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Modeling the cost and impact of injectable opioid agonist therapy on overdose and overdose deaths

Published:September 08, 2022DOI:https://doi.org/10.1016/j.jsat.2022.108871

      Abstract

      Aims

      Unsupervised injectable opioid agonist therapy (iOAT) may decrease the unmet treatment needs for people who inject opioids. We aimed to model whether unsupervised iOAT may be effective in reducing fatal and non–fatal overdose, and estimate the cost per life saved.

      Methods

      The study used a decision tree model based on Australian and international parameters for overdose risk in people who inject opioids who are: not on OAT; new/stable to methadone/buprenorphine treatment; on iOAT; or on unsupervised iOAT. We modeled scenarios of (1) current OAT only (status quo), or current OAT plus either (2) 5% supervised iOAT, (3) 5% supervised or 5.69% unsupervised iOAT (based on willingness to enroll), OR (4) 1.2% supervised and 10% unsupervised iOAT (the same cost as scenario 2). The study measured overdoses (fatal and nonfatal) and treatment costs per 10,000 people who inject opioids per annum, and cost-per deaths averted on implementation of iOAT.

      Results

      With current OAT, the study found an estimated 1655.5 (1552.7–1705.3) overdoses, 19.3 (17.9–20.3) overdose deaths and AUD 23,335,081 in treatment costs per 10,000 people per annum. Implementation of 5% enrollment in supervised iOAT costs an additional AUD 14,807,855 and showed a reduction of 122.9 (95% UI 114.2–130.5) overdoses and 2.0 (1.8–2.0) overdose deaths per 10,000 people per annum ($7,774,172 [7,283,182–8,146,989] per death averted). For the same treatment costs, additional coverage of 10% unsupervised iOAT and 1.2% supervised iOAT could be achieved, which the study estimated to prevent 269.0 (95% UI 250.0–278.7) overdoses and 4.0 (3.7–4.2) overdose deaths per 10,000 people per annum ($3,723,340 (3,385,878–3,894,379) per death averted), alongside further benefits of treatment unaccounted for in this study.

      Conclusion

      An implementation scenario with greater unsupervised iOAT compared to supervised iOAT allows for an increased reduction in overdose and overdose deaths per annum at the same cost, with the additional benefit of increased treatment coverage among people who inject opioids.

      Keywords

      Summary

      Question

      Can increasing treatment through access of supervised and unsupervised iOAT reduce opioid harms?

      Findings

      In this modelling study of 10,000 people who inject opioids increased resources allocated to unsupervised iOAT compared to supervised iOAT yielded the lowest cost per overdose averted and cost per death averted.

      Meaning

      Unsupervised iOAT, when used in conjunction with OAT and supervised iOAT, has the potential to reduce overdoses and overdose deaths compared to scenarios where OAT and supervised iOAT is used exclusively.

