimation
The following categories of data were required to populate the decision model:
likelihood of events, resource use and costs, and outcomes. Overall, there were
relatively few sources of data to populate the model. The limitations of these
are explored in the sensitivity analyses and the implications discussed in
Chapter 6.
Likelihood of events
Likelihood of treatment
The probability of treatment assigned to each pathway was estimated using
primary data sourced from the DDW. The source sample comprised adult
offenders (n = 81,082) who used opiates
or crack cocaine on a weekly, or more frequent basis, provided they
acknowledged such drug use at a prison and/or probation assessment. A
subset of these (n = 35,611) were
recorded by the PNC as being arrested for a criminal offence (index
arrest), of any type, between 1 April 2005 and 31 March 2007.
Participants who were imprisoned between their index arrest and
subsequent arrest were excluded. This was to ensure a sample that were
in the community, had the opportunity to enter treatment and were at
risk of subsequent offending and arrest. The probability of treatment at
a branch node is the equivalent of an absolute risk (n
of event/n of relevant sample). The decision tree
depicts four separate treatment chance nodes (see ):
treatment or no treatment
entry into treatment or already in treatment
subsequent treatment entry (considered unrelated to the DIP/no
DIP decision) or no subsequent treatment entry
treatment ongoing or treatment ceased.
Likelihood of offending behaviour
The probability of further offending behaviour assigned to each pathway
was also estimated using the prison/probation sample derived from the
DDW (described above). Again, it was calculated as the absolute risk
(n of event/n of relevant sample)
of further recorded offending behaviour within a 1-year time horizon.
The decision tree depicts these events as the following decision nodes
(see ):
recorded offence or no recorded offence
arrest or no arrest
technical offence (breach of conditions) or new offence
prison or remain in community (probation or bail)
probation or no probation
new-recorded offence or no new-recorded offence.
Probability distributions
Treatment probabilities and offending probabilities were assigned beta
distributions, with parameter approximation utilising estimates of the mean
and standard deviation (SD). A series of logistic regressions were used to
predict progress through the model based on available covariates in the
probation/prison sample. Where low pathway numbers precluded distribution
estimation, similar pathways were pooled to obtain probability
distributions.
Resource use and costs
Pathway costs include the following:
cost of DIP with or without drug test
cost of drug test
cost of drug treatment
costs associated with arrest
costs associated with prison
costs associated with remaining in the community after arrest and
conviction
costs associated with subsequent recorded offence.
The offences associated with the index arrest are assumed to be the same
whether a person follows the DIP or no DIP pathway. This implies that there
will be no difference in the type and costs of community sentences between
DIP and no DIP. Accordingly, the costs of the initial sentences are excluded
from the primary analysis. The impact of assuming that DIP also has an
impact on the type and cost of community sentence at this stage is explored
in sensitivity analysis. All unit costs were adjusted to 2012 values using
the annual percentage increase in the Retail Price Index, accessed via the
ONS.109 The cost of DIP
was derived from unit costs provided by the National Treatment Agency for
Substance Misuse (now part of Public Health England). This analysis costed
contact per treatment entry via DIP at a range of values from £85 to
£213, at 2004/5 prices.
The cost of a drug test was derived from the Home Office report,
Evaluation of Drug Testing in the Criminal Justice
System.106 Cost
per on-charge drug test across nine UK sites ranged from £44 to
£168, with a mean unit cost of £79 (2001 prices). Not all
people who receive DIP have a drug test; the unit cost of the drug test was
weighted by the probability of having the test, based on actual proportions
receiving a drug test in the DDW prison/probation sample.
The average (mean) cost per day of drug treatment was derived from the DTORS
cost-effectiveness analysis.42
The total cost of treatment from triage to second follow-up was divided by
the number of days of treatment received from triage to second follow-up,
for the DTORS participants who received treatment. This cost per day was
then multiplied by the number of days of treatment recorded for the DDW
sample.
The costs associated with offending behaviour included:
Unit costs of offending were derived from a Home Office report,107 supplemented by the costs
of offences produced for the DTORS study.42 The unit costs of prison and probation are
the average costs per offender, rather than the cost per offender receiving
a prison or probation sentence, which is the cost required for the economic
model. Published statistics111 reporting the proportion of offenders in prison and serving
community-based sentences (community orders and suspended sentences) were
applied to estimate the cost per offender sentenced to prison and the cost
per offender having probation.
