Mental health conditions are highly prevalent in young offenders9 but, given the limited evidence on diagnostic accuracy and clinical effectiveness, a decision was made to constrain the policy question addressed by the decision model to focus on the screening and subsequent management of one common unmet need in the young offending population: depression.
The rationale for constraining the policy question and developing an ‘exemplar’ case study for the decision model was based on the following reasons: (1) depression is highly prevalent in young offenders (up to 15% within the UK system); (2) as discussed in Chapters 4 and 6, taken together there is more evidence on the effectiveness of screening for depression and treatment in young offenders than on the effectiveness of screening for other mental health conditions; and (3) unlike other common mental health problems found in young offenders (e.g. conduct disorder), depression is not externalising and may therefore be more likely to go undetected.
The findings of the decision model should be considered within the limitations of the available evidence emerging from the systematic reviews of diagnostic accuracy and clinical effectiveness studies. However, the decision model makes an important contribution to the overall evidence by providing an exemplar based on a formal quantitative framework that provides a clear indication of the various inputs and data sources required to appropriately inform cost-effectiveness assessments. Importantly, the model provides an iterative basis for updating and revisiting the findings as new evidence emerges in the future.
Setting the decision context
Detection and treatment of mental health conditions in young offenders is, by definition, an intersectoral issue. When developing a decision-analytic model it is important to establish the context for informing resource allocation decisions.
The decision analysis primarily considers costs and health outcomes [expressed in quality-adjusted life-years (QALYs)] from the perspective of the UK health services. Current policy stipulates that screening occurs at the initial contact with the criminal justice system or at the first available opportunity, whereas the treatment pathway is expected to follow based on the outcome of screening.
Adopting this conventional health service-only perspective could infer certain limitations as the costs and benefits of treating mental health issues in young offenders may go beyond the health-care system. To capture further intersectoral effects, supplemental analysis extends the perspective to consider costs and benefits that may be realised by the youth justice system in terms of future crimes averted as a result of treating depression in young offenders.
The decision problem
Joint initiatives between the Youth Justice Board and the Department of Health aim to implement the CHAT, which in part assesses mental health. To date, UK policy has provided guidance on screening for mental health problems in young people who offend;79 however, the clinical and economic benefits of this policy remain to be demonstrated. Providing this ‘exemplar’ decision model for depression represents an important first step in bringing together available evidence to develop a framework for future decision-making.
Ideally, specification of a decision model should facilitate comparisons of all identification strategies that could feasibly be used in the NHS and/or youth justice system. The systematic review of all available evidence provided a range of potential parameters for identification and treatment for modelling; however, there remain several unknowns required to appropriately address the decision problem. The evidence that is currently available (as reviewed in previous chapters) places important constraints on the structural framework of any potential model and this exemplar provides a preliminary basis to inform the future research agenda within the context of current decision uncertainty.
A further constraint within the context of the decision problem is specifying the appropriate perspective to address the intersectoral nature of the problem. For example, health-care provision within the youth justice system raises additional complexities for decision-makers over how the benefits of identification and treatment are to be valued for decision-making. Furthermore, as unaddressed mental health need can increase criminal justice costs, the question is how to value benefits not directly relevant to the conventional health-care decision-maker (such as a reduction in reoffending rates after treating depression). The model provides a basis for considering where the main costs and benefits are being incurred and areas where broader improvements in public sector efficiency may be possible.
Methods
The objective of the exemplar model was to estimate, based on best available data, the costs and health outcomes for a range of feasible identification strategies. As already explained, the analysis is primarily set to the conventional health services perspective and this initial perspective is extended to also consider the youth justice system perspective. All costs are expressed in present-day values (2013) and health outcomes are expressed in QALYs. The time horizon for the analysis of depression is 1 year; hence, no discounting of costs or benefits was applied.
The model was made up of two parts: (1) an identification model, reflecting the diagnostic performance and administration costs of the alternative identification strategies, and (2) a treatment model that evaluated the subsequent costs and outcomes (expressed in QALYs). To consider intersectoral implications, the effect of treatment on recidivism rates was incorporated as a cost offset against the cost of the identification strategy.