      1. Introduction

      Opioid use and harms have been growing substantially over the past decade (
      • Ciccarone D.
      The triple wave epidemic: Supply and demand drivers of the US opioid overdose crisis.
      ;
      • Scholl L.
      • Seth P.
      • Kariisa M.
      • Wilson N.
      • Baldwin G.
      Drug and opioid-involved overdose deaths - United States, 2013–2017.
      ), in particular among people who inject opioids. People who inject opioids are at increased risk of a range of poor health outcomes (
      Australian Institute of Health and Welfare
      Alcohol, tobacco & other drugs in Australia.
      ). This growth has led to an increased focus on evidence-based treatments, such as opioid agonist therapy (OAT). OAT involving methadone and buprenorphine maintenance therapy in particular have a large evidence base demonstrating their effectiveness in reducing opioid use and related mortality (
      • Mattick R.P.
      • Breen C.
      • Kimber J.
      • Davoli M.
      Methadone maintenance therapy versus no opioid replacement therapy for opioid dependence.
      ,
      • Mattick R.P.
      • Breen C.
      • Kimber J.
      • Davoli M.
      Buprenorphine maintenance versus placebo or methadone maintenance for opioid dependence.
      ;
      • Sordo L.
      • Barrio G.
      • Bravo M.J.
      • Indave B.I.
      • Degenhardt L.
      • Wiessing L.
      • Pastor-Barriuso R.
      Mortality risk during and after opioid substitution treatment: Systematic review and meta-analysis of cohort studies.
      ). Nevertheless, an estimated 5–10 % of people who use opioids are not attracted to or do not benefit from current OAT therapies (
      • Strang J.
      • Groshkova T.
      • Metrebian N.
      EMCDDA INSIGHTS. New heroin-assisted treatment. Recent evidence and current practices of supervised injectable heroin treatment in Europe and beyond.
      ;
      • Strang J.
      • Metrebian N.
      • Lintzeris N.
      • Potts L.
      • Carnwath T.
      • Mayet S.
      • Forzisi L.
      Supervised injectable heroin or injectable methadone versus optimised oral methadone as treatment for chronic heroin addicts in England after persistent failure in orthodox treatment (RIOTT): A randomised trial.
      ).
      Injectable OAT (iOAT) typically involves self-administration of short-acting opioids, such as diacetylmorphine and hydromorphone, and has proven to be effective in treating those people who are opioid-dependent and who do not respond to treatment with conventional OAT (
      • Oviedo-Joekes E.
      • Brissette S.
      • Marsh D.C.
      • Lauzon P.
      • Guh D.
      • Anis A.
      • Schechter M.T.
      Diacetylmorphine versus methadone for the treatment of opioid addiction.
      ;
      • Strang J.
      • Groshkova T.
      • Uchtenhagen A.
      • van den Brink W.
      • Haasen C.
      • Schechter M.T.
      • Metrebian N.
      Heroin on trial: Systematic review and meta-analysis of randomised trials of diamorphine-prescribing as treatment for refractory heroin addiction.
      ;
      • Strang J.
      • Metrebian N.
      • Lintzeris N.
      • Potts L.
      • Carnwath T.
      • Mayet S.
      • Forzisi L.
      Supervised injectable heroin or injectable methadone versus optimised oral methadone as treatment for chronic heroin addicts in England after persistent failure in orthodox treatment (RIOTT): A randomised trial.
      ). This treatment is distinct from other injectable types of OAT, such as long acting injectable buprenorphine (LAIB), which is neither self-administered or short acting. A systematic review and Cochrane review have demonstrated that iOAT is effective in reducing opioid use (
      • Ferri M.
      • Davoli M.
      • Perucci C.A.
      Heroin maintenance for chronic heroin-dependent individuals.
      ;
      • Strang J.
      • Groshkova T.
      • Uchtenhagen A.
      • van den Brink W.
      • Haasen C.
      • Schechter M.T.
      • Metrebian N.
      Heroin on trial: Systematic review and meta-analysis of randomised trials of diamorphine-prescribing as treatment for refractory heroin addiction.
      ). More recent studies have demonstrated noninferiority of hydromorphone in treatment effectiveness compared to diacetylmorphine treatment (
      • Oviedo-Joekes E.
      • Guh D.
      • Brissette S.
      • Marchand K.
      • MacDonald S.
      • Lock K.
      • Schechter M.T.
      Hydromorphone compared with diacetylmorphine for long-term opioid dependence: A randomized clinical trial.
      ;
      • Oviedo-Joekes E.
      • Palis H.
      • Guh D.
      • Marsh D.C.
      • MacDonald S.
      • Harrison S.
      • Schechter M.T.
      Adverse events during treatment induction with injectable diacetylmorphine and hydromorphone for opioid use disorder.
      ). Consequently in recent years, some countries have adopted iOAT as a third-line treatment for clients who do not achieve good treatment outcomes with OAT (
      • Ferri M.
      • Davoli M.
      • Perucci C.A.
      Heroin maintenance for chronic heroin-dependent individuals.
      ;
      • Kimmel S.
      • Bach P.
      • Walley A.Y.
      Comparison of treatment options for refractory opioid use disorder in the United States and Canada: A narrative review.
      ).
      Despite the evidence of its effectiveness, iOAT is not widely available. One factor that limits its availability is the difficulties in delivering and upscaling iOAT. This is due to it being provided in a highly structured way with supervised administration requiring dedicated infrastructure and oversight by medical and nursing staff. The rationale for supervision includes the greater risk of injected relative to oral or sublingual OAT. Previous trials have shown small increases in risk of overdose and respiratory depression in iOAT, requiring intervention from medical staff on site (
      • Ferri M.
      • Davoli M.
      • Perucci C.A.
      Heroin maintenance for chronic heroin-dependent individuals.
      ;
      • Strang J.
      • Groshkova T.
      • Uchtenhagen A.
      • van den Brink W.
      • Haasen C.
      • Schechter M.T.
      • Metrebian N.
