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Economic Evaluation of Interventions to Address Opioid Misuse: A Systematic Review of Methods Used in Simulation Modeling Studies

Open ArchivePublished:July 25, 2020DOI:https://doi.org/10.1016/j.jval.2020.03.015

      Highlights

      • Cost-effectiveness simulation models can guide and inform clinical and public health responses to the opioid crisis and can be used to improve complex decision making about opioid policy. Despite the strong evidence base for individual interventions that address these priorities, policy makers need guidance on how to combine them while ensuring an efficient use of limited resources.
      • We find that all economic evaluation using a simulation approach focused on 2 areas: pharmacologic treatments and harm reduction though naloxone distribution. The cost-effectiveness of interventions focused on prevention (eg, prescription drug monitoring programs), recovery support (eg, social supports), and harm reduction approaches other than naloxone (eg, safe injection facilities) has not yet been evaluated using simulation modeling.
      • We find that that no model to date has considered the economic impact of a combination of interventions in the continuum of opioid use disorder prevention, harm reduction, and treatment. Accounting for synergy between interventions would provide guidance on the optimal allocation of resources for communities facing specific challenges relating to opioid misuse. This is a priority area for health economic research on opioid misuse.

      Abstract

      Objectives

      Several evidence-based interventions exist for people who misuse opioids, but there is limited guidance on optimal intervention selection. Economic evaluations using simulation modeling can guide the allocation of resources and help tackle the opioid crisis. This study reviews methods employed by economic evaluations using computer simulations to investigate the health and economic effects of interventions meant to address opioid misuse.

      Methods

      We conducted a systematic mapping review of studies that used simulation modeling to support the economic evaluation of interventions targeting prevention, treatment, or management of opioid misuse or its direct consequences (ie, overdose). We searched 6 databases and extracted information on study population, interventions, costs, outcomes, and economic analysis and modeling approaches.

      Results

      Eighteen studies met the inclusion criteria. All of the studies considered only one segment of the continuum of care. Of the studies, 13 evaluated medications for opioid use disorder, and 5 evaluated naloxone distribution programs to reduce overdose deaths. Most studies estimated incremental cost per quality-adjusted life-years and used health system and/or societal perspectives. Models were decision trees (n = 4), Markov (n = 10) or semi-Markov models (n = 3), and microsimulations (n = 1). All of the studies assessed parameter uncertainty though deterministic and/or probabilistic sensitivity analysis, 4 conducted formal calibration, only 2 assessed structural uncertainty, and only 1 conducted expected value of information analyses. Only 10 studies conducted validation.

      Conclusions

      Future economic evaluations should consider synergies between interventions and examine combinations of interventions to inform optimal policy response. They should also more consistently conduct model validation and assess the value of further research.

      Keywords

      Introduction

      There is a crisis with regards to the inappropriate use of opioids and related morbidity and mortality. Globally, about 127 000 people died in 2015 as a result of opioid use disorder (OUD). Additionally, about 10.6 million people across the world who engage in injection drug use suffer from hepatitis C and human immunodeficiency virus (HIV).
      United Nations Office on Drugs and Crime
      World Drug Report 2018.
      In the United States, where a plurality of global opioid-related deaths have occurred in recent years, the opioid epidemic has resulted in high economic costs (up to $504 billion in 2015)
      The Council of Economic Advisers
      The underestimated cost of the opioid crisis.
      driven by premature death, crime, lost productivity, and health-related costs.
      Several prevention, treatment, and harm reduction interventions have been employed to address the crisis.
      • Hawk K.F.
      • Vaca F.E.
      • D’Onofrio G.
      Focus: addiction: reducing fatal opioid overdose: prevention, treatment and harm reduction strategies.
      Prevention initiatives including drug take-back programs,
      • Gray J.A.
      • Hagemeier N.E.
      Prescription drug abuse and DEA-sanctioned drug take-back events: characteristics and outcomes in rural Appalachia.
      educational initiatives targeting providers and the public,
      • Albert S.
      • Brason F.W.
      • Sanford C.K.
      • Dasgupta N.
      • Graham J.
      • Lovette B.
      Project Lazarus: community-based overdose prevention in rural North Carolina.
      and prescription drug monitoring programs
      • Fink D.S.
      • Schleimer J.P.
      • Sarvet A.
      • et al.
      Association between prescription drug monitoring programs and nonfatal and fatal drug overdoses: a systematic review.
      • Moyo P.
      • Simoni-Wastila L.
      • Griffin B.A.
      • et al.
      Impact of prescription drug monitoring programs (PDMPs) on Opioid utilization among medicare beneficiaries in 10 US states.
      • Patrick S.W.
      • Fry C.E.
      • Jones T.F.
      • Buntin M.B.
      Implementation of prescription drug monitoring programs associated with reductions in opioid-related death rates.
      seek to limit the number of people inappropriately using opioids. Treatments include medication for opioid use disorder (MOUD)
      • Connery H.S.
      Medication-assisted treatment of opioid use disorder: review of the evidence and future directions.
      • Larochelle M.R.
      • Bernson D.
      • Land T.
      • et al.
      Medication for opioid use disorder after nonfatal opioid overdose and association with mortality: a cohort study.
      • Volkow N.D.
      • Wargo E.M.
      Overdose prevention through medical treatment of opioid use disorders.
      • Wakeman S.E.
      • Barnett M.L.
      Primary care and the opioid-overdose crisis—buprenorphine myths and realities.
      and behavioral therapies, which have been shown to enhance the effectiveness of MOUD.
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      • Abraham A.
      • Seymour B.
      • McLoyd K.
      • Chalk M.
      • Festinger D.
      A systematic review on the use of psychosocial interventions in conjunction with medications for the treatment of opioid addiction.
      Harm reduction strategies, including overdose prevention with naloxone
      • Bird S.M.
      • McAuley A.
      • Perry S.
      • Hunter C.
      Effectiveness of Scotland's national naloxone programme for reducing opioid-related deaths: a before (2006–10) versus after (2011–13) comparison.
      • Freeman P.R.
      • Hankosky E.R.
      • Lofwall M.R.
      • Talbert J.C.
      The changing landscape of naloxone availability in the United States, 2011-2017.
      • McDonald R.
      • Campbell N.D.
      • Strang J.
      Twenty years of take-home naloxone for the prevention of overdose deaths from heroin and other opioids—conception and maturation.
      and supervised injection facilities,
      • Kral A.H.
      • Davidson P.J.
      Addressing the nation’s opioid epidemic: lessons from an unsanctioned supervised injection site in the US.
      seek to limit the consequences of opioid use.
      Identifying the optimal mix of interventions is complex, so community leaders need guidance on how to allocate resources to address the epidemic. Economic evaluations identify, measure, and value the costs and outcomes of alternative strategies to guide decisions.
      • Drummond M.
      • Sculpher M.
      • Torrance G.
      • O'Brien B.
      • Stoddart G.
      Methods for the Economic Evaluation of Health Care Programmes.
      A simulation model is an analytic approach that projects outcomes and costs associated with alternative strategies.
      • Neumann P.J.
      • Sanders G.D.
      • Russels L.B.
      • Siegel J.E.
      • Ganiats T.G.
      Cost-Effectiveness in Health and Medicine.
      Simulation modeling draws information from multiple sources, offering an approach to integrate information on the trajectory of OUD and associated complications with the clinical and economic impact of public health strategies to inform the best response to the opioid crisis.
      • Briggs A.
      • Sculpher M.
      • Claxton K.
      Decision Modelling for Health Economic Evaluation.
      It offers several advantages, including (1) extrapolating beyond the data observed in a trial, (2) linking intermediate endpoints (eg, treatment retention) to final outcomes (eg, overdose death), (3) generalizing to other settings, (4) synthesizing head-to-head comparisons, (5) accounting for the synergistic effect of multiple interventions, and (6) informing decisions in the absence of data.
      • Buxton M.J.
      • Drummond M.F.
      • VanHout B.A.
      • et al.
      Modelling in economic evaluation: an unavoidable fact of life.
      Simulation modeling offers the ideal framework to identify uncertainty around relevant variables and set priorities for further research.
      • Claxton K.
      The irrelevance of inference: a decision-making approach to the stochastic evaluation of health care technologies.
      ,
      • Sculpher M.
      • Claxton K.
      Establishing the cost-effectiveness of new pharmaceuticals under conditions of uncertainty--when is there sufficient evidence?.
      In addition, long-term decision modeling can capture the multiplicity of outcomes characteristic of OUD, with periods of relapse and recovery accompanied by several comorbid conditions.
      A recent study conducted a systematic review of the literature on economic evaluations of interventions for OUD.
      • Murphy S.M.
      • Polsky D.
      Economic evaluations of opioid use disorder interventions.
      This study found 43 economic evaluations conducted up to August 2015, with most of the studies focusing on MOUD with methadone maintenance treatment, and found strong support for the cost-effectiveness of methadone. This previous review did not focus on economic evaluations with a decision-analysis simulation-modeling approach, was limited to treatment only, and focused on the results of the individual studies rather than the methods used. In addition, several relevant economic evaluations have been published since 2015. Our study reviews the methods employed by economic evaluations that used simulation modeling to investigate the health and economic effects of interventions meant to address opioid misuse and appraises the approaches in the context of best practices.