These costs were used to estimate the costs for each individual in the DDW
prison/probation sample with an arrest. The arrests were costed by type of
offence(s) occurring within a 1-year time horizon of the index arrest. A
proportion (27%) of individuals arrested in the DDW prison/probation sample
were charged with committing more than one offence. For those people in the
DDW prison/probation sample with only one offence, the cost of arrest
included the CJS cost of proceedings for that offence. In addition, the
wider non-CJS costs of offence were added to the costs of proceedings.
The costs associated with a number of crime types were not available (drugs
offences – misuse; drugs offences – supply; fraud and
forgery; other indictable offences; and other summary offences). Costs
assigned to these categories were estimated using the average CJS unit costs
associated with minor crime (theft; theft of vehicle; theft from vehicle;
attempted vehicle theft; criminal damage).
For the primary analysis, the costs of subsequent offending were estimated
from the model to take into account the uncertainty in the data. For the
sensitivity analysis the costs associated with subsequent offending were
estimated using the mean total offending costs of arrested individuals in
the sample:
Costs associated with the model were assigned gamma (mean and SD) or
triangular distributions (best estimate and range).
Outcomes, utility values and quality-adjusted life-years
Utilities assigned to each pathway were derived from the DTORS
cost-effectiveness analysis.42
DTORS participants completed a self-report measure of health (Short Form
questionnaire-12 items).112
This assesses physical function, limitations in role as a result of physical
or emotional problems, the effect of pain on normal work and activities,
general health, vitality, and the impact of physical or emotional problems
on social activities and mental health.42 Utility weights derived from a general
population sample were used to aggregate question responses into a composite
measure of health-related quality of life.113
The data from DTORS were reanalysed to estimate the mean utilities of the
index arrest and utility while in treatment. SDs were calculated to estimate
distributions for the model.
The DTORS participants were referred from a variety of CJS and non-CJS, not
all of which were formal DIP schemes. However, at baseline the reported
health status and utility values did not vary between the different forms of
CJS referral and referral from other sources (linear regression,
p > 0.20). Accordingly, the
full DTORS sample who reported offending in the 4 weeks prior to baseline
was used to estimate the starting utilities for the DIP with or without drug
test pathways. There were differences in the utility values at follow-up and
by whether or not the person started treatment. For those who started
treatment, utility increased as time in treatment increased. Accordingly,
separate utility values were estimated for those who entered treatment and
those who did not, which were applied to the treatment and no treatment
events in the model. The utility values were multiplied by time spent in the
treatment pathways to estimate QALYs for this section of the model.
The DTORS sample was characterised by differences in the utility values of
those who reported offending in the 4 weeks prior to follow-up and those who
did not. For pathways resulting in treatment and no recorded offence, the
utility value was estimated from the DTORS sample completing a follow-up
assessment, receiving treatment and not reporting an offence in the previous
4 weeks. QALYs for this section of the model were estimated as 365 days
minus time in treatment.
For pathways resulting in treatment and a recorded offence, the utility value
was estimated from the DTORS sample who completing a follow-up assessment,
had treatment and reported an offence in the previous 4 weeks. It was not
possible to estimate utility values from the DTORS data for arrest and
subsequent imprisonment or community sentence. For the primary analysis, it
was assumed that arrest and imprisonment would reduce health status and
utilities to baseline values, but that arrest and community sentence would
not. The DTORS sample who reported offending at follow-up were used to
estimate the utility values to apply to the model pathways for community
sentences. These utility values were applied to the time remaining following
treatment, for those who received treatment and had a recorded offence.
Analysis of economic model
A probabilistic sensitivity analysis (PSA) was conducted for the primary analysis
and each of the sensitivity analyses. This approach takes into account the
uncertainty inherent in each of the estimates of the probability, cost and
outcomes associated with the model events and pathways. Monte Carlo simulation
with 10,000 iterations was used to estimate the (expected) costs and outcomes
for the PSAs. The Monte Carlo simulation samples from the distribution of
possible values for each parameter in the decision model. This means that mean
costs and outcomes, and measures of variance (SD and 95% CI) can be estimated to
assess the uncertainty inherent in the data used for the model.