      Heroin on trial: Systematic review and meta-analysis of randomised trials of diamorphine-prescribing as treatment for refractory heroin addiction.
      ). The cost to provide the infrastructure, specifically staffing requirements to supervise injections and dedicated facilities, is one factor that limits widescale provision of iOAT. The cost remains a large barrier to increasing coverage and reducing opioid-related harm and mortality through this treatment.
      Currently, people who inject opioids in Australia have access to OAT formulations of methadone and buprenorphine, but injectable naltrexone is not an approved treatment for opioid use disorder in Australia. Oral naltrexone has low uptake among people who inject opioids, and no naltrexone formulation (including injectable) has been approved or funded for the treatment of opioid use disorder in Australia as of this writing. Recommendations for trials of diacetylmorphine (
      • Bammer G.
      • Douglas R.M.
      The ACT heroin trial proposal: An overview. Australian Capital Territory.
      ) and hydromorphone (
      • Hall W.D.
      • Kimber J.
      • Mattick R.P.
      Breaking the deadlock over an australian trial of injectable opioid maintenance.
      ) did not progress, but a trial of iOAT, funded by the National Health and Medical Research Council, has been planned (
      Australian Government National Health and Medical Research Council
      2018 Partnership Projects Third Call for Funding Commencing in 2019 National Health and Medical Research Council.
      ).
      In addition to the infrastructure required to provide iOAT, the intensity of the treatment is a barrier to its widespread use from the consumer perspective (
      • Demaret I.
      • Litran G.
      • Magoga C.
      • Deblire C.
      • Dupont A.
      • De Roubaix J.
      • et al.
      Why do heroin users refuse to participate in a heroin-assisted treatment trial?.
      ;
      • Romo N.
      • Poo M.
      • Ballesta R.
      PEPSATeam
      From illegal poison to legal medicine: A qualitative research in a heroin-prescription trial in Spain*.
      ;
      • Strang L.
      • Taylor J.
      Heroin-assisted treatment and supervised drug consumption sites: Experience from four countries.
      ). Those receiving iOAT must come to a dedicated service to self-administer supervised injections 2–3 times a day. Both the attendance requirements and the rigidity of the treatment model are two key barriers to this treatment perceived by potential clients (
      • Nielsen S.
      • Sanfilippo P.
      • Belackova V.
      • Day C.
      • Silins E.
      • Lintzeris N.
      • Larance B.
      Perceptions of injectable opioid agonist treatment (iOAT) among people who regularly use opioids in Australia: Findings from a cross-sectional study in three Australian cities.
      ). As such, not all at-risk clients who might benefit from iOAT are willing to enter this form of treatment.
      In the past year, an alternative to supervised iOAT has been piloted in Vancouver, Canada, in which clients have unsupervised access to a specified amount of hydromorphone tablets through dispensing machines (
      • Brooks M.
      Can 'world's first' opioid vending machine cut overdose deaths? Medscape.
      ). Other models have involved provision of hydromorphone through treatment services as a means of low-threshold iOAT that allows people in treatment to self-administer without the supervision of clinicians. These models of care have the potential to increase treatment access for clients who do not respond to conventional OAT and are unable or unwilling to enroll in current supervised iOAT settings. However some scholars have questioned the appropriateness of providing tablets for injection and some have advocated for the safe supply of injectable opioids (
      • Lam V.
      As a doctor, I was taught ‘first do no harm.’ That’s why I have concerns with the so-called ‘safe supply’ of drugs.
      ).
      To date, no studies have assessed the relative risks versus benefits or costs of unsupervised iOAT compared to existing treatment options. Although supervised iOAT has lower risk than unsupervised iOAT, the former has comparatively lower access. The risks associated with unsupervised iOAT are unclear given its recent inception, but previous studies demonstrate a small risk of overdose with supervised iOAT, which may translate to increased risk of an overdose if the injection was unsupervised (
      • Strang J.
      • Groshkova T.
      • Uchtenhagen A.
      • van den Brink W.
      • Haasen C.
      • Schechter M.T.
      • Metrebian N.
      Heroin on trial: Systematic review and meta-analysis of randomised trials of diamorphine-prescribing as treatment for refractory heroin addiction.
      ). With that said, the literature has also established that being out of treatment has its own risks (
      • Sordo L.
      • Barrio G.
      • Bravo M.J.
      • Indave B.I.
      • Degenhardt L.
      • Wiessing L.
      • Pastor-Barriuso R.
      Mortality risk during and after opioid substitution treatment: Systematic review and meta-analysis of cohort studies.
      ). Studies have yet to determine if the benefits of increased treatment coverage for out-of-treatment clients may outweigh the potential risks of such treatment.
      Given the lack of studies examining unsupervised iOAT, we aimed to model the relative risks and benefits of expanding treatment capacity through increased availability of unsupervised iOAT using available parameters and estimates. We modeled the provision of supervised and unsupervised iOAT in Australia, where these programs are not currently available. We focused on people who inject opioids as the key risk group for whom iOAT is relevant. The aim was to model four scenarios to compare efficacy and cost effectiveness among:
      • 1)
        No iOAT;
      • 2)
        Investment in supervised iOAT only;
      • 3)
        A mix of supervised iOAT and unsupervised iOAT based on willingness to enter supervised versus unsupervised treatment; and
      • 4)
        The same resource allocation as scenario 2 but with a mix of supervised and unsupervised iOAT.
      We identified the best- and worst-case scenarios with cost-effectiveness and mortality rates.