      Methods

       Overview

      We conducted a systematic mapping review to characterize the health economic evaluations of OUD interventions that used simulation techniques.
      • Grant M.J.
      • Booth A.
      A typology of reviews: an analysis of 14 review types and associated methodologies.
      In general, a systematic mapping review involves a systematic search and the categorization of existing literature according to study design and other key features. We followed relevant Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines in conducting and reporting the review.
      • Moher D.
      • Shamseer L.
      • Clarke M.
      • et al.
      Preferred reporting items for systematic review and meta-analysis protocols (prisma-p) 2015 statement.
      ,
      • Shamseer L.
      • Moher D.
      • Clarke M.
      • et al.
      Preferred reporting items for systematic review and meta-analysis protocols (prisma-p) 2015: elaboration and explanation.

       Search Strategy

      The search strategy included search terms relating to 3 dimensions: (1) opioids (eg, heroin), interventions (eg, methadone), and related consequences (eg, dependence); (2) simulation and modeling (eg, Markov); and (3) economic evaluation (eg, cost-effectiveness). A research librarian reviewed the search terms and created tailored searches for the following databases: PubMed, Embase, PsycINFO, CINAHL, Web of Science, and EconLit (see Appendix 1 in Supplemental Materials found at https://doi.org/10.1016/j.jval.2020.03.015). We restricted our search to full-text studies published in English between 2000 and the time of the search (January 2019).

       Eligibility Criteria

      Included studies satisfied 3 criteria. First, the studies had to focus on prevention, treatment, or harm reduction interventions targeting opioid misuse and/or direct consequences of misuse (ie, overdose). Studies of needle exchange programs were not included because the outcomes reported did not directly target opioid misuse. Additionally, studies that described interventions targeting drug use in general for which methods and results could not be clearly subset to opioids were not included. Studies also had to be economic evaluations, meaning that they compared the costs and effects of at least 2 strategies.
      • Drummond M.
      • Sculpher M.
      • Torrance G.
      • O'Brien B.
      • Stoddart G.
      Methods for the Economic Evaluation of Health Care Programmes.
      Cost-effectiveness analyses (CEAs), cost-utility analyses (CUAs), and cost-benefit analyses (CBAs) were considered. Cost analyses that did not compare an intervention with another strategy were not included. Finally, studies had to use a simulation modeling technique. Economic evaluations based entirely on trials or observational data were not included.

       Study Selection

      Two authors screened titles and abstracts for inclusion. Each author was primarily responsible for half of the identified studies, checked 10% of the other author’s list, and discussed studies that either author was unsure about. Studies were excluded if they clearly did not meet the inclusion criteria. Studies not excluded during title and abstract screening were reviewed in full.

       Data Collection

      We developed an extraction form that focused on the components of economic analysis and modeling (see Appendix 2 in Supplemental Materials). The extraction form followed the principles of the Consolidated Health Economic Evaluation Reporting Standards (CHEERS)
      • Husereau D.
      • Drummond M.
      • Petrou S.
      • et al.
      Consolidated health economic evaluation reporting standards (cheers)—explanation and elaboration: a report of the ISPOR Health Economic Evaluation Publication Guidelines Good Reporting Practices Task Force.
      and other guidelines for reporting economic evaluations and simulation models.
      • Drummond M.
      • Sculpher M.
      • Torrance G.
      • O'Brien B.
      • Stoddart G.
      Methods for the Economic Evaluation of Health Care Programmes.
      ,
      • Bennett C.
      • Manuel D.G.
      Reporting guidelines for modelling studies.
      ,
      • Nuijten M.J.
      • Pronk M.H.
      • Brorens M.J.
      • et al.
      Reporting format for economic evaluation.
      The extraction form captured details on the study population and intervention(s), outcomes and costs, modeling approach, and economic analysis characteristics.

      Results

       Search Results

      A total of 216 unduplicated records were identified (see Appendix 3 in Supplemental Materials). After the initial screening, 34 were selected for full-text review. Of those, 16 more were excluded (see Appendix 4 in Supplemental Materials) because they did not satisfy the inclusion criteria, leaving 18 studies for data extraction (Fig. 1).
      • Adi Y.
      • Juarez-Garcia A.
      • Wang D.
      • et al.
      Oral naltrexone as a treatment for relapse prevention in formerly opioid-dependent drug users: a systematic review and economic evaluation.
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      • Jackson H.
      • Mandell K.
      • Johnson K.
      • Chatterjee D.
      • Vanness D.J.
      Cost-effectiveness of injectable extended-release naltrexone compared with methadone maintenance and buprenorphine maintenance treatment for opioid dependence.
      • Kenworthy J.
      • Yi Y.
      • Wright A.
      • Brown J.
      • Maria Madrigal A.
      • Dunlop W.C.N.
      Use of opioid substitution therapies in the treatment of opioid use disorder: results of a UK cost-effectiveness modelling study.
      • King J.B.
      • Sainski-Nguyen A.M.
      • Bellows B.K.
      Office-based buprenorphine versus clinic-based methadone: a cost-effectiveness analysis.
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      • Stephen J.H.
      • Halpern C.H.
      • Barrios C.J.
      • et al.
      Deep brain stimulation compared with methadone maintenance for the treatment of heroin dependence: a threshold and cost-effectiveness analysis.
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      Figure thumbnail gr1
      Figure 1Flowchart of examined studies.
      HIV indicates human immunodeficiency virus.