For an identification strategy to be cost-effective, it is important that a cost-effective treatment strategy is available. Without a known cost-effective treatment, identification of an effective screening strategy would not be useful for the decision-maker because the identified patients would not be offered a cost-effective treatment. Hence, a treatment model is required to evaluate the cost-effectiveness of identification strategies in terms of the health benefits of identifying mental health conditions. Given the importance of the subsequent treatment, the treatment model for young offenders with depression is considered first.
summarises the stages of the analysis, detailing sequentially the screening strategies evaluated and the perspectives adopted.
Summary of the stages of analysis
The treatment model
To allow decision-makers to evaluate cost-effectiveness evidence across health conditions, generic assessments of health outcomes should be expressed in terms of QALYs. The systematic review of cost-effectiveness evidence (see Chapter 7) identified no previous studies within the young offender population to inform this treatment model. As such, a bespoke treatment model was developed to serve as the exemplar for the management of depression in young offenders.
The systematic review of effectiveness studies of depression in young offenders identified one study that provided relevant evidence on the effectiveness of treating depression in young offenders.64 This study reported the health outcome in terms of depression-free days (DFDs), which is not a generic measure of health and would provide limited evidence to allow decision-makers to compare cost-effectiveness evidence across health conditions. Hence, to construct the treatment model in the absence of generic measurements of health, a mapping approach was used to translate DFDs into generic health-related utility measures by assigning a utility value to each DFD,80–82 which then allowed us to calculate QALYs over the period of the study.
As this model aims to serve primarily as an exemplar, in the modelling strategy we opted to avoid the additional complexities of developing a de novo disease-specific model and selected from the identified literature on clinical effectiveness any study containing the prerequisites to model QALYs directly.
To reflect uncertainty in the input values, the sensitivity of the input parameters was evaluated using deterministic sensitivity analysis.
Parameter inputs for the treatment model
The intervention
Rohde et al.64 evaluated the clinical effectiveness of group CBT compared with a life skills control condition within a young offending population with major depressive disorder. As described in more detail in Chapter 6, the group CBT programme used the CWD-A course, which was provided to an average group size of 10.4 participants. The control condition was a life skills course in which young offenders reviewed recent events and received life skills training (such as filling out job applications) and academic tutoring. Although usual care within the UK youth justice system is unclear, life skills were generally consistent with the expected usual care arrangements for young offenders.
Relative treatment effect
The major depressive disorder recovery rate post treatment was 39% for the CWD-A course and 19% for life skills. Furthermore, over 64 weeks a Kaplan–Meier product-limit survival curve provides the proportion of individuals recovering from the depressed state at each 4-week interval. Extracting these data on recovery over the period of the study, DFDs were calculated as the number of days that the average individual in each group was depressed. Health-related utility values were assigned to the DFDs and days depressed for each month.81 These were summed over the study period using an area under the curve approach and QALYs were calculated (see Appendix 6 for further details).
Depression and recidivism
The evidence in the literature suggests that depressed young offenders are more likely to reoffend than non-depressed young offenders. To incorporate the impact of treating depression on the recidivism rate, Harshbarger83 estimated the relative risk of reoffending given depression (compared with no depression) as 1.3034 per year.
Overall, Ministry of Justice statistics84 report that 35.3% of offenders reoffend per year. Taking this as the overall probability of reoffending [i.e. P(Reoffend) = 0.353] and adjusting the probability based on data from Harshbarger,83 the probability of reoffending conditional on being depressed [i.e. P(Reoffend|Depression)] was estimated to be 0.441.
Impact of cognitive–behavioural therapy on recidivism
In a Campbell review, Lipsey et al.85 report the effect of CBT on recidivism (using the criterion of no further offending in the 12 months after the intervention). The meta-analysis includes 58 studies of the effectiveness of the intervention as a mean odds ratio (i.e. the odds of not reoffending in the subsequent 12 months following treatment compared with the control). The mean odds ratio was 1.53 (p < 0.001), which implies that offenders receiving CBT were one and a half times more likely to not reoffend within 12 months post treatment than those not receiving CBT.
Incorporating the mean odds ratio for the effect of CBT on recidivism into the conditional probability of reoffending given being depressed, the probability of reoffending given being depressed and having received CBT was derived as 0.34. This conditional probability is utilised to estimate the expected reduction in recidivism for individuals with depression receiving CBT – this approach also highlights the potential importance of the intersectoral perspective. Assigning this probability of reoffending assumes that CBT for depression has the same impact on recidivism as CBT treatments that may more directly target recidivism, which may not be the case. This uncertainty is explored in the sensitivity analyses.