      2. Methods

      We modeled the potential impact on overdose deaths and average cost from the government perspective of scaling up both supervised and unsupervised iOAT in Australia. We used an integrated decision tree model developed based on key predetermined parameters (Fig. 1). The model divides people who inject opioids into seven different treatment states (Fig. 1):
      • 1.
        Initiating methadone maintenance
      • 2.
        Stable to methadone maintenance
      • 3.
        Initiating buprenorphine maintenance
      • 4.
        Stable buprenorphine maintenance
      • 5.
        iOAT (Supervised)
      • 6.
        iOAT (Unsupervised)
      • 7.
        No OAT (i.e. out of treatment)
      Fig. 1
      Fig. 1a. Population subgroups.
      b. Parameters of subgroups.
      The per capita model considers outcomes for a hypothetical cohort of 10,000 people who inject opioids over the course of one year, which could then be scaled to represent the likely effect of implementation of iOAT in different regions of Australia based on local estimates of the number of people who inject opioids (e.g. in larger metropolitan cities in Victoria or New South Wales, Australia, which have an estimated 22,000 and 36,000 people who inject opioids, respectively (
      • Larney S.
      • Hickman M.
      • Guy R.
      • Grebely J.
      • Dore G.J.
      • Gray R.T.
      • Degenhardt L.
      Estimating the number of people who inject drugs in Australia.
      ), and so outcomes would be approximately 2.2 or 3.6 times the reported results). Inputs are provided for the percentage of people in each treatment state, with the proportion of people in each treatment state remaining constant, although these stable proportions in each state may be represented by individuals moving between different treatment states (e.g., from new to stable in treatment) over time.
      The model provides outputs for the total number of no overdoses, fatal and non–fatal overdoses per year, allowing different parameters for the probability of overdosing, the proportion of overdoses witnessed, and naloxone availability between groups. The model included naloxone availability, reflecting the use of naloxone for reversing opioid induced fatal respiratory depression, modeled based on local data on naloxone access.
      The probabilities of each parameter included in the model, identified through a targeted literature search of PubMed without restrictions in language through June 20, 2020, with the following keywords: injectable opioid agonist therapy, methadone, buprenorphine, naloxone, maintenance therapy, hydromorphone, diacetylmorphine. We also searched the reference lists from key systematic reviews for additional studies (
      • Degenhardt L.
      • Bucello C.
      • Mathers B.
      • Briegleb C.
      • Ali H.
      • Hickman M.
      • McLaren J.
      Mortality among regular or dependent users of heroin and other opioids: A systematic review and meta-analysis of cohort studies.
      ;
      • Ferri M.
      • Davoli M.
      • Perucci C.A.
      Heroin maintenance for chronic heroin-dependent individuals.
      ;
      • Sordo L.
      • Barrio G.
      • Bravo M.J.
      • Indave B.I.
      • Degenhardt L.
      • Wiessing L.
      • Pastor-Barriuso R.
      Mortality risk during and after opioid substitution treatment: Systematic review and meta-analysis of cohort studies.
      ;
      • Strang J.
      • Groshkova T.
      • Uchtenhagen A.
      • van den Brink W.
      • Haasen C.
      • Schechter M.T.
      • Metrebian N.
      Heroin on trial: Systematic review and meta-analysis of randomised trials of diamorphine-prescribing as treatment for refractory heroin addiction.
      ). The study team also performed a targeted literature review relevant to Australian parameters, inclusive of investigator knowledge and contact with key experts in the implementation of iOAT. The team determined other relevant Australian parameters through grey literature and a continuing, large cohort study that collected annual information on overdose frequency, naloxone, and treatment access (
      • Nambiar D.
      • Agius P.A.
      • Stoové M.
      • Hickman M.
      • Dietze P.
      Mortality in the Melbourne injecting drug user cohort study (MIX).
      ). The research team extracted results pertaining to model parameters and performed a weighted average for parameters with multiple results identified in the literature search. We then calculated a probability of 1-year risk of overdose and overdose deaths for each treatment option, which was then multiplied to calculate the final risk of each end result. A summary of parameters can be found in Table 1 with full details including the sources of data and references in Supplementary Table 1.
      Table 1Probabilities of overdose by intervention and treatment condition
      See Supplementary Table 1 for full details of the additional information and source data and references for each point estimates.
      .
      Probability of overdoseOAT (initiating methadone maintenance)OAT (on stable to methadone maintenance)OAT (initiating buprenorphine maintenance)OAT (on stable buprenorphine maintenance)(Supervised) iOAT(Unsupervised) iOATNo OAT
      Probability of overdose2.77%1.14%2.82%0.68%8.27%8.27%32.35 %
      Probability of being witnessed on overdose86.84%86.84%83.33%83.33%99.99%85.09%77.03 %
      Probability of access to naloxone44.03%44.03%31.82%31.82%99.99%37.93%23.70 %
      Probability of fatal overdose on naloxone administration0.86%0.86%0.86%0.86%0.10%0.86%0.86 %
      Probability of fatal overdose without naloxone administration0.26%0.26%0.07%0.08%0.01%0.11%1.27 %
      Probability of fatal overdose without being witnessed0.26%0.26%0.07%0.08%0.01%0.17%1.27 %
      a See Supplementary Table 1 for full details of the additional information and source data and references for each point estimates.
      For each model, the study classified the cohort by three outcomes: no overdose, fatal overdose, and non–fatal overdose. To determine the number of people in the population who experienced each of the three outcomes, the study multiplied the number of participants by each parameter probability until reaching one of the three outcomes seen in Fig. 1. With each treatment condition a sum total of each of the three outcomes were tallied to provide an overall result for each of the four model scenarios. A stepwise instruction further describes reproducing the model using author parameter inputs (Supplementary Table 2). Whether an overdose was fatal or not was dependent on whether the event was witnessed, and if witnessed, if naloxone was available. The research team used Excel (version 1908) to perform the calculations for the modeling. Reporting of this study was conducted in accordance with the Consolidated Health Economic Evaluation Reporting Standards (CHEERS) checklist (Supplementary List 2)(
      • Husereau D.
      • Drummond M.
      • Petrou S.
      • Carswell C.
      • Moher D.
      • Greenberg D.
      • Loder E.
      Consolidated health economic evaluation reporting standards (CHEERS) statement.
      ).
      To understand the impacts of incorporating unsupervised iOAT in the public health response to opioid injecting, we calculated the percent of the cohort who died from overdose over one year and the total cost of treatment for four scenarios, which we determined based on published data on current treatment reach, likely treatment uptake of different treatment iOAT modalities, and different funding availability (
      Australian Institute of Health and Welfare
      National opioid pharmacotherapy statistics annual data collection 2019.
      ;
      • Nielsen S.
      • Sanfilippo P.
      • Belackova V.
      • Day C.
      • Silins E.
      • Lintzeris N.
      • Larance B.
      Perceptions of injectable opioid agonist treatment (iOAT) among people who regularly use opioids in Australia: Findings from a cross-sectional study in three Australian cities.
      ;
      • Strang L.
      • Taylor J.
      Heroin-assisted treatment and supervised drug consumption sites: Experience from four countries.
      ):
      • 1.
        No iOAT: Based on current estimates of overdose, overdose fatality, naloxone, and treatment from Australia (
        Australian Institute of Health and Welfare
        National opioid pharmacotherapy statistics annual data collection 2019.
        );
      • 2.
        Mix of OAT and 5% iOAT (Supervised): Based on a conservative estimate of the proportion likely to receive supervised iOAT uptake following program implementation from comparing different rates of treatment reach described internationally (
        • Strang L.
        • Taylor J.
        Heroin-assisted treatment and supervised drug consumption sites: Experience from four countries.
        );
      • 3.
        Mix of OAT, 5% iOAT (Supervised), 5.69% iOAT (Unsupervised): The percentage who may enter unsupervised iOAT, determined by multiplying the proportion of people who inject opioids not interested in supervised iOAT, by the proportion of people who inject opioids who are eligible for but not interested in supervised iOAT (
        • Nielsen S.
        • Sanfilippo P.
        • Belackova V.
        • Day C.
        • Silins E.
        • Lintzeris N.
        • Larance B.
        Perceptions of injectable opioid agonist treatment (iOAT) among people who regularly use opioids in Australia: Findings from a cross-sectional study in three Australian cities.
        );
      • 4.
        Mix of OAT, 1.2% iOAT (Supervised), 10% iOAT (Unsupervised): The study based this scenario on using the same total treatment costs as scenario 2, but with greater allocation of funds to 10% of unsupervised iOAT as a predicted best-case scenario to see how far outcomes could be optimized. This scenario assumed a 1.2% enrollment in supervised iOAT (1.2% represents an approximate 120 treatment places in an average clinic, similar to current reach of iOAT in Vancouver of 150 places for an estimated 12,900 people who inject opioids) (
        • Strang L.
        • Taylor J.
        Heroin-assisted treatment and supervised drug consumption sites: Experience from four countries.
        ), with the remainder of investment in unsupervised iOAT.