       Study Population and Intervention

      The included studies were conducted in the United States (n = 10; Table 1), the United Kingdom (n = 4), Canada (n = 3), and Russia (n = 1). Of the studies conducted in North America, 4 applied to specific states, provinces, or cities. Most studies (n = 13) evaluated MOUD, including methadone, buprenorphine, naltrexone, hydromorphone, and diacetylmorphine. In 12 studies, a medication was compared with nonpharmacologic treatments (eg, psychosocial support), other pharmacologic agents (eg, methadone vs buprenorphine), other formulations of the same pharmacologic agent (eg, implantable vs sublingual buprenorphine), other modalities (eg, maintenance vs detoxification), or no treatment. In one study, methadone maintenance was the comparator for deep-brain stimulation.
      • Stephen J.H.
      • Halpern C.H.
      • Barrios C.J.
      • et al.
      Deep brain stimulation compared with methadone maintenance for the treatment of heroin dependence: a threshold and cost-effectiveness analysis.
      The remaining studies were economic evaluations of naloxone distribution (n = 5), and one of the naloxone studies evaluated naloxone with linkage to addiction treatment and/or pre-exposure prophylaxis.
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.
      Studies modeling MOUD focused on people with OUD, except for one
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      that focused on heroin users without a formal diagnosis. Studies modeling naloxone focused on people at risk of opioid overdose, usually heroin users.
      Table 1Summary of studies included in the review: study population and interventions
      StudyCountry/stateDelivery settingTarget populationInterventionComparator
      Adi et al,
      • Adi Y.
      • Juarez-Garcia A.
      • Wang D.
      • et al.
      Oral naltrexone as a treatment for relapse prevention in formerly opioid-dependent drug users: a systematic review and economic evaluation.
      2007
      UKNHSDetoxified patients who were previously opioid dependentOral naltrexone; psychosocial supportPsychosocial support only
      Bansback et al,
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      2018
      British Columbia, CanadaHealthcare clinicPatients with severe OUDInjectable hydromorphoneOral methadone maintenance; injectable diacetylmorphine
      Carter et al,
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      2017
      USAOffice-based clinicOpioid-dependent, clinically stable adultsSubdermal, implantable buprenorphine; psychosocial supportSublingual buprenorphine; psychosocial support
      Cipriano and Zaric,
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.
      2018
      Ontario, CanadaToronto School District secondary schoolsStudentsNaloxone kits in schoolsNo naloxone
      Coffin and Sullivan,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      2013
      USACommunityHeroin usersNaloxone distribution for lay administration to 20% of heroin usersNo naloxone distribution
      Coffin and Sullivan,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      2013
      RussiaCommunityHeroin usersNaloxone distribution for lay administration to 20% of heroin usersNo naloxone distribution
      Connock et al,
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      2007
      UKNHSPatients with OUDMethadone or buprenorphine maintenanceNo opioid substitution therapy or methadone compared with buprenorphine
      Jackson et al,
      • Jackson H.
      • Mandell K.
      • Johnson K.
      • Chatterjee D.
      • Vanness D.J.
      Cost-effectiveness of injectable extended-release naltrexone compared with methadone maintenance and buprenorphine maintenance treatment for opioid dependence.
      2015
      USAOTPs/primary care/specialty careAdult males initiating OUD treatmentExtended-release, injectable naltrexoneMethadone or buprenorphine maintenance
      Kenworthy et al,
      • Kenworthy J.
      • Yi Y.
      • Wright A.
      • Brown J.
      • Maria Madrigal A.
      • Dunlop W.C.N.
      Use of opioid substitution therapies in the treatment of opioid use disorder: results of a UK cost-effectiveness modelling study.
      2017
      UKNHSPatients with OUDMethadone or buprenorphine maintenance treatmentNo opioid substitution therapy
      King et al,
      • King J.B.
      • Sainski-Nguyen A.M.
      • Bellows B.K.
      Office-based buprenorphine versus clinic-based methadone: a cost-effectiveness analysis.
      2016
      USAOTPs/primary careAdult patients with OUDOffice-based buprenorphine maintenanceClinic-based methadone maintenance
      Krebs et al,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      2018
      California, USAOTPsAdults presenting for publicly funded OUD treatment (first treatment)100% access to methadone treatmentStandard of care: 54.3% medically managed withdrawal, with 2 previous failures
      Langham et al,
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      2018
      UKNHSAdults at risk of heroin overdoseNaloxone distribution (assumed 30% of heroin users)No naloxone to adults at risk of heroin overdose
      Masson et al,
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      2004
      USAOTPAdults with OUDMethadone maintenance (14 months and 2-month detoxification); group therapy (1 hour/week for 6 months); individual therapy (1 hour/month)Methadone detoxification (6 months); group therapy (2 hours/week); individual therapy (1 hour/week); education sessions (14 sessions in 6 months)
      Nosyk et al,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      2012
      CanadaTreatment facilitiesAdults with chronic, refractory OUD (more than 5 years of use and 2 or more prior failed substitution treatment attempts)DiacetylmorphineMethadone maintenance
      Schackman et al,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      2012
      USAPrimary careClinically stable patients with OUD who had been in office-based buprenorphine-naloxone treatment for 6 monthsLong-term office-based buprenorphine-naloxone treatmentNo treatment
      Stephen et al,
      • Stephen J.H.
      • Halpern C.H.
      • Barrios C.J.
      • et al.
      Deep brain stimulation compared with methadone maintenance for the treatment of heroin dependence: a threshold and cost-effectiveness analysis.
      2012
      USAHealthcare facilitiesPatients with heroin dependenceNucleus accumbens deep-brain stimulationMethadone maintenance
      Uyei et al,
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.
      2017
      Connecticut, USASyringe services programsHIV-negative people who inject drugsFour alternative strategies: (1) naloxone distribution, (2) naloxone distribution plus linkage to addiction treatment (referral to methadone program), (3) naloxone distribution plus PrEP, and (4) naloxone distribution plus linkage to addiction treatment and PrEPNo intervention
      Zarkin et al,
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      2005
      USAMethadone clinicUS adult population of heroin users and non-usersIncrease of 100% in methadone treatment, increase of 25% in length of stay and no treatmentCurrent methadone treatment
      NHS indicates National Health Service (UK); OUD, opioid use disorder; OTP, opioid treatment program (ie, facility permitted to deliver methadone for OUD in the United States); PrEP, preexposure prophylaxis.
      In general, studies evaluating MOUD found it to be cost-effective,
      • Adi Y.
      • Juarez-Garcia A.
      • Wang D.
      • et al.
      Oral naltrexone as a treatment for relapse prevention in formerly opioid-dependent drug users: a systematic review and economic evaluation.
      ,
      • Kenworthy J.
      • Yi Y.
      • Wright A.
      • Brown J.
      • Maria Madrigal A.
      • Dunlop W.C.N.
      Use of opioid substitution therapies in the treatment of opioid use disorder: results of a UK cost-effectiveness modelling study.
      ,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      ,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      ,
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      with methadone being more cost-effective than buprenorphine
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      and less cost-effective than hydromorphone and diacetylmorphine.
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      ,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      One study found that a long-acting formulation of buprenorphine (implant) was less expensive and more effective than oral buprenorphine.
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      Four studies that evaluated naloxone distribution found it to be highly cost-effective.
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      ,
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      ,
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.
      The exception was a model of a naloxone distribution in high schools, which found that the cost-effectiveness of the program was heavily dependent on the overdose frequency among students.
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.