Resource utilisation and cost inputs
Cost of group cognitive–behavioural therapy
The estimates of unit costs relevant to the health service were taken from Netten and Curtis86 and specific costs relevant to the justice system were taken from Brookes et al.87 These were combined with the intervention protocol described in the Rohde et al.64 study. The intervention in the Rohde study was made up of 16 sessions each lasting for 2 hours and the average group size for the programme was 10.4 participants. This information was used to estimate the cost of CBT per participant. Rohde et al.64 state that the intervention included ‘two interventionists to better monitor in-session behaviour’ (p. 662); however, as it is unclear if this potential modification of treatment delivery (i.e. two therapists per session) may apply to the UK criminal justice system, the cost-effectiveness of treatment is calculated for both one and two interventionists.
Cost of crime averted
The effectiveness of CBT in reducing rates of recidivism was translated into the expected number of crimes averted. The Ministry of Justice84 reports the reoffending of juveniles during 2010–11. Taking the percentage change in number of offenders since 2000 (2.5%), the expected numbers of offenders and reoffenders were estimated for 2013.
Home Office research study 21788 reports estimates of the costs of crime under ‘notifiable offence categories’. Costs per category are divided into three categories to reflect the true costs of crime: the anticipation of crimes (costs of security and insurance); the consequence of criminal events (e.g. value stolen and damaged, emotional and physical impacts, and impacts on health services); and responses to crime (costs spent tackling criminals to the criminal justice system).
In the model, Ministry of Justice data provide expectations around offending and reoffending and Home Office data provide estimates of the monetary value of potential reductions in crime (for more specific details see Appendix 6).
Consumption value of health benefits on crime
The National Institute for Health and Care Excellence (NICE) uses cost-effectiveness analysis as a means of comparing the expected health benefits for additional costs falling on the fixed health-care budget. For the case presented within this review, economic effects that occur outside the health-care system would require a wider ‘societal perspective’. This raises issues of the relevance of non-health benefits to the restricted NHS budget. To accommodate the wider perspective required when considering mental health problems in youth justice settings, the value of the benefits occurring outside of the remit of the health system (i.e. within the wider society) must be explored. However, to ensure that any analyses remain relevant to the restricted health budget, alternative policy perspectives may be adjusted by applying the notion of the consumption value of health, that is, the amount of consumption that is equivalent to 1 unit of health (see Claxton et al.89 for a more comprehensive summary of the approach).
Extending the perspective conventionally adopted by NICE to consider the net consumption value of health raises empirical questions. The consumption value approach was taken to integrate costs of crime averted into the economic evaluation by assuming a consumption value of health of £60,000. This reflects the fact that costs and benefits falling outside of the health system may not be valued the same by a health services decision-maker or, if they are, the willingness-to-pay (WTP) threshold of the health services decision-maker is likely to be higher than the conventional threshold used for economic evaluation from a health services perspective. Decision-makers’ WTP (given the level of uncertainty in the parameters) is likely to be closer to the lower bound of £20,000 per QALY. As such, the incorporation of the cost of crime offset through treatment was down-weighted by a factor of three.
Utility weights: converting depression-free days to quality-adjusted life-years
Depression-free days extrapolated from the Rohde et al.64 study indicate the incremental number of days per individual without depression. Revicki and Wood81 provide health-related utility weights, which can be applied to the mild (0.685), moderate (0.59) and non-depressed (0.85) states. DFDs indicate the proportion of total time spent in non-depressed and depressed states; they provide the basis for weighting using the identified utility weights for depression.81
Rohde et al.64 report at baseline an average score on the BDI of 16.6 for a cohort of non-incarcerated adolescents with comorbid major depression and conduct disorder; as this would indicate that the majority of the cohort had mild depression,90 a Revicki and Wood81 utility weight for mild depression (0.685) was assumed for the whole population (as described subsequently, this assumption was subjected to sensitivity analysis). The non-depressed state was weighted by 0.85.
Health utilities were calculated for the full study period (64 weeks) for both group CBT and the control condition. Incremental QALYs of treatment are the differences between the two groups averaged over 52 weeks (for further details see Appendix 6).