      2.1 Assumptions

      The study aligned model parameters to best reflect Australian estimates, with uncertainty and sensitivity analysis to examine inter-parameter variability. The study made several assumptions:
      • 1.
        The probability of overdose per annum was assumed to be equal for supervised and unsupervised iOAT, based on the injection of the same pharmaceutical opioid in comparable doses, as no literature was available to enable an estimate overdose risk for unsupervised iOAT. We did not assume the outcome of the overdose would be the same, as the probability of naloxone administration was high with supervised iOAT due to trained staff being onsite to respond, in contrast to unsupervised iOAT;
      • 2.
        The probability of dying from an overdose with no naloxone available was equal if the overdose was witnessed or unwitnessed given both circumstances entail a lack of access to naloxone, and no data were available to allow for an alternative estimate;
      • 3.
        The study assumed risk of overdose and death to be the same based on varying degrees of co-use of other substances (alcohol, benzodiazepines, and illicit opioids). The study originally included differential risks based on estimates of overdose prevalence in each treatment group with and without co-use of other substances, but due to a lack of evidence to enable quantifying the additional risk of co-use, the study team excluded this from the main analysis. The sensitivity analysis explores increased risks for a subset who co-use.
      Given the limited evidence in estimating the cost of iOAT in the Australian context and in UK clinic models and operating costs along with the likely model of care in Australia, we drew our iOAT cost estimates from
      • Byford S.
      • Barrett B.
      • Metrebian N.
      • Groshkova T.
      • Cary M.
      • Charles V.
      • Strang J.
      Cost-effectiveness of injectable opioid treatment v. oral methadone for chronic heroin addiction.
      . The study estimated the cost of OAT treatment through Australian data from
      • Doran C.M.
      • Shanahan M.
      • Mattick R.P.
      • Ali R.
      • White J.
      • Bell J.
      Buprenorphine versus methadone maintenance: A cost-effectiveness analysis.
      study, given differences exist in OAT delivery between the UK and Australia (Supplementary Table 1) (
      • Byford S.
      • Barrett B.
      • Metrebian N.
      • Groshkova T.
      • Cary M.
      • Charles V.
      • Strang J.
      Cost-effectiveness of injectable opioid treatment v. oral methadone for chronic heroin addiction.
      ;
      • Doran C.M.
      • Shanahan M.
      • Mattick R.P.
      • Ali R.
      • White J.
      • Bell J.
      Buprenorphine versus methadone maintenance: A cost-effectiveness analysis.
      ).
      Given the limited evidence in parametrizing supervised iOAT outcomes, the study made several assumptions:
      • 1.
        The likelihood of an overdose being witnessed was much higher with supervised iOAT (Estimates at 99.99%, given the supervised nature of treatment).
      • 2.
        Given the presence of clinic staff, access to naloxone for supervised iOAT was estimated at 99.99%
      Given the limited evidence in parametrizing unsupervised iOAT outcomes, the study made additional assumptions:
      • Overdose
      • 1.
        Probability of overdose is the same as supervised iOAT due to the identical drugs used in the two groups.
      • 2.
        Probability of an overdose being witnessed for unsupervised iOAT meant we assumed it to be equal to the probability for oral OAT treatment given that oral OAT and unsupervised iOAT are considered out-of-clinic treatment.
      • Naloxone access
      • 3.
        Naloxone access in unsupervised iOAT was the average of naloxone access in OAT treatment groups (and lower than with supervised iOAT), as the study assumed that naloxone access was related to being in contact with opioid treatment in general as opposed to the specific type of treatment.
      • Fatality
      • 4.
        Probability of fatal overdose where an overdose was witnessed and naloxone administered were equal to the probabilities observed for clients on OAT treatment
      The proportions of people in each treatment group are summarized in Table 2.
      Table 2Percentage of clients in each treatment groups for modeling scenarios.
      Treatment groupScenario 1: OAT
      Based on current treatment statistics in Australia (Larney, Peacock, et al., 2017).
      Scenario 2: OAT and supervised iOAT
      Assuming clients in OAT stay in treatment and 5 % of people who inject opioids out of treatment enter supervised iOAT (representing 500 treatment places within Victoria, Australia).
      Scenario 3: OAT, 5 % supervised and 5.69 % unsupervised iOAT
      Expanding treatment again by attracting clients not interested in supervised iOAT into treatment with unsupervised iOAT based on intention to enter treatment (Nielsen et al., 2020).
      Scenario 4: OAT, 1.2 % supervised and 10 % unsupervised iOAT
      Changing the distribution of therapy to maximize treatment places on the same budget—with 120 people in supervised iOAT (might be more realistic, would represent one crosstown clinic being built, for example), with the rest of the money going to unsupervised treatment.
      OAT (initiating methadone maintenance)6.50 %6.50 %6.50 %6.50 %
      OAT (on stable to methadone maintenance)25.01 %25.01 %25.01 %25.01 %
      OAT (initiating buprenorphine maintenance)4.21 %4.21 %4.21 %4.21 %
      OAT (on stable buprenorphine maintenance)16.28 %16.28 %16.28 %16.28 %
      iOAT (supervised)0.00 %5.00 %5.00 %1.20 %
      iOAT (unsupervised)0.00 %0.00 %5.69 %10.00 %
      No OAT48.00 %43.00 %37.31 %36.80 %
      a Based on current treatment statistics in Australia (
      • Larney S.
      • Peacock A.
      • Leung J.
      • Colledge S.
      • Hickman M.
      • Vickerman P.
      • Degenhardt L.
      Global, regional, and country-level coverage of interventions to prevent and manage HIV and hepatitis C among people who inject drugs: A systematic review.
      ).
      b Assuming clients in OAT stay in treatment and 5 % of people who inject opioids out of treatment enter supervised iOAT (representing 500 treatment places within Victoria, Australia).
      c Expanding treatment again by attracting clients not interested in supervised iOAT into treatment with unsupervised iOAT based on intention to enter treatment (
      • Nielsen S.
      • Sanfilippo P.
      • Belackova V.
      • Day C.
      • Silins E.
      • Lintzeris N.
      • Larance B.
      Perceptions of injectable opioid agonist treatment (iOAT) among people who regularly use opioids in Australia: Findings from a cross-sectional study in three Australian cities.
      ).
      d Changing the distribution of therapy to maximize treatment places on the same budget—with 120 people in supervised iOAT (might be more realistic, would represent one crosstown clinic being built, for example), with the rest of the money going to unsupervised treatment.

      2.2 Costs

      The study calculated the average cost from the government perspective, considering the direct cost of treatment only. This included: Drug costs, clinic costs, weekly case management costs, and urine tests (no clinic costs for unsupervised iOAT) but did not include staff accommodation, hospital services, community services, and criminal justice services. The study estimated annual costs of buprenorphine and methadone based on the most recent Australian cost-effective analysis and adjusted for inflation (
      • Doran C.M.
      • Shanahan M.
      • Mattick R.P.
      • Ali R.
      • White J.
      • Bell J.
      Buprenorphine versus methadone maintenance: A cost-effectiveness analysis.
      ). The study team estimated annual costs of supervised iOAT based on the most recent UK cost-effective analysis and adjusted it for exchange rate and inflation (
      • Byford S.
      • Barrett B.
      • Metrebian N.
      • Groshkova T.
      • Cary M.
      • Charles V.
      • Strang J.
      Cost-effectiveness of injectable opioid treatment v. oral methadone for chronic heroin addiction.
      ). We conducted the calculation for inflation using an inflation calculator supplied from the Reserve Bank of Australia with specific calculations reported in Supplemental Table 1 (
      Reserve Bank of Australia
      Inflation calculator.
      ). Given the lack of literature on the cost of unsupervised iOAT, we estimated the cost of unsupervised iOAT through subtracting the clinic costs from supervised iOAT costs (
      • Byford S.
      • Barrett B.
      • Metrebian N.
      • Groshkova T.
      • Cary M.
      • Charles V.
      • Strang J.
      Cost-effectiveness of injectable opioid treatment v. oral methadone for chronic heroin addiction.
      ). All costs are reported in 2020 AUD and were not discounted as the analysis time frame was one year.