       Characteristics of Economic Analyses

       Health outcomes and economic analysis framework

      Details on economic analyses are presented in Table 2. Most studies (n = 15) were CUAs using quality-adjusted life-years (QALYs) as the main health outcome, as recommended by US and international best practice guidelines.
      • Neumann P.J.
      • Sanders G.D.
      • Russels L.B.
      • Siegel J.E.
      • Ganiats T.G.
      Cost-Effectiveness in Health and Medicine.
      ,
      • Garrison Jr., L.P.
      • Neumann P.J.
      • Willke R.J.
      • et al.
      A health economics approach to U.S. value assessment frameworks—summary and recommendations of the ISPOR Special Task Force Report [7].
      • Neumann P.J.
      • Cohen J.T.
      QALYs in 2018—advantages and concerns.
      NICE
      Guide to Methods of Technology Appraisal.
      Four studies were CEAs using natural units as the health outcome (eg, opioid-free days); one of these conducted a CUA and a CEA.
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      One study was a CBA, which is a less common approach for decision making in the healthcare field because of the difficulty and controversy inherent in placing a monetary value on health, including survival.
      • Drummond M.
      • Sculpher M.
      • Torrance G.
      • O'Brien B.
      • Stoddart G.
      Methods for the Economic Evaluation of Health Care Programmes.
      ,
      • Neumann P.J.
      • Sanders G.D.
      • Russels L.B.
      • Siegel J.E.
      • Ganiats T.G.
      Cost-Effectiveness in Health and Medicine.
      ,
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      One study
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      valued life-years gained using lifetime earnings.
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      Table 2Summary of studies included in the review: health outcomes, costs, and economic analysis.
      StudyMain health outcome(s)Other health out-come(s)Intervention costsPerspective(s)Costs included in addition to intervention costsTime horizonDiscount rateYear and currencyAnalytical frame-work
      Adi et al,
      • Adi Y.
      • Juarez-Garcia A.
      • Wang D.
      • et al.
      Oral naltrexone as a treatment for relapse prevention in formerly opioid-dependent drug users: a systematic review and economic evaluation.
      2007
      QALYs (standard gamble)-Drug costs, counseling, laboratoriesHealth system,
      Main study perspective
      societal
      NHS and PSS, CJS
      Costs included in secondary perspective
      and crime victimization
      Costs included in secondary perspective
      12 monthsn/a2004 GBPCost utility
      Bansback et al,
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      2018
      QALYs (EQ-5D)Drug use, mortalityDrug costs, medication managementSocietal,
      Main study perspective
      health system
      Healthcare, CJS, and crime victimizationLifetime5.0%2015 CADCost utility
      Carter et al,
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      2017
      QALYs (standard gamble)Treatment retention, drug useDrug costs, medication managementSocietalHealthcare, productivity, CJS, crime victimization, patient out of pocket12 monthsn/a2016 USDCost utility
      Cipriano and Zaric,
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.
      2018
      QALYs (SF-6D)Overdoses, overdose deaths, life-yearsNaloxone costs and training costsDescribed as societal, but healthcare perspective was adoptedMedical costs associated with overdose and age-adjusted future healthcare costs based on epidemiological dataLifetime1.5%2017 CADCost utility
      Coffin and Sullivan,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      2013
      QALYs (SF-6D)Overdose deaths, mortality, heroin use, relapseNaloxone costs and distributionSocietalCosts related to overdoses (ED/EMS costs), “excess” health and CJS/victimization costsLifetime3.0%2012 USDCost utility
      Coffin and Sullivan,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      2013
      QALYs (EQ-5D)Overdose deaths, mortality, heroin use, relapseNaloxone costs and distributionSocietalCosts related to overdoses (ED/EMS costs), “excess” health and CJS costs (assumed)Life-time5.0%2010 USDCost utility
      Connock et al,
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      2007
      QALYs (standard gamble)Treatment retention, drug useDrug costs, counseling, laboratoriesHealth system,
      Main study perspective
      societal
      NHS and PSS, CJS
      Costs included in secondary perspective
      and crime victimization costs
      Costs included in secondary perspective
      12 monthsn/a2004 GBPCost utility
      Jackson et al,
      • Jackson H.
      • Mandell K.
      • Johnson K.
      • Chatterjee D.
      • Vanness D.J.
      Cost-effectiveness of injectable extended-release naltrexone compared with methadone maintenance and buprenorphine maintenance treatment for opioid dependence.
      2015
      Opioid-free days-Drug costs, counseling, medication managementPayerNone6 monthsn/aUSD (year not described)Cost-effectiveness
      Kenworthy et al,
      • Kenworthy J.
      • Yi Y.
      • Wright A.
      • Brown J.
      • Maria Madrigal A.
      • Dunlop W.C.N.
      Use of opioid substitution therapies in the treatment of opioid use disorder: results of a UK cost-effectiveness modelling study.
      2017
      QALYs (standard gamble)-Drug costs, counseling, laboratoriesHealth system,
      Main study perspective
      societal
      NHS and PSS, costs associated with HIV and HCV infection, CJS
      Costs included in secondary perspective
      and crime victimization costs
      Costs included in secondary perspective
      12 monthsn/a2016 GBPCost utility
      King et al,
      • King J.B.
      • Sainski-Nguyen A.M.
      • Bellows B.K.
      Office-based buprenorphine versus clinic-based methadone: a cost-effectiveness analysis.
      2016
      Opioid abuse-free weeksTreatment retentionDrug costs, medication management, counseling, laboratoriesPayerNone12 monthsn/a2014 USDCost-effectiveness
      Krebs et al,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      2018
      QALYs (SF-6D)HIV sero-conversion, mortalityDirect and indirect costs of methadone maintenance including medication managementSocietal,
      Main study perspective
      health system
      Healthcare costs, CJS, crime victimizationLifetime3.0%2016 USDCost utility
      Langham et al,
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      2018
      QALYs (SF-6D)Overdose deathsNaloxone, distribution, and trainingHealth system,
      Main study perspective
      societal
      Costs related to overdoses (ED/EMS costs), CJS
      Costs included in secondary perspective
      , and crime victimization
      Costs included in secondary perspective
      Lifetime3.5%2016 GBPCost utility
      Masson et al,
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      2004
      Life-years gained; QALYs (assumed utility decrements)-Costs of treatment arms through microcostingHealth systemHealthcare costs (hospital stays, ED visits, ambulatory care, and behavioral health treatment)Life-time3.0%USD (year not described)Cost effectiveness and cost utility
      Nosyk et al,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      2012
      QALYs (EQ-5D)-Drug costs, medication managementSocietal,
      Main study perspective
      health system
      Healthcare, CJS, crime victimization1, 5, and 10 years, and lifetime5.0%2009 CADCost utility
      Schackman et al,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      2012
      QALYs (standard gamble)Treatment retention, drug useDrug costs, medication management, laboratoriesHealth system and patientPatient costs: time spent, transportation24 months3.0%2010 USDCost utility
      Stephen et al,
      • Stephen J.H.
      • Halpern C.H.
      • Barrios C.J.
      • et al.
      Deep brain stimulation compared with methadone maintenance for the treatment of heroin dependence: a threshold and cost-effectiveness analysis.
      2012
      QALYs (standard gamble)-Reimbursement cost for methadone, and surgery with follow-up for DBSSocietalHealthcare, productivity, CJS, crime victimization,6 monthsn/a2011 USDCost utility
      Uyei et al,
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.
      2017
      QALYs (SF-6D)Survival, life expectancy, overdose deaths, HIV-related deathsNaloxone and distribution, PrEP costs (medication, staffing, laboratories)Health systemHealthcare costs (EMS/ED, HIV antiretroviral costs)5, 10, and 20 years3.0% (applied to costs only)2015 USDCost utility
      Zarkin et al,
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      2005
      Years using heroin, life-years saved-Direct and indirect costs of methadone maintenance including medication, managementSocietalHealthcare, employment, CJSLifetime3.0%2001 USDCost benefit
      CAD indicates Canadian dollar; CJS, criminal justice system; DBS, deep-brain stimulation; ED, emergency department; EMS, emergency medical services; GBP, Great Britain pound; HCV, hepatitis C virus; n/a, not applicable; NHS, National Health Service; PrEP, pre-exposure prophylaxis; PSS, Personal Social Services; QALY, quality-adjusted life-year; USD, United States dollar.
      Main study perspective
      Costs included in secondary perspective
      Utility values varied among studies that used QALYs, but all had lower utilities associated with opioid use compared with not using opioids. One applied utility decrements based on frequency of heroin use,
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      3 used utility values based on EuroQol 5-Dimension (EQ-5D) dimensions,
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      ,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      ,
      The EuroQol Group
      EuroQol-a new facility for the measurement of health-related quality of life.
      5 used values based on SF-6D dimensions,
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      ,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      ,
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.
      ,
      The EuroQol Group
      EuroQol-a new facility for the measurement of health-related quality of life.
      ,
      • Brazier J.
      • Roberts J.
      • Tsuchiya A.
      • Busschbach J.
      A Comparison of the EQ-5D and SF-6D across seven patient groups.
      and 6 used utility values from a panel of 22 UK respondents using the standard gamble technique.
      • Adi Y.
      • Juarez-Garcia A.
      • Wang D.
      • et al.
      Oral naltrexone as a treatment for relapse prevention in formerly opioid-dependent drug users: a systematic review and economic evaluation.
      ,
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      ,
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      ,
      • Kenworthy J.
      • Yi Y.
      • Wright A.
      • Brown J.
      • Maria Madrigal A.
      • Dunlop W.C.N.
      Use of opioid substitution therapies in the treatment of opioid use disorder: results of a UK cost-effectiveness modelling study.
      ,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      ,
      • Stephen J.H.
      • Halpern C.H.
      • Barrios C.J.
      • et al.
      Deep brain stimulation compared with methadone maintenance for the treatment of heroin dependence: a threshold and cost-effectiveness analysis.
      ,
      • Stein K.
      • Dyer M.
      • Crabb T.
      • et al.
      A pilot internet “Value of Health” panel: recruitment, participation and compliance.
      Seven used utilities generated in a country different from the country of analysis,
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      ,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      ,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      ,
      • Stephen J.H.
      • Halpern C.H.
      • Barrios C.J.
      • et al.
      Deep brain stimulation compared with methadone maintenance for the treatment of heroin dependence: a threshold and cost-effectiveness analysis.
      and 2 assumed the baseline utilities of substance users to be the same as for other conditions (eg, depression, HIV).
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      ,
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.
      Several studies shared the same utility values (Fig. 2). Several CUA studies also reported on other outcomes, such as mortality
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      ,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.
      and drug use.
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      ,
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      ,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      ,
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      Figure thumbnail gr2
      Figure 2Links between included studies. Solid arrow denotes common model structure. Dashed arrow denotes common utility values. Rectangles represent studies that adopted model structure characteristics or utility values from source studies, which are represented by circles.
      Seven studies modeled time horizons of 1 year or less, 1 study used a time horizon of 2 years, 2 considered multiple time horizons up to 20 years or a lifetime, and 8 used a lifetime horizon. Studies with shorter time horizons were at risk of underestimating the benefits of interventions that may accrue later. Studies with time horizons longer than 1 year applied discount rates between 1.5% and 5% annually. Five studies estimated results for subgroups; 2 stratified by demographic characteristics,
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      ,
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.
      and 3 stratified by opioid use characteristics, including novice versus experienced users,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      heroin versus prescription opioids,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      and route of administration (oral vs injection).
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      ,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      One study also stratified results by HIV serostatus.
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      Studies that stratify their populations into subgroups may uncover different responses to interventions from different segments of the population. This can have important policy implications, but conducting stratified analysis requires data unique to specific subgroups, which can present a challenge to modelers.