Implications of the treatment model (health and intersectoral)
Before considering whether or not identification strategies represent good value for money, it is worth reiterating that a cost-effective treatment should be identified first. Although the Rohde et al.64 study provides the means of constructing a model (i.e. by estimating DFDs and therefore QALYs), it should be noted upfront that the study included only 93 adolescents and had low power to detect a statistically significant difference between the groups. More importantly, this model highlights the need for larger and more definitive clinical trials to better inform future decision-making.
Estimating incremental QALYs from treating young offenders with depression using a group CBT approach suggests that an individual would gain 0.0113 QALYs compared with the control condition. The cost of the 16 group sessions in the CBT programme is calculated to be £2054 with one interventionist or £3910 assuming the modified treatment protocol in which two therapists were used. Per individual, the average cost would be £197.51 and £375.97 respectively. Adopting primarily the health-service perspective on treatment, this suggests that in the best-case scenario group CBT would cost £17,542 per QALY and using the modified protocol (two therapists per session) group CBT would cost £33,393 per QALY.
Applying NICE’s WTP threshold of £20,000–30,000 would suggest that only single-therapist group CBT is cost-effective, with the modified protocol not representing value for money. As such, evaluation within the identification model uses the conventional single interventionist to provide group CBT in the youth justice setting.
The identification model
The identification model assumed a decision tree structure to capture the outcomes of varying the sensitivity and specificity of the diagnostic strategies. Four possible outcomes are considered for each diagnostic strategy and relevant costs and outcomes evaluated for: (1) true positive, (2) false negative, (3) true negative and (4) false positive. The identification model is driven by the prevalence of depression, the sensitivity and specificity of specific diagnostic tools and the cost associated with each strategy.
Strategies evaluated
The decision problem would ideally compare all potential identification strategies that are feasible to implement within the youth justice system. However, in reality, evaluation of these options has been constrained by the availability of evidence. Chapter 4 was used to inform the identification strategies considered in the economic analysis and only studies containing sufficient data were used to form the basis of the parameters included.
The base-case analysis considered single-stage screening followed by treatment or no treatment for depression based on the outcome of screening. In addition to the base-case analysis, separate scenarios were considered that explored a range of alternative strategies (discussed in more detail subsequently). The alternative approaches considered included (1) the effects of two-stage screening in which the second stage uses a gold standard confirmatory interview; (2) the impact of diagnostic accuracy on recidivism; and (3) varying estimates of input parameters in the model (such as prevalence).
The diagnostic component
Model structure and key assumptions
To consider the implications of screening populations entering the youth justice system and the potential gains for those specifically with depression, illustrates the outcomes of screening and treatment and describes the associated costs and outcomes considered.
Schematic of the identification model and the implied treatment outcomes.
Within this screening framework, all young offenders (depressed or not) entering the criminal justice system are screened on first contact with the system (as per guidelines under CHAT). For the purpose of the current analysis it is assumed that mental health need will be unknown up until the point of screening.
Each individual entering the system would receive an intervention strategy incurring the cost of the related screen. Here we consider the time taken by the health-care professional (within the criminal justice system) to conduct the screening as the main cost element.
The Offender Health Research Network indicates that reception health screening is typically carried out by nurses.91 To apply the specific unit cost to the required time for screening, a value of £24 per hour for ‘Prisons: Nurse (mental health)’ taken from Brookes et al.87 was used. The specific cost parameter for each individual diagnostic tool evaluated is presented in .
Screening tools, administration time and associated costs
Of the total screened, those expected to screen positive (either true positive or false positive) receive the intervention for depression (e.g. group CBT). Dependent on the distribution across the four diagnostic outcomes, the expected number of QALYs and the cost were calculated. For individuals who screened as false negative (i.e. screened negative despite depression), the mental health need is unmet and the risk of reoffending remains high.
To inform the expected prevalence of depression within the youth justice system, we used data from Fazel et al.,2 who determined prevalence rates of mental disorders (including depression) among adolescents in juvenile detention using a summary of 25 surveys. The results from this review were extracted and presented by gender, indicating that the depression rate in males is 11% (95% CI 7% to 14%) and that in females is 29% (95% CI 22% to 37%).
Sensitivity analysis
Sensitivity analysis explored the impact of considering alternative values for three key drivers in the model: (1) prevalence of depression under usual care; (2) utility weights assigned to DFDs; and (3) the effect of CBT on recidivism.