      2.3 Outcomes

      For each scenario, the study estimated the number of overdoses, number of deaths, and the total cost of treatment per 10,000 people who inject opioids per annum. The team compared outcomes to Scenario 1 (current treatment provision) and calculated the cost per overdose averted and cost per life saved.

      2.4 Uncertainty and sensitivity analyses

      A multivariate probabilistic uncertainty analysis determined confidence intervals for outcomes using a visual based for applications (VBA) macro in Excel. The study generated 1000 random parameter sets, with parameters drawn at random from within their individual uncertainty range if it was available, or ±10% where otherwise (uncertainty ranges were available for annual probability of fatal and non–fatal overdose for new, stable methadone and buprenorphine, supervised iOAT, and no OAT). We report 95% uncertainty intervals (95% UIs) as the central 95 percentiles of the corresponding 1000 model runs.
      The study also conducted univariate sensitivity analyses to assess the impact of variations in individual parameters and verify the stability of the model predictions when key parameters change. Key model parameters included probability of overdose witnessed, probability of overdose, probability of fatal non–witnessed overdose, probability of fatal witnessed overdose, cost of iOAT; and the study identified the proportion on treatment based on the availability of literature to inform model parameters. The study conducted sensitivity analyses only for key model parameters in scenarios 3 and 4.

      2.5 Ethics approval

      Our analysis of modeling data, which is based on existing literature and estimates, did not require ethics approval.

      3. Results

      Within a population of 10,000 people who inject opioids over a one-year period, scenario 1 (current status quo of treatment in Australia), assumed 52.00% of the population was on OAT at an average cost to government of AUD 4,488 per person on treatment per annum (Fig. 2). This tallied to a total cost of AUD 23,335,081 per 10,000 people who inject opioids per annum to implement scenario 1. After the 1-year period, an estimated 1655.5 overdoses (95% UI: 1552.7–1705.3) and 19.3 deaths (17.9–20.3) were expected per 10,000 people (Table 3).
      Table 3Overdose, mortality and cost outcomes in a population of 10,000 people who inject opioids during a 1-year period under different treatment scenarios.
      Outcome measuresScenario 1: OAT
      Scenarios include clients not in treatment within the population of 10,000 people who inject opioids.
      Scenario 2: OAT and 5 % supervised iOAT
      Scenarios include clients not in treatment within the population of 10,000 people who inject opioids.
      Scenario 3: OAT, 5 % supervised and 5.69 % unsupervised iOAT
      Scenarios include clients not in treatment within the population of 10,000 people who inject opioids.
      Scenario 4: OAT, 1.2 % supervised and 10 % unsupervised iOAT
      Scenarios include clients not in treatment within the population of 10,000 people who inject opioids.
      Projections in 1 year
      Number of overdoses per 10,000 people who inject opioids per annum (95 % UI)1655.5 (1552.7–1705.3)1534.4 (1439.7–1586.0)1383.7 (1317.7–1433.4)1349.2 (1284.7–1422.6)
      Number of overdose deaths per 10,000 people who inject opioids per annum (95 % UI)19.3 (17.9–20.3)17.4 (16.3–18.2)15.4 (14.3–16.2)14.9 (14.1–15.9)
      Total cost per 10,000 people who inject opioids per annum (AUD)$23,335,081$38,142,936$44,547,786$38,142,936
      Percent on treatment (%)52.00 %57.00 %62.69 %63.20 %
      Average cost per person on treatment (AUD)$4488$6692$7106$6035
      Difference compared to scenario 1
      Additional costs per 10,000 people who inject opioids per annum compared to baseline (AUD)$14,807,855$21,212,705$14,807,855
      Overdoses averted per 10,000 Ppeople who inject opioids per annum (95 % UI)122.9 (114.2–130.5)262.3 (246.4–276.5)269.0 (250.0–278.7)
      Deaths averted per 10,000 people who inject opioids per annum (95 % UI)2.0 (1.8–2.0)4.1 (3.8–4.3)4.0 (3.7–4.2)
      Cost per overdose averted$124,139 (113,468-129,652)$82,750 (76,722-86,093)$56,598 (50,655-59,637)
      Cost per death averted$7,774,172 (7,283,182-8,146,989)$5,311,639 (4,951,842-5,638,807)$3,723,340 (3,385,878-3,894,379)
      a Scenarios include clients not in treatment within the population of 10,000 people who inject opioids.
      Scenario 2, with the provision of supervised iOAT for 5.00% of the population (equating to 500 treatment spots per 10,000 people), increased the population coverage of treatment to 57% with an average cost of AUD 6,692 per person on treatment per annum, totaling AUD 38,142,936 per 10,000 people who inject opioidsper annum for scenario 2. This was an additional AUD 14,807,855 (163%) compared to scenario 1. This scenario resulted in 1534.4 (1439.7–1586.0) overdoses and 17.4 (16.3–18.2) overdose deaths per 10,000 PWIO per annum, which is 122.9 (114.2–130.5) overdoses and 2.0 (1.8–2.0) overdose deaths fewer than scenario 1. The cost per overdose averted and cost per death averted were $124,139 (113,468–129,652) and $7,774,172 (7,283,182–8,146,989) respectively.
      Scenario 3 (52.00% OAT, 5.00% supervised and 5.69% unsupervised iOAT, equating to 5200, 500 and 569 respective treatment spots per 10,000 people), increased the population coverage of treatment to 63%, with an average cost per person at AUD 7,106 on treatment per annum, totaling to AUD 44,547,786 per 10,000 people who inject opioids per annum for scenario 2. This was an additional AUD 21,212,705 (191%) compared to scenario 1. Scenario 3 estimated 1383.7 overdoses (1317.7–1433.4) and 15.4 overdose deaths (14.3–16.2), with preventing an additional 262.3 overdoses (246.4–276.5) and 4.1 overdose deaths (3.8–4.3). The cost per overdose and cost per death averted were $82,750 (76,722–86,093) and $5,311,639 (4,951,842–5,638,807), respectively.
      Scenario 4 (OAT, 1.20% supervised and 10.00 % unsupervised iOAT) increased treatment coverage to 63.2%. This was at an average cost of AUD 6035, the lowest of all iOAT scenarios, and at the same total cost of scenario 2. This scenario prevented an additional 269.0 overdoses (250.0–278.7) and 4.0 overdose deaths (3.7–4.2) compared to the status quo. The cost per overdose and cost per death averted were $56,598 (50,655–59,637) and $3,723,340 (3,385,878–3,894,379), respectively.
      Compared to the status quo (scenario 1), scenarios 3 and 4 demonstrated the most additional overdoses and additional deaths averted per 10,000 people who inject opioids per annum as there were no significant differences between the two scenarios. However, when compared to scenario 2 (supervised iOAT alone) the study found no significant difference in overdoses and overdose deaths with both scenarios that included unsupervised iOAT, with scenario 4 achieving this at no additional cost. Scenario 4 had the lowest cost per overdose and cost per death averted.