       Included costs and study perspective

      All of the studies included the costs of strategies. For MOUD strategies, costs included the full costs of the drugs (ie, medication costs and staff time for medication management) and the costs of associated services (eg, laboratory tests or psychotherapy as appropriate). Two studies relied on reimbursement rates from state Medicaid fee schedules and the Centers for Medicare & Medicaid Services Physician Fee Schedule, respectively,
      • Jackson H.
      • Mandell K.
      • Johnson K.
      • Chatterjee D.
      • Vanness D.J.
      Cost-effectiveness of injectable extended-release naltrexone compared with methadone maintenance and buprenorphine maintenance treatment for opioid dependence.
      ,
      • King J.B.
      • Sainski-Nguyen A.M.
      • Bellows B.K.
      Office-based buprenorphine versus clinic-based methadone: a cost-effectiveness analysis.
      1 used a detailed microcosting approach,
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      and the remaining 15 drew intervention costs from published studies or government reports.
      Thirteen studies self-described as adopting a societal perspective as the primary perspective or a secondary perspective, and all 13 applied higher costs to health states or scenarios resulting in opioid use compared with abstinence from opioids.
      • Adi Y.
      • Juarez-Garcia A.
      • Wang D.
      • et al.
      Oral naltrexone as a treatment for relapse prevention in formerly opioid-dependent drug users: a systematic review and economic evaluation.
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      ,
      • Kenworthy J.
      • Yi Y.
      • Wright A.
      • Brown J.
      • Maria Madrigal A.
      • Dunlop W.C.N.
      Use of opioid substitution therapies in the treatment of opioid use disorder: results of a UK cost-effectiveness modelling study.
      ,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      ,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      ,
      • Stephen J.H.
      • Halpern C.H.
      • Barrios C.J.
      • et al.
      Deep brain stimulation compared with methadone maintenance for the treatment of heroin dependence: a threshold and cost-effectiveness analysis.
      ,
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      All 13 included healthcare costs beyond intervention costs, and all but 1 included costs from other sectors.
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.
      Healthcare costs in studies of MOUD included all healthcare utilization whether it was directly related to opioid use or not. Twelve of the 13 studies that adopted a societal perspective included criminal activity or the criminal justice system costs. With the exception of 1 study that assumed criminal justice costs due to lack of available data,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      all studies include costs incurred by crime victims in addition to costs incurred by the criminal justice system. Of the 13 studies with a societal perspective, 3 included productivity costs,
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      ,
      • Stephen J.H.
      • Halpern C.H.
      • Barrios C.J.
      • et al.
      Deep brain stimulation compared with methadone maintenance for the treatment of heroin dependence: a threshold and cost-effectiveness analysis.
      ,
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      and only 1 included patient out-of-pocket healthcare costs.
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      Of 5 studies that did not adopt a societal perspective, 1 adopted a healthcare system perspective,
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      2 US–based studies were conducted from the payer perspective,
      • Jackson H.
      • Mandell K.
      • Johnson K.
      • Chatterjee D.
      • Vanness D.J.
      Cost-effectiveness of injectable extended-release naltrexone compared with methadone maintenance and buprenorphine maintenance treatment for opioid dependence.
      ,
      • King J.B.
      • Sainski-Nguyen A.M.
      • Bellows B.K.
      Office-based buprenorphine versus clinic-based methadone: a cost-effectiveness analysis.
      1 focused on the treatment system and included patient costs (eg, time costs in treatment),
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      and 1 adopted a narrow perspective focusing on costs relating to consequences addressed by its interventions (eg, costs related to overdose and HIV treatment).
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.

       Modeling Approach

       Model structure

      Four studies used decision trees to track costs and outcomes for 1 year or less (Table 3).
      • Adi Y.
      • Juarez-Garcia A.
      • Wang D.
      • et al.
      Oral naltrexone as a treatment for relapse prevention in formerly opioid-dependent drug users: a systematic review and economic evaluation.
      ,
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      ,
      • Kenworthy J.
      • Yi Y.
      • Wright A.
      • Brown J.
      • Maria Madrigal A.
      • Dunlop W.C.N.
      Use of opioid substitution therapies in the treatment of opioid use disorder: results of a UK cost-effectiveness modelling study.
      ,
      • Stephen J.H.
      • Halpern C.H.
      • Barrios C.J.
      • et al.
      Deep brain stimulation compared with methadone maintenance for the treatment of heroin dependence: a threshold and cost-effectiveness analysis.
      Thirteen studies used a cohort Markov model approach, which tracks a cohort’s progression through defined health states over discrete time cycles.
      • McLellan A.T.
      • Lewis D.C.
      • O'Brien C.P.
      • Kleber H.D.
      Drug dependence, a chronic medical illness: implications for treatment, insurance, and outcomes evaluation.
      Of the Markov studies, 3 integrated a decision tree to model overdose events, which occur over a short period and are suitably modeled as a decision tree,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      ,
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      and 3 incorporated history by defining health states in terms of time in state and treatment history.
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      ,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      One study
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      was a microsimulation that defined transitions and probabilities of events based on age and gender, heroin use, history of criminal activity and employment, and the success or failure of the last treatment episode. Generally, the decision tree models represented intervention effects as differences in treatment retention. The 3 studies that embedded decision trees into Markov models evaluated naloxone and applied differences in overdose mortality as the intervention effect. Other Markov model studies represented the intervention effect by varying transition probabilities across strategies. Among the 18 studies included in the review, 9 shared major model structure characteristics with at least one other (see Fig. 2). Fourteen studies reported the software used: R (n = 5), TreeAge Pro (n = 4), Excel (n = 4), and Arena (n = 1).
      Table 3Summary of studies included in the review: modeling approach.
      StudyModel structureIntervention effectModeling softwareApproach to uncertainty/sensitivity AnalysisValidation approach
      Adi et al,
      • Adi Y.
      • Juarez-Garcia A.
      • Wang D.
      • et al.
      Oral naltrexone as a treatment for relapse prevention in formerly opioid-dependent drug users: a systematic review and economic evaluation.
      2007
      Decision treeTreatment retention varied across strategies.TreeAge Pro 2005PSA; 1-way SA for key parametersNot described.
      Bansback et al,
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      2018
      Cohort semi-MarkovTPs varied across treatment strategies; utilities varied across treatment states.RPSA; multiway SA using alternative transition ratesInternal validation: compared results of base case model with results from the underlying trial.