Results
The results are presented in two parts: (1) the primary (base-case) results including the outputs of the base-case model (as outlined above) and (2) sensitivity analysis evaluating the impact of varying input parameters on the cost-effectiveness analysis. Both sets of results are presented using two perspectives, that is, the health services perspective and an intersectoral perspective. The intersectoral analysis estimates the cost offset to the youth justice system through reduced criminal activity as a result of identifying and treating depressed offenders.
Primary results
The analysis was conducted for single-stage screening and two-stage screening strategies. Single-stage screening may use the gold standard approach (i.e. DISC with a sensitivity and specificity of 1) or may use a relatively imperfect but less resource-intensive screening tool with a sensitivity and specificity of < 1 (such as MAYSI-2). Single-stage screening is followed by a treatment decision based on the outcome of screening. The two-stage screening strategy involves the administration of a gold standard instrument on individuals who screened positive (both true and false positives) on the single-stage screening measure (as expected, two-stage screening does not apply to the case when the gold standard tool is used as the first screening tool).
Cost-effectiveness of using single-stage screening tools from a health-care perspective
presents the cost-effectiveness estimates of single-stage screening compared with usual practice. Usual practice for the purposes of the model is initially simulated as no active detection (i.e. no formal screening employed). Note that, in terms of treatment costs, the primary analysis assumed that one therapist would be present during the group CBT sessions.
Cost-effectiveness of single-stage detection strategies to inform the treatment decision (health-care perspective)
In general, shows that, compared with current practice (i.e. no active screening), single-screening strategies identified in the systematic review are not likely to be cost-effective based on the commonly used WTP threshold in the UK for an additional unit of health outcome (i.e. £20,000–30,000 per QALY).
As emphasised earlier, there is limited evidence on the effectiveness and cost-effectiveness of treatments for depression in young offenders, which suggests that, even if screening had no cost and had a sensitivity and specificity of 1 (which is unrealistic), treating the true positives with group CBT would cost £17,542 per QALY (based on a health services perspective). Therefore, introducing screening costs would only increase the cost per QALY because of the additional costs of screening and the loss of false-negative cases who would have benefited from treatment. Hence, it is not surprising that none of the single screening strategies was found to be cost-effective. This further reinforces that, for screening to be cost-effective, it is important to have a treatment strategy that produces a significant improvement in outcomes at a relatively low cost.
Cost-effectiveness of two-stage screening strategies from a health-care perspective
Use of single screening tools alone is not cost-effective as the imperfect accuracy of each tool implies that false positives receive unnecessary treatment, increasing the overall cost, and false negatives miss out on the treatment and potential gains in outcome. Although the second stage (the gold standard) in the two-stage screening process does not deal with the issue of false negatives, it differentiates the true positives from the false positives, ensuring that treatment is provided only to those who are truly depressed.
presents the comparison between this two-stage strategy and usual practice. The cost per QALY analysis suggests a significant efficiency gain over the use of single screening tools alone. However, only the MFQ and Short MFQ (disease-specific tools for depression) are potentially within the upper bound of the WTP threshold of £20,000–30,000 per QALY.
Cost-effectiveness of two-stage screening strategies to inform the treatment decision (health-care perspective)
It should be noted, however, that the analyses of both single and two-stage screening assume that there is no cost associated with false negatives. This assumption may not hold in practice; however, we did not find any evidence on health service resource use because of untreated depression in the young offending population.
Cost-effectiveness of two-stage screening strategies from an intersectoral perspective
The decision to treat a mental health need in young offenders may have wider-reaching benefits than the health outcomes alone. In adopting the intersectoral perspective of the health and youth justice services, the aim is to examine the extent of the potential costs and benefits of various detection strategies; this would be relevant if an improved mental health status had consequences for future criminal behaviour (specifically, changes in recidivism rates).
presents the results of the cost-effectiveness analysis including the expected cost offset from the potential reductions in recidivism rates. Given that only the two-stage detection strategies were found to be cost-effective within the health-care perspective, only these strategies were analysed from an intersectoral perspective.
Cost-effectiveness of two-stage screening strategies with the inclusion of the cost offset from reduced rates of recidivism (intersectoral perspective)
Including the expected cost offset from reduced recidivism to the evaluated two-stage detection strategies, all strategies except for MMPI-A fall within the range of the decision-maker’s WTP. This model provides a provisional indication that gains in health status (through appropriate detection and treatment) may be justified by the potential cost offset to the youth justice system. However, it should be noted that the base-case intersectoral analysis gives equal weight to costs incurred or saved by the health and youth justice systems (i.e. the analysis assumes that costs incurred by the health system can be compensated in a 3 : 1 ratio by cost savings in the youth justice system).