      3.1 Sensitivity analysis

      The sensitivity analysis for scenario 4 determined that the parameters with the greatest influence on the main outcomes by comparing base scenario results were: 1. The probability of overdose, 2. The probability of a fatal non–witnessed overdose 3. The probability of fatal witnessed overdose, and 4. Proportion on unsupervised iOAT is double that of supervised iOAT (Table 4).
      Table 4Sensitivity analysis examining outcomes of additional cost, overdose, overdose deaths averted, and cost ratios for adopting unsupervised iOAT for scenario 4: mixed OAT, 1.2 % supervised and 10 % unsupervised iOAT.
      Probability variationAdditional costs of scenario compared to baseline (AUD)Overdoses averted (95 % CI)Deaths averted (95 % CI)Cost per overdose averted (compared with scenario 1)Cost per death averted (compared with scenario 1)
      Point estimates from scenario 4
      No probability variation (baseline scenario 4)$14,807,855269.0 (250.0–278.7)4.0 (3.7–4.2)$56,598 (50,655-59,637)$3,723,340 (3,385,878-3,894,379)
      OAT (initiating methadone maintenance)
      Probability of an overdose witnessed is −10% than estimate$14,807,855274.3 (249.5–288.3)4.1 (3.8–4.3)$55,301 (51,359-59,352)$3,724,804 (3,426,522-3,929,771)
      OAT (on stable methadone maintenance)
      Probability of an overdose witnessed is −10% than estimate$14,807,855275.3 (251.5–289.4)4.1 (3.8–4.3)$55,057 (51,171-58,880)$3,728,641 (3,429,626-3,918,653)
      OAT (initiating buprenorphine maintenance)
      Probability of an overdose witnessed is −10% than estimate$14,807,855277.6 (255.5–290.5)4.1 (3.7–4.3)$54,980 (50,972-57,949)$3,810,761 (3,414,853-4,031,867)
      OAT (on stable buprenorphine maintenance)
      Probability of an overdose witnessed is −10% than estimate$14,807,855273.2 (250.1–289.6)4.0 (3.7–4.2)$55,720 (51,137-59,208)$3,745,110 (3,495,767-4,062,074)
      Unsupervised iOAT
      Probability of overdose is +20 % for the estimated 18.52 % of people who inject opioids who co-use EtOH, Benzos, and the 37.86% who co-use IO iOAT(US)$14,807,855268.5 (172.3–368.7)4.7 (2.75.5)
      Bolded results represent the parameters with the greatest influence on the main outcomes by comparing base scenario results.
      $60,379 (40,162-85,940)$3,772,875 (2,575,842-5,003,993)
      Probability of overdose is +10% for the estimated 18.52% of people who inject opioids who co-use EtOH, Benzos OR the 37.86% who co-use IO iOAT(US)$14,807,855266.7 (166.1–333.2)3.9 (2.4–5.7)$61,977 (44,438-89,140)$4,230,406 (2,570,427-5,670,834)
      Probability of an overdose witnessed is −10% than estimate$14,807,855274.6 (249.5–288.1)4.1 (3.8–4.2)$55,641 (51,405-59,343)$3,741,438 (3,496,632-3,951,525)
      Probability of fatal non-witnessed overdose is +20% for the estimated 18.52% of people who inject opioids who co-use EtOH, Benzos, and the 37.86% who co-use IO iOAT(US)$14,807,855279.0 (157.0–344.2)4.4 (2.75.7)
      Bolded results represent the parameters with the greatest influence on the main outcomes by comparing base scenario results.
      $96,033 (70,128-128,021)$6,136,439 (4,417,386-8,777,812)
      Probability of fatal non-witnessed overdose is +10% for the estimated 18.52% of people who inject opioids who co-use EtOH, Benzos OR the 37.86 % who co-use IO iOAT(US)$14,807,855289.4 (198.0–360.8)4.3 (2.4–5.5)$56,121 (41,048-74,806)$3,955,908 (2,613,039-6,057,731)
      Probability of fatal witnessed overdose is +20% for the estimated 18.52% of people who inject opioids who co-use EtOH, Benzos, and the 37.86% who co-use IO iOAT(US)$14,807,855298.4 (203.1335.7)
      Bolded results represent the parameters with the greatest influence on the main outcomes by comparing base scenario results.
      4.2 (2.6–5.5)$54,997 (44,115-72,905)$3,925,034 (2,705,554-5,773,959)
      Probability of fatal witnessed overdose is +10% for the estimated 18.52% of people who inject opioids who co-use EtOH, Benzos OR the 37.86% who co-use IO iOAT(US)$14,807,855295.5 (200.9377.5)
      Bolded results represent the parameters with the greatest influence on the main outcomes by comparing base scenario results.
      4.6 (2.75.7)
      Bolded results represent the parameters with the greatest influence on the main outcomes by comparing base scenario results.
      $58,410 (39,231-73,723)$3,538,651 (2,503,627-5,201,775)
      Supervised iOAT
      Probability of overdose is +20% for the estimated 18.52% of people who inject opioids who co-use EtOH, Benzos, and the 37.86% who co-use IO iOAT(US)$14,807,855305.7 (185.1362.5)
      Bolded results represent the parameters with the greatest influence on the main outcomes by comparing base scenario results.
      4.4 (2.9–5.8)$55,049 (40,848-80,128)$3,556,984 (2,478,129-4,621,026)
      Probability of overdose is +10% for the estimated 18.52% of people who inject opioids who co-use EtOH, Benzos OR the 37.86% who co-use IO iOAT(US)$14,807,855285.2 (181.6–349.1)4.3 (2.4–5.2)$57,782 (42,418-81,532)$3,922,468.93 (2,784,102.56-5,912,237.94)
      Probability of an overdose witnessed is −10% than estimate$14,807,855277.6 (253.7–288.8)4.1 (3.8–4.4)$54,927 (51,272-58,369)$3,737,019 (3,374,305-3,882,756)
      No OAT
      Probability of an overdose witnessed is −10% than estimate$14,807,855271.4 (253.0–284.2)3.9 (3.6–4.1)$55,386 (52,101-58,538)$3,873,151 (3,580,049-4,103,094)
      Cost of iOAT
      Cost iOAT(US) -0.52% (Ratio of UK-AUS cost for methadone)$9,042,779271.4 (252.2–286.4)4.1 (3.8–4.4)$33,783 (31,572-35,855)$2,288,593 (2,080,661–2,410,508)
      Proportion on treatment
      Proportion on iOAT(US) doubled of iOAT(S) (Scenario 4)$26,054,585506.0 (473.2530.8)
      Bolded results represent the parameters with the greatest influence on the main outcomes by comparing base scenario results.
      7.8 (7.28.0)
      Bolded results represent the parameters with the greatest influence on the main outcomes by comparing base scenario results.
      $52,742 (49,085-55,056)$3,534,375 (3,251,303-3,628,570)
      low asterisk Bolded results represent the parameters with the greatest influence on the main outcomes by comparing base scenario results.
      If the probability of overdose was 20% higher than estimated, deaths averted by scenario 4 would be 4.7 (2.7–5.5) per 10,000 people who inject opioids per year (Table 4, row 13), compared to a model baseline of 4.0 (3.7–4.2) deaths averted. If the probability of fatal non–witnessed overdose was 20% higher than estimated, it results in an increase to 4.4 (2.7–5.7) deaths averted compared to baseline (Table 4, row 16). When probability of fatal witnessed overdose is 20% higher than estimated, it resulted in a change of 269.0 (250.0–278.7) overdoses averted on baseline to 298.4 (203.1–335.7) overdoses averted (Table 4, row 18). When this probability is 10% higher than estimated, the study found 295.5 (200.9–377.5) overdoses averted and 4.6 (2.7–5.7) deaths averted (Table 4, row 19).
      When the probability of overdose in supervised iOAT is 20% higher than estimated, overdoses averted increased to 305.7 (185.1–362.5) from baseline (Table 4, row 21).
      Finally, when varying proportion on treatment by changing proportion on unsupervised iOAT doubled that of supervised iOAT, overdoses averted increased to 506.0 (473.2–530.8) and deaths averted increased to 7.8 (7.2–8.0) from baseline (Table 4, row 29).
      By varying these parameters, our sensitivity analysis of scenario 4 showed the greatest variation in outcomes compared to varying other parameters. These aforementioned parameter variations had the greatest influence on the total number of overdoses and overdose deaths in the status quo, and hence more accurate estimates of overdose probabilities would reduce uncertainty in the number of deaths averted.