      External validation: compared mortality rate with published study.
      Carter et al,
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      2017
      Cohort MarkovInitiation of opioid use while in treatment varied by strategy.Not describedPSA; 1-way SA of all parametersExternal validation: compared total direct medical cost of the sublingual cohort with a cost of illness study.
      Cipriano and Zaric,
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.
      2018
      Cohort MarkovApplied a reduction in mortality associated with overdose for naloxone.ExcelPSA; series of 3-way SAs varying 2 key parameters with every other parameter one at a timeNot described.
      Coffin and Sullivan,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      2013
      Cohort Markov with integrated decision treeApplied a reduction in mortality associated with overdose for naloxone.ExcelPSA; 1-way SA of all parameters; multi-way SA representing best and worst cases; calibrated parameters and parameter structure to epidemiological data using trial-and-error search algorithmNot described.
      Coffin and Sullivan,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      2013
      Cohort Markov with integrated decision treeApplied a reduction in mortality associated with overdose for naloxone.Excel with TreePlan add-inPSA; 1-way SA with extreme values of all parameters; calibrated parameters and model structure to epidemiological data using trial-and-error search algorithmExternal validation: compared model predictions with estimates from other studies (eg, rate of overdose).
      Connock et al,
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      2007
      Decision treeTreatment retention varied across strategies.TreeAge Pro 2005PSA; multi-way sensitivity analyses with alternative utility values and buprenorphine prescribing policiesNot described.
      Jackson et al,
      • Jackson H.
      • Mandell K.
      • Johnson K.
      • Chatterjee D.
      • Vanness D.J.
      Cost-effectiveness of injectable extended-release naltrexone compared with methadone maintenance and buprenorphine maintenance treatment for opioid dependence.
      2015
      Cohort MarkovTransition out of treatment and probability of opioid use while in treatment varies across strategies.Not describedMulti-way SA based on best- and worst-case parameter sets; 1-way SA focused on key parametersNot described.
      Kenworthy et al,
      • Kenworthy J.
      • Yi Y.
      • Wright A.
      • Brown J.
      • Maria Madrigal A.
      • Dunlop W.C.N.
      Use of opioid substitution therapies in the treatment of opioid use disorder: results of a UK cost-effectiveness modelling study.
      2017
      Decision treeTreatment retention varied across strategies; utilities varied across treatment states.RPSA; 1-way SA on key parameters, including removal of crime victimization costsCross validation: outputs were validated against the related Excel model previously published.
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      King et al,
      • King J.B.
      • Sainski-Nguyen A.M.
      • Bellows B.K.
      Office-based buprenorphine versus clinic-based methadone: a cost-effectiveness analysis.
      2016
      Cohort MarkovTransition out of treatment and probability of opioid use while in treatment varies across strategies.Not describedPSA; 1-way SA on key parameters; 2-way SA for drug costsNot described.
      Krebs et al,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      2018
      Cohort semi-MarkovAccess to opioid agonist treatment varies by strategy. The alternative approach (medically managed withdrawal) has a higher associated probability of relapse and a higher probability of death than methadone treatment.RPSA; conditional PSA (PSA with select parameters held constant); 1-way SA on key parameters; multi-way SA on transition parameters relating to out-of-treatment states, and analyses of structural uncertainty (eg, relaxation of structural assumptions)External validation: compared projected mortality, HIV incidence, and proportion of time in treatment with observed outcomes.
      Langham et al,
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      2018
      Cohort Markov with integrated decision treeApplied a reduction in mortality associated with overdose for naloxone and accounted for the probability that it is available and used.RPSA; 1-way SA of all parametersCross-validation: confirmed that the model was replicated correctly by comparing outcomes with published outcomes from a related model.
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      Masson et al,
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      2004
      Cohort MarkovMortality (a function of heroin use) varied across strategies.Not described1-way SA on key parametersExternal validation: model produced mortality rates in line with observed rates.
      Nosyk et al,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      2012
      Cohort semi-MarkovAccess to diacetylmorphine varies by strategy. The alternative approach (methadone maintenance) has a higher associated probability of relapse than diacetylmorphine.RPSA; 1-way SA on key parameters; analyses of structural uncertainty (eg, relaxation of structural assumptions); calibrated Weibull parameters representing time to discontinuation of abstinence to fit external dataInternal validation: compared model results with underlying trial data.

      External validation: compared modeled mortality with published data.
      Schackman et al,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      2012
      Cohort MarkovProbability of relapse varies by strategy.TreeAge Pro 2009PSA; EVPPI analysis; 1- and 2-way SA on key parameters; conditional PSA (holding select parameters at chosen value and varying all other parameters using PSA)Not described.
      Stephen et al,
      • Stephen J.H.
      • Halpern C.H.
      • Barrios C.J.
      • et al.
      Deep brain stimulation compared with methadone maintenance for the treatment of heroin dependence: a threshold and cost-effectiveness analysis.
      2012
      Decision treeDecision tree end nodes vary by strategy and are specific to that strategy.TreeAge Pro 20091-way SA for all parameters; 2-way SA for most influential parameters (based on 1-way SA)Not described.
      Uyei et al,
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.
      2017
      Cohort MarkovApplied a reduction in mortality associated with overdose for naloxone and accounted for the probability that it is available and used. Treatment linkages increased the probability of entering treatment and discontinuing injection drug use.ExcelPSA; 1-way SA on key parametersExternal validation: compared modeled no-intervention scenario with published epidemiologic studies for 4 targets: 5-year mortality, 10-year mortality, HIV incidence, and HIV prevalence.
      Zarkin et al,
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      2005
      Individual-level microsimulationVary by strategy and are explicit. Interventions are modeled by changing baseline parameters to represent the strategy under consideration.Arena1-way SA for parameters based on assumption or limited data; calibrated transition to abstinence and probability of crime parameters so that model outputs would match external dataExternal validation: compared findings from single-treatment episode scenario with a previously published CBA.
      CBA indicates cost-benefit analysis; EVPPI, expected value of partial perfect information; PSA, probabilistic sensitivity analysis; SA, sensitivity analysis; TP, transition probability.

       Uncertainty

      All of the studies reported conducting deterministic or probabilistic sensitivity analysis (PSA) to evaluate parameter uncertainty, and 14 reported both, as recommended by the ISPOR-SMDM Modeling Good Research Practices Task Force.
      • Briggs A.H.
      • Weinstein M.C.
      • Fenwick E.A.
      • et al.
      Model parameter estimation and uncertainty: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6.
      Fifteen studies used one-way sensitivity analyses on some or all parameters, and 9 conducted multiway sensitivity analyses (ie, varying 2 or more parameters simultaneously while holding the rest constant) to test best- or worst-case scenarios or alternative assumptions on a combination of input parameters. Two studies conducted conditional PSAs, which held select parameters constant and conducted the PSA on the remaining parameters.
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      Four studies
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      ,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      ,
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      reported formal calibration to generate model parameters.
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      ,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      ,
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      ,
      • Briggs A.H.
      • Weinstein M.C.
      • Fenwick E.A.
      • et al.
      Model parameter estimation and uncertainty: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6.
      For example, one study
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      calibrated both models to epidemiologic outcomes using a trial-and-error algorithm until it hit all targets simultaneously. Two studies examined structural uncertainty in their models
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      ; for example, one study
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      relaxed an assumption that transition from relapse or medically managed withdrawal to abstinence was impossible. One study performed expected value of partially perfect information analysis.
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.

       Validation

      Validation represents the extent to which a model reproduces reality.
      • Eddy D.M.
      • Hollingworth W.
      • Caro J.J.
      • Tsevat J.
      • McDonald K.M.
      • Wong J.B.
      Model transparency and validation: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force–7.
      Only 10 studies included a validation approach, and only 2 used multiple types (ie, internal and external validation).
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      ,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      Two studies cross-validated their model against earlier models also included in the review,
      • Kenworthy J.
      • Yi Y.
      • Wright A.
      • Brown J.
      • Maria Madrigal A.
      • Dunlop W.C.N.
      Use of opioid substitution therapies in the treatment of opioid use disorder: results of a UK cost-effectiveness modelling study.
      ,
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      but the authors of the original models did not report their approach to validation,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      ,
      • Connock M.
      • Juarez-Garcia A.
      • Jowett S.
      • et al.
      Methadone and buprenorphine for the management of opioid dependence: a systematic review and economic evaluation.
      thus limiting the importance of cross-validation. Two studies conducted internal validation by comparing base case results from trials that informed key parameter sources to model results.
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      ,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      Of the 8 studies
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      ,
      • Carter J.A.
      • Dammerman R.
      • Frost M.
      Cost-effectiveness of subdermal implantable buprenorphine versus sublingual buprenorphine to treat opioid use disorder.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal in Russian cities.
      ,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Masson C.L.
      • Barnett P.G.
      • Sees K.L.
      • et al.
      Cost and cost-effectiveness of standard methadone maintenance treatment compared to enriched 180-day methadone detoxification.
      ,
      • Nosyk B.
      • Guh D.P.
      • Bansback N.J.
      • et al.
      Cost-effectiveness of diacetylmorphine versus methadone for chronic opioid dependence refractory to treatment.
      ,
      • Uyei J.
      • Fiellin D.A.
      • Buchelli M.
      • Rodriguez-Santana R.
      • Braithwaite R.S.
      Effects of naloxone distribution alone or in combination with addiction treatment with or without pre-exposure prophylaxis for HIV prevention in people who inject drugs: a cost-effectiveness modelling study.
      ,
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      that reported conducting external validation, 5 validated against a single parameter type (eg, mortality rates) and thus did not validate multiple components of the model.
      • Eddy D.M.
      • Hollingworth W.
      • Caro J.J.
      • Tsevat J.
      • McDonald K.M.
      • Wong J.B.
      Model transparency and validation: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force–7.