To compare strategies and indicate which may represent the most efficient use of resources, results can be presented on a cost-effectiveness frontier. The frontier connects incremental cost-effectiveness ratios (ICERs) of strategies on the cost-effectiveness plane to identify strategies that dominate other less cost-effective strategies. Strategies that lie on the frontier line represent value for money and options falling on the line are compared to indicate whether or not incremental health benefits justify any incremental costs. The incremental analysis compared with no active detection is presented in the cost-effectiveness plane in .
Cost-effectiveness plane of a two-stage screen detection strategy (single screen + gold standard) including the cost offset by reductions in recidivism attributed to treatment of depression. DISC Pred., the DISC predictive scales (DPS). (more...)
Examining the cost-effectiveness plane suggests that two-stage screening using the MFQ or the Short MFQ in the first stage is most cost-effective, as represented by the cost-effectiveness frontier on the cost-effectiveness plane. The cost-effectiveness frontier represents the most efficient points among all screening strategies examined (i.e. the frontier represents the strategies that for a given level of effect have the highest cost or vice versa).
Although the exemplar approach provides a framework for future cost-effectiveness analyses of screening strategies in young offenders, the analyses presented so far have several limitations, in particular the limited data available with which to construct a model. The following section presents the results of sensitivity analyses to illustrate how sensitive the model is to variation in the input parameters.
Sensitivity analysis
Given the uncertainty in the current literature surrounding the real-world practice of the detection and treatment of mental health needs, this section presents deterministic sensitivity analysis of the input parameters driving the model. The impacts of variation in three parameters are presented, namely the prevalence of undetected depression under usual care; utility values and the severity of depression; and the level of effectiveness of CBT for depression on reducing recidivism.
Prevalence rate of undetected depression under usual care
The model utilises gender-specific prevalence rates of depression in young offenders in the UK as reported by Fazel et al.2 The base-case exemplar uses these prevalence rates, which suggest that, on aggregate, 15% of all individuals in the system are depressed. However, the model assumes that, in the absence of an active detection strategy (single or two stage), all depressed individuals will go undetected and, therefore, untreated.
In the real-world setting, the prevalence rate under usual care will be made up of previously detected cases and currently undetected cases. illustrates how variation in the prevalence of depression driving the model alters the level of cost-effectiveness under the intersectoral perspective.
Results of sensitivity analysis [cost per QALY (£)]: prevalence of depression (two-stage screening strategy, intersectoral perspective)
suggests that, as the prevalence of depression in the young offending population increases (compared with the base-case prevalence of 15%), the ICER becomes smaller and vice versa. However, the analysis suggests that the change in the ICER is relatively small and the strategies that were cost-effective in the base-case analysis remain cost-effective in the sensitivity analysis, assuming a WTP threshold of £20,000–30,000 per QALY.
Utility values and the severity of depression
In applying the utility value to DFDs in the model to obtain QALYs, the base-case analysis is conservative in estimating the potential gains in identifying and treating depression because it assumes that all depressed individuals have mild depression. In reality, there is likely to exist a mixed picture of depression severity in the youth justice system; future research will benefit from better understanding levels of severity of depression in this specific population.
– examine the effect of varying this assumption for all three scenarios previously discussed in the main results (single screen, two-stage screen and two-stage screen including the cost offset from reduced recidivism respectively).
Results of sensitivity analysis [cost per QALY (£)]: ratio of mild to moderate depression – single screen (health-care perspective)
Results of the sensitivity analysis [cost per QALY (£)]: ratio of mild to moderate depression – two-stage screening strategy (intersectoral perspective)
Results of sensitivity analysis [cost per QALY (£)]: ratio of mild to moderate depression – two-stage screening strategy (health-care perspective)
Overall, these analyses suggest that the cost-effectiveness of all of the screening strategies across the three scenarios in – is highly sensitive to assumptions about the severity of depression. As expected, as the level of moderate depression increases (with a constant overall prevalence), all screening strategies become more cost-effective. For example, if the prevalence of mild to moderate depression is 40 : 60, the scenario for the use of single screening tools alone indicates that the use of the MFQ or the gold standard is likely to fall within the decision-maker’s WTP threshold.