      4. Discussion

      We modeled four scenarios of OAT provision for a population of 10,000 people who inject opioids, including introducing and varying supervised and unsupervised iOAT coverage. Depending on the model the study showed 1349.2 to 1655.5 overdoses and 14.9 to 19.3 overdose deaths per 10,000 people who inject opioids per annum, and OAT coverage ranged from the status quo (52.00 %) to 63.00 % of people who inject opioids per annum. The study saw the lowest average cost per person on iOAT treatment, excluding the status quo, with the greatest use of unsupervised iOAT without any negative impact on overdoses and overdose deaths, though further evaluation in real world implementation would need to be conducted to qualify model assumptions. Our modeling suggests that placing the most resources in upscaling unsupervised iOAT may demonstrate the greatest overall benefit without additional cost. The increase treatment coverage, by about 10% compared to the status quo, comes from brining in those who are unwilling to enter conventional OAT, or for whom conventional OAT does not provide clinical benefits.
      Some people may prefer unsupervised iOAT due to greater flexibility and reduced clinic attendance (
      • Nielsen S.
      • Sanfilippo P.
      • Belackova V.
      • Day C.
      • Silins E.
      • Lintzeris N.
      • Larance B.
      Perceptions of injectable opioid agonist treatment (iOAT) among people who regularly use opioids in Australia: Findings from a cross-sectional study in three Australian cities.
      ). Our findings may suggest an important opportunity to engage more people in treatment, at a lower cost than expanding supervised iOAT. While supervision may be adding more safety for clients compared to no supervision, upscaling unsupervised iOAT at a greater capacity may be more cost effective and represent no greater risk at the population level. Upscaling will enable a larger number of people to benefit from OAT in general, and reflects the relative safety of using a pharmaceutical opioid compared to using illicit opioids of unknown potency. In turn, retaining some supervised iOAT treatment capacity for those considered unsuitable or uninterested in unsupervised iOAT may present an optimal balance.
      The variations in the proportion of iOAT availability that we modeled draw parallels from countries with different implementation capacities for iOAT. Vancouver, Canada, with an estimated population of 12,900 people who inject opioids (
      The Centre for Global Public Health University of Manitoba
      Estimation of key population size of people who use injection drugs (PWID), men who have sex with men (MSM) and sex workers (SW) who are at risk of acquiring HIV and hepatitis C in the five health regions of the province of British Columbia.
      ), has attempted to upscale unsupervised iOAT treatment in hopes of increasing treatment engagement, which is currently limited to approximately 1% of people who inject