      Discussion

      We conducted a systematic review of the methods employed by economic evaluations that used simulation modeling to assess the health and economic impacts of interventions to address opioid misuse. We reviewed the studies’ methods to understand current practice and to identify gaps that need to be addressed to better inform the optimal deployment of resources to combat the opioid crisis.
      Simulation modelers face several interrelated decisions among alternative model structures, perspectives, valuation approaches, and methods to address uncertainty and validation. The choice of model structure depends on the decision problem, individual versus cohort unit of analysis, the time horizon, and data availability.
      • Neumann P.J.
      • Sanders G.D.
      • Russels L.B.
      • Siegel J.E.
      • Ganiats T.G.
      Cost-Effectiveness in Health and Medicine.
      ,
      • Briggs A.
      • Sculpher M.
      • Claxton K.
      Decision Modelling for Health Economic Evaluation.
      ,
      • Brennan A.
      • Chick S.E.
      • Davies R.
      A taxonomy of model structures for economic evaluation of health technologies.
      ,
      • Roberts M.
      • Russell L.B.
      • Paltiel A.D.
      • et al.
      Conceptualizing a model: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-2.
      Decision trees are best applied to situations with no or few recurrent events and in which the time horizon is short and fixed.
      • Drummond M.
      • Sculpher M.
      • Torrance G.
      • O'Brien B.
      • Stoddart G.
      Methods for the Economic Evaluation of Health Care Programmes.
      Because of the chronic nature of OUD, which is characterized by recurrent relapse and recovery and multiple treatment episodes,
      • McLellan A.T.
      • Lewis D.C.
      • O'Brien C.P.
      • Kleber H.D.
      Drug dependence, a chronic medical illness: implications for treatment, insurance, and outcomes evaluation.
      a long-term horizon, ideally lifetime, can better capture all of the relevant consequences of the strategies under consideration. Thus, for decision problems related to OUD, Markov models with long time horizons are superior to decision trees because they are particularly adept for decision problems involving disease progression or the potential for alternating episodes of recovery and relapse. Other common modeling approaches include dynamic compartmental models, which compartmentalize the population assuming homogeneity and use a system of equations representing stocks and flows of people among compartments over time, and agent-based models, which permit interaction between simulated people. Although both approaches have been used for opioid use and OUD,
      • Enns E.A.
      • Zaric G.S.
      • Strike C.J.
      • Jairam J.A.
      • Kolla G.
      • Bayoumi A.M.
      Potential cost-effectiveness of supervised injection facilities in Toronto and Ottawa, Canada.
      • Keane C.
      • Egan J.E.
      • Hawk M.
      Effects of naloxone distribution to likely bystanders: results of an agent-based model.
      • Wakeland W.
      • Nielsen A.
      • Geissert P.
      Dynamic model of nonmedical opioid use trajectories and potential policy interventions.
      • Wakeland W.
      • Nielsen A.
      • Schmidt T.D.
      • et al.
      Modeling the impact of simulated educational interventions on the use and abuse of pharmaceutical opioids in the United States: a report on initial efforts.
      • Zaric G.S.
      • Barnett P.G.
      • Brandeau M.L.
      HIV transmission and the cost-effectiveness of methadone maintenance.
      no study using these approaches met our inclusion criteria.
      Modelers also need to determine the appropriate unit of analysis for their model. Of the 18 studies in our review, 17 were cohort models and 1 was an individual-level simulation.
      • Zarkin G.A.
      • Dunlap L.J.
      • Hicks K.A.
      • Mamo D.
      Benefits and costs of methadone treatment: results from a lifetime simulation model.
      Although there are clear advantages to using individual-level models in that they permit the model to capture variability by individual-level characteristics—including individual histories—they require data to support parameterization, calibration, and validation at the individual level and are often more computationally intensive than models with higher-level units of analysis.
      • Briggs A.
      • Sculpher M.
      • Claxton K.
      Decision Modelling for Health Economic Evaluation.
      Individual-level models should be considered when data and computational resources are available to support them, but failing that, cohort models are appropriate tools to analyze many policies and often reach similar conclusions to those of individual-level models.
      • Briggs A.
      • Sculpher M.
      • Claxton K.
      Decision Modelling for Health Economic Evaluation.
      When an individual-level model cannot be supported, modelers should consider conducting a subgroup analysis to provide more granular detail about costs and the effectiveness of interventions for different groups. Several studies included in the review did this,
      • Bansback N.
      • Guh D.
      • Oviedo-Joekes E.
      • et al.
      Cost-effectiveness of hydromorphone for severe opioid use disorder: findings from the Salome randomized clinical trial.
      ,
      • Cipriano L.E.
      • Zaric G.S.
      Cost-effectiveness of naloxone kits in secondary schools.
      ,
      • Coffin P.O.
      • Sullivan S.D.
      Cost-effectiveness of distributing naloxone to heroin users for lay overdose reversal.
      ,
      • Krebs E.
      • Enns B.
      • Evans E.
      • et al.
      Cost-effectiveness of publicly funded treatment of opioid use disorder in California.
      ,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      whereas others acknowledged the value in doing so but cited data limitations as a barrier.
      • Adi Y.
      • Juarez-Garcia A.
      • Wang D.
      • et al.
      Oral naltrexone as a treatment for relapse prevention in formerly opioid-dependent drug users: a systematic review and economic evaluation.
      ,
      • Langham S.
      • Wright A.
      • Kenworthy J.
      • Grieve R.
      • Dunlop W.C.N.
      Cost-effectiveness of take-home naloxone for the prevention of overdose fatalities among heroin users in the United Kingdom.
      Because calibration can be used to estimate parameters that are not directly observable,
      • Briggs A.H.
      • Weinstein M.C.
      • Fenwick E.A.
      • et al.
      Model parameter estimation and uncertainty: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6.
      it should be considered to overcome data limitations to subgroup analysis.
      The Second Panel on Cost-Effectiveness in Health and Medicine recommended that all CEAs report 2 reference case analyses: one with a healthcare sector perspective and another with a societal perspective, and the use of an “impact inventory” table that contains all consequences.
      • Neumann P.J.
      • Sanders G.D.
      • Russels L.B.
      • Siegel J.E.
      • Ganiats T.G.
      Cost-Effectiveness in Health and Medicine.
      ,
      • Sanders G.D.
      • Neumann P.J.
      • Basu A.
      • et al.
      Recommendations for conduct, methodological practices, and reporting of cost-effectiveness analyses: Second Panel on Cost-Effectiveness in Health and Medicine.
      Most of the studies included, however, were published before the Second Panel recommendations were released in 2016, and the recommendations from the original panel
      • Gold M.R.
      • Siegel J.E.
      • Russell L.B.
      • Weinstein M.C.
      Cost-Effectiveness in Health and Medicine.
      ,
      • Weinstein M.C.
      • Siegel J.E.
      • Gold M.R.
      • Kamlet M.S.
      • Russell L.B.
      Recommendations of the Panel on Cost-Effectiveness in Health and Medicine.
      did not include an impact inventory table and recommended only a societal perspective. Studies that adopted a societal perspective presented a subset of all the possible consequences of the intervention(s) they evaluated. They omitted important consequences such as out-of-pocket patient costs (which should also be included in the healthcare perspective); caregiver time costs; the health-related quality-of-life impact on family, friends, and crime victims; and the cost of unpaid productivity. Nevertheless, it should be noted that the inclusion of a broad societal perspective that encompasses all possible consequences might not be practical because of data availability and might make the analysis too cumbersome, particularly for narrow research questions.
      The choice of outcome and method of valuation in a health economic evaluation is of paramount importance because alternative choices can lead to different appraisals of an intervention. The Second Panel recommends that all CEAs use QALYs to incorporate morbidity and mortality in measuring health consequences.
      • Neumann P.J.
      • Sanders G.D.
      • Russels L.B.
      • Siegel J.E.
      • Ganiats T.G.
      Cost-Effectiveness in Health and Medicine.
      Several studies identified the dearth of information on utility values for relevant health states as a limitation, and most made strong assumptions regarding these values. Among included studies, valuation approaches varied (eg, some studies relied on EQ-5D values, whereas others relied on Short Form 6-Dimension [SF-6D] values), which might lead to differences in utility values and hinder comparisons.
      • Brazier J.
      • Roberts J.
      • Tsuchiya A.
      • Busschbach J.
      A Comparison of the EQ-5D and SF-6D across seven patient groups.
      A recent study published US–representative utilities for health states for prescription and illicit drug misuse,
      • Wittenberg E.
      • Bray J.W.
      • Aden B.
      • Gebremariam A.
      • Nosyk B.
      • Schackman B.R.
      Measuring benefits of opioid misuse treatment for economic evaluation: health-related quality of life of opioid-dependent individuals and their spouses as assessed by a sample of the US Population.
      providing an important contribution to future economic evaluations of interventions to address opioid misuse.
      An important feature of health economic models is the ability to measure the impact of uncertainty. Models provide insight into phenomena or policy scenarios that cannot be directly observed; thus model parameters are often selected with considerable uncertainty.
      • Briggs A.
      • Sculpher M.
      • Claxton K.
      Decision Modelling for Health Economic Evaluation.
      Consistent with best practices,
      • Briggs A.H.
      • Weinstein M.C.
      • Fenwick E.A.
      • et al.
      Model parameter estimation and uncertainty: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-6.
      all of the studies conducted sensitivity analyses, and 14 of 18 conducted deterministic and probabilistic sensitivity analyses. Only one study, however, conducted value of information analysis,
      • Schackman B.R.
      • Leff J.A.
      • Polsky D.
      • Moore B.A.
      • Fiellin D.A.
      Cost-effectiveness of long-term outpatient buprenorphine-naloxone treatment for opioid dependence in primary care.
      an approach to establish the value of additional research compared with making decisions with current information.
      • Claxton K.P.
      • Sculpher M.J.
      Using value of information analysis to prioritise health research - some lessons from recent UK experience.
      Because many parameter values are largely uncertain in models involving OUD, value of sample information can be a valuable tool to prioritize future research,
      • Ades A.E.
      • Lu G.
      • Claxton K.
      Expected value of sample information calculations in medical decision modeling.
      and future studies should include it.
      Finally, all models should address validation (ie, how well the model reproduces reality).
      • Eddy D.M.
      • Hollingworth W.
      • Caro J.J.
      • Tsevat J.
      • McDonald K.M.
      • Wong J.B.
      Model transparency and validation: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force–7.
      ,
      • Caro J.J.
      • Briggs A.H.
      • Siebert U.
      • Kuntz K.M.
      Modeling good research practices--overview: a report of the ISPOR-SMDM Modeling Good Research Practices Task Force-1.
      Only 10 of 18 studies in our review reported their validation approach, and only 2 conducted multiple types of validation. External validation is particularly challenging in models of opioid use because of data limitations.
      • Smart R.
      • Kase C.A.
      • Meyer A.
      • Stein B.D.
      Data sources and data-linking strategies to support research to address the opioid crisis.
      Studies in the review that conducted external validation compared model outputs with epidemiologic data on mortality or disease incidence. Future modeling studies should put more effort into internal validation, external validation, and cross-validation.
      • Vemer P.
      • Corro Ramos I.
      • van Voorn G.A.
      • Al M.J.
      • Feenstra T.L.
      Advishe: a validation-assessment tool of health-economic models for decision makers and model users.
      A common feature of the models included in this review is that they focused on a narrow set of interventions delivered at individual stages of the continuum of care, rather than a more comprehensive response. Changing the course of the opioid crisis will require a multipronged approach,
      • Chen Q.
      • Larochelle M.R.
      • Weaver D.T.
      • et al.
      Prevention of prescription opioid misuse and projected overdose deaths in the United States.
      which requires evaluating combinations of different interventions. A recent study
      • Pitt A.L.
      • Humphreys K.
      • Brandeau M.L.
      Modeling health benefits and harms of public policy responses to the US opioid epidemic.
      developed a dynamic compartmental model of pain status, opioid use status, and substance use disorder status to project the effect of policies aimed at reducing deaths in the United States. The study concluded that no single policy is likely to have a large enough effect to substantially reduce opioid-related deaths over 5 or even 10 years, and a portfolio of interventions is likely needed. Another recent study
      • Irvine M.A.
      • Kuo M.
      • Buxton J.A.
      • et al.
      Modelling the combined impact of interventions in averting deaths during a synthetic-opioid overdose epidemic.
      developed a hierarchical latent Markov process model to estimate the individual and combined effect of large-scale opioid overdose interventions implemented in British Columbia in response to the overdose crisis. Neither study, however, accounted for the broader societal consequences of opioid misuse, its economic implications, or the cost of the interventions. Despite the resources now devoted to the opioid epidemic, funding is limited, and decision makers need to account for the effectiveness and cost of strategies. A necessary next step in refining those recently developed models is the incorporation of costs so they can guide resource allocation decisions, such as selecting an optimal set of interventions from a portfolio of possible investments.
      Our review has 3 main limitations. First, there is a lack of diversity in the types of interventions represented in the models in our review. Most studies in the review evaluated MOUD, and about one-quarter evaluated naloxone distribution. No economic evaluation using simulation modeling has assessed the cost-effectiveness of prevention interventions, and although our review included studies that examined naloxone distribution, other harm reduction strategies (eg, supervised injection facilities [SIFs]) were not included. Important work has been done to examine the cost-effectiveness of SIFs,
      • Enns E.A.
      • Zaric G.S.
      • Strike C.J.
      • Jairam J.A.
      • Kolla G.
      • Bayoumi A.M.
      Potential cost-effectiveness of supervised injection facilities in Toronto and Ottawa, Canada.
      ,
      • Bayoumi A.M.
      • Zaric G.S.
      The cost-effectiveness of Vancouver's supervised injection facility.
      but these studies were excluded because they focused on the impact of SIFs on HIV and hepatitis C transmission, without reporting outcomes related to the impact of the intervention on opioid misuse. Second, we did not conduct a formal quality assessment of the studies included in this review. Although formal quality appraisal is appropriate in systematic reviews that evaluate specific interventions, we adopted a review method that does not require a quality assessment of each study
      • Grant M.J.
      • Booth A.
      A typology of reviews: an analysis of 14 review types and associated methodologies.
      because our goal was not to synthesize evidence for a particular intervention, but rather to examine methods used to evaluate different but related interventions. Finally, because some models included in our review were adapted and reused in later studies included in the review, the frequencies describing methodological choices in the results of this review should not be considered representative of modeling practice.