These simulated data were used for a cost-effectiveness acceptability analysis
(CEAA). The CEAA estimated the probability that DIP with or without drug test
was cost-effective compared with no DIP with or without drug test. This is an
approach recommended by NICE for health technology appraisals.102 The approach revalues effects
or outcomes in monetary terms. However, in the UK there is no universally agreed
monetary value for the types of outcome measures used in cost-effectiveness
analyses. An approach used in health care is to ask the question: what is the
maximum amount decision-makers are willing to pay to gain one unit of outcome?
An analysis of decisions made by NICE suggests a range of implicit values
between £15,000 and £30,000 for the amount a decision-maker is
prepared to pay to gain one QALY.114
For this analysis, the outcomes were revalued using a range of maximum
willingness-to-pay values from £1 to £30,000 to gain one unit of
outcome. These reflect a range of hypothetical willingness-to-pay thresholds
(WTPTs) from decision-makers being willing to pay £1 to gain a one unit
increase in outcome to them being willing to pay £30,000 to gain a one
unit increase in outcome. The unit of outcome for the primary analysis was the
QALY, the measure used to define the range of hypothetical values implied by
NICE decisions. However, some of the sensitivity analyses used alternative
measures of outcome, such as reduction in offending. Decision-makers may not be
willing to pay the same to gain these other types of outcome measured as they
would to gain one QALY.
The data for the cost-effectiveness acceptability curve (CEAC) are derived by
first revaluing each of the 10,000 net outcomes from the simulation by a single
WTPT. This is repeated for each WTPT. A net benefit (NB) statistic for each pair
of simulated net costs and net outcomes for each WTPT can then be calculated
as:
where O = net outcome score and C = net cost.
This calculation was repeated for each WTPT. Cost-effectiveness acceptability
curves plot the proportion of simulations where the NB of an intervention is
greater than zero for each WTPT.115–118
Sensitivity analysis and key assumptions
One- and multiple-way sensitivity analyses, varying elements of the model
structure, time horizons, measures of health benefit, probabilities, cost and
utility estimates were used to identify whether or not changes would affect the
conclusions of the primary analysis. The costs, effects, incremental
cost-effectiveness ratios (ICERs) and CEACs were re-estimated for each
sensitivity analysis. PSA was used to assess parameter uncertainty for each of
the sensitivity analyses.
A number of simplifying assumptions were used for the primary analysis and these
were explored in the sensitivity analyses.
Key assumptions
The offences associated with the index arrest are assumed to be the
same whether a person follows the DIP or no DIP pathway. This
suggests that there will be no difference in the type and costs of
community sentences between DIP and no DIP. Accordingly, the costs
of the initial sentences are excluded from the primary analysis.
The primary analysis focuses on the population of offenders who will
receive a community sentence for the offences associated with the
index arrest.
The primary analysis includes people who are already attending
treatment at the index arrest.
The primary analysis assigns all DIP and treatment costs at the start
of the 1-year time horizon. This assumes that there will be no
additional DIP or treatment costs following subsequent offences. The
approach gives an accurate estimate of the total DIP costs and
community-based treatment for the first year (estimated from the
DDW). However, it may underestimate the costs of prison-based
treatment services for those who reoffend and receive a prison
sentence.
For the primary analysis, the probability and costs of recorded
offences, arrests, type of offence and whether a person received a
prison or community sentence was assumed to be the same for the DIP
and no DIP arms of the model. This was based on the assumption that
the main effect of a CJS treatment referral was on entry into
treatment. A related assumption is that subsequent offending
behaviour depended on engagement with treatment and the
effectiveness of treatment services. It is also supported by the
analysis of DDW data used to estimate parameter values. However, it
is important to note that the DDW data may reflect selection biases
because of differences in the characteristics of people who received
CJS treatment referral via the DIP and those who did not. In
addition, it is possible CJS treatment referral also affected the
severity of offending behaviour and the CJS and non-CJS costs of
offences.
Health status and utility was higher after treatment than before. It
was also assumed that any gains in utility were maintained after
treatment, for those people who did not reoffend. This implies
either that there was no relapse or that relapse did not affect
health status and utility.
People who entered treatment and had a recorded offence after the
index arrest did so because treatment was less effective or
ineffective at dealing with the drug use problem and, therefore,
offending behaviour. Accordingly, the health status and utility of
people with a recorded offence following the index arrest was
assumed to be lower than during treatment, resulting in lower
overall QALYs. In addition, it was assumed that health status after
treatment remained higher than that at baseline, for people with a
recorded offence.