In part, these results are a reflection of the limitations of the available evidence on screening and treatment parameters. These results highlight the need for more research to measure quality of life and the severity of depression in young offenders, all of which are critical to address the current decision uncertainty.
Cognitive–behavioural therapy, rates of recidivism and consumption value of the quality-adjusted life-year
As the base-case results of the model suggest, potential additional gains through offsetting the cost of the discussed strategies may be highly influential in the cost-effectiveness analysis. However, two key assumptions have been made to present the base-case analysis, namely the consumption value of the QALY in adjusting cost offsets and the level of effect of CBT on reducing recidivism rates in the depressed population.
A decision-maker may apply the WTP threshold of £20,000–30,000 per QALY and a consumption value of health of £60,000 to down-weight the expected cost of crime averted. This therefore assumes that the cost of crime averted is divisible by three to estimate intersectoral cost-effectiveness.
The base-case exemplar assumes a 3 : 1 ratio for the consumption value of health. It is also feasible that, with greater certainty, a decision-maker’s WTP may lie at the upper bound of £30,000 per QALY, implying that the cost offset should alternatively be down-weighted by a ratio of 2 : 1. provides a comparison of the effects of varying the assumed consumption value of health.
Results of sensitivity analysis [cost per QALY (£)]: consumption value of health – two-stage screening strategy (intersectoral perspective)
If a decision-maker working under greater certainty used the £30,000 per QALY threshold (implying that the non-health cost offset should be adjusted on a ratio of 2 : 1), a larger proportion of the two-stage detection strategies fall under the WTP threshold. This raises an interesting methodological question about weighting non-health costs and benefits when taking a broader intersectoral or societal perspective in evaluating health-care programmes (as in the case of the detection and treatment of mental health in young offenders).
The model uses the estimate of the effect of CBT on reducing recidivism as reported in the systematic review by Lipsey et al.85 This may present an optimistic additional expectation from treatment and is higher than the expected benefit of treatment for depression as reported in Rohde et al.64 and it may be more realistic to assume that the level of effect on reoffending may actually be lower.
The odds ratio for the treatment effect of CBT on recidivism in the base-case analysis was 1.53.85
and present sensitivity analyses in which the odds ratio of the treatment effect of CBT for depression on recidivism was varied (for both the 3 : 1 and the 2 : 1 consumption values of health respectively).
Results of sensitivity analysis [cost per QALY (£)]: odds ratio of the treatment effect of CBT for depression on recidivism (assuming a ratio for the consumption value of health of 3 : 1) – two-stage screening strategy (more...)
Results of sensitivity analysis [cost per QALY (£)]: odds ratio of the treatment effect of CBT for depression on recidivism (assuming a ratio for the consumption value of health of 2 : 1) – two-stage screening strategy (more...)
Overall, this sensitivity analysis illustrates that the level of effect of CBT on recidivism is a major driver of whether or not strategies falls within the WTP threshold. As the odds ratio decreases (i.e. becomes closer to 1), the cost-effectiveness ratio increases. For instance, in the analysis with a consumption value of health of 3 : 1 (see ), MFQ and Short MFQ in a two-stage strategy are likely to be cost-effective assuming the full effect of CBT on recidivism (1.53). However, small changes in the odds ratio alter the cost-effectiveness ratio so that it is now close to the upper bound of the WTP threshold. assumes that a decision-maker’s WTP threshold is £30,000 per QALY and implies that a larger proportion of strategies may be cost-effective.
In the base-case scenario, the staff time for conducting the indicated screening programme within the criminal justice settings was costed using Unit Costs in Criminal Justice (i.e. ‘Prisons: Nurse (mental health)’] at £24 per hour.87 However, compared with Unit Costs of Health and Social Care86 [i.e. Nurse (Mental Health) at a cost of £35 per hour], the base-case staff cost may be considered conservative. illustrates the effect of using the higher cost for staff time using a two-stage screening strategy and an intersectoral perspective.