      Conclusions

      Cost-effectiveness simulation models can guide and inform clinical and public health responses to the opioid crisis and can be used to improve complex decision making about opioid policy. Future models should assess the effect of a combination of interventions and consider synergies across interventions in the continuum of OUD prevention, harm reduction, and treatment. Policy makers need guidance on how to combine interventions efficiently. Despite data challenges, future models should account for the heterogeneity in the characteristics of the opioid epidemic at state and local levels.
      • Unick G.J.
      • Ciccarone D.
      US regional and demographic differences in prescription opioid and heroin-related overdose hospitalizations.
      • Ruhm C.J.
      Geographic variation in opioid and heroin involved drug poisoning mortality rates.
      • Haffajee R.L.
      • Lin L.A.
      • Bohnert A.S.B.
      • Goldstick J.E.
      Characteristics of US counties with high opioid overdose mortality and low capacity to deliver medications for opioid use disorder.
      • Abraham A.J.
      • Andrews C.M.
      • Yingling M.E.
      • Shannon J.
      Geographic disparities in availability of opioid use disorder treatment for medicaid enrollees.
      • Rigg K.K.
      • Monnat S.M.
      • Chavez M.N.
      Opioid-related mortality in rural America: geographic heterogeneity and intervention strategies.
      The cost-effective set of alternatives for one community could differ from that of another community. Future models should also more consistently report on validation, account for uncertainty in model parameters, and assess the value of further research.

      Acknowledgment

      The authors gratefully acknowledge Mark Howell, MLS, who provided literature search support for this article and 3 anonymous reviewers who provided helpful feedback and suggestions.

      Supplemental Material

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