Results of sensitivity analysis [cost per QALY (£)]: personnel cost for screening – two-stage screening strategy (intersectoral perspective)
Utilities for various depression states were required to inform the DFD approach to estimating QALYs for the treatment model. Revicki and Wood81 provided the most suitable study having ascertained utilities using standard gamble interviews. Although these data are favourable in describing various states of depression, they have limitations in that the data are not UK or adolescent specific. Byford et al.92 compared selective serotonin reuptake inhibitors and routine specialist care with and without CBT in adolescents with major depression. At baseline, this study provides a measure of utility (0.5) from a sample of 208 adolescents, aged 11–17 years, with moderate to severe major or probable major depression. illustrates how this utility would alter the base-case results.
Results of the sensitivity analysis [cost per QALY (£)]: variation in utility referencing – two-stage screening strategy (intersectoral perspective)
Discussion
The cost-effectiveness analysis was conducted within the limitations of the available evidence on the effectiveness of screening and treatment strategies for mental health conditions in young offenders. Because of the limited evidence, we developed an exemplar model for depression to evaluate the cost-effectiveness of single-screening and two-stage screening followed by a treatment decision based on the screening outcome. Depression was chosen for the exemplar analysis for the reasons highlighted in the introduction to this chapter.
The limitations of the data are considerable and the results of the exemplar model must be interpreted within the context of these. This includes limitations in data availability for both screening and treatment parameters. For example, data on treatment were limited to a single study. In addition, the lack of data for a number of additional key input parameters, such as the impact of treatment on the rates of recidivism, limits the implications that can be drawn from the exemplar decision model.
The economic model identified key drivers required for decision analysis, which included the prevalence and severity of the mental health condition, the diagnostic accuracy of the screening instruments, the treatment effect on health outcomes and recidivism and the perspective of the economic analysis. The exemplar analysis demonstrated how strongly these key drivers could influence the cost-effectiveness decision. These key parameters are likely to be influential when further cost-effectiveness analyses are conducted in this population (whether for depression or other mental health conditions); hence, the cost-effectiveness analysis also informs areas of research prioritisation to reduce uncertainty in the current evidence base to allow evaluation of screening strategies in the future.
The economic analysis also highlighted the value of having an effective treatment for any screening strategy to be cost-effective. For the exemplar model, our systematic review found only one relevant study (i.e. Rohde et al.64) that could be used to derive DFDs and in turn QALYs. The treatment model was based on data from this single study, with a relatively small sample size of only 93 adolescents; moreover, although the recovery functions used to derive DFDs showed small gains after CBT, these functions were not statistically significantly different from each other. Moreover, using point estimates of recovery rates from the Rohde et al. study,64 the treatment model showed that, if all depressed young offenders could be treated with CBT (assuming that they could be identified at no cost), the cost per QALY was £17,542. Given that screening strategies are imperfect and result in unnecessary treatment costs because of false-positive individuals and missing out potential health gains for false-negative individuals, the cost per QALY estimates would only become higher, in turn making screening less cost-effective. This puts the emphasis on finding effective evidence-based treatment strategies that would produce reasonable health benefits after identifying screen-positive individuals. This could be achieved by conducting larger, high-quality clinical trials to identify or develop effective treatment strategies for screen-positive individuals.
The cost-effectiveness analysis also raised interesting methodological issues around the perspective of the economic analysis and the valuing of non-health benefits and costs for health services decision-making. The exemplar model suggests that several screening strategies that were not likely to be cost-effective from the health services perspective (given the available evidence) may become cost-effective when an intersectoral perspective is adopted. Moreover, the consumption value of a QALY used in the analysis was found to be another important determinant in the cost-effectiveness analysis.
The evidence on the sensitivity and specificity of screening instruments used in the exemplar model shows that either most instruments have poor diagnostic ability or there is significant uncertainty around sensitivity and specificity or both. Our analysis suggested that, if an instrument produces a high number of false-positive results, introducing two-stage screening (with the second stage being the gold standard) may be more cost-effective if the second screening cost could offset the cost of incorrectly treating the false positives. Although uncertainty in the available evidence does not allow us to reach definite conclusions, the exemplar model indicates that in the presence of poor diagnostic properties a two-stage screening strategy may be more cost-effective than single-stage screening.
In conclusion, the cost-effectiveness analysis presented here is primarily an exemplar. It provides an insight into the decision problem and identifies key drivers of cost-effectiveness and demonstrates the effects of our level of uncertainty about model parameters. This is of use in informing future research priorities, which will be discussed in Chapter 10. Before these future research priorities are identified, the current evidence base is assessed against UK NSC criteria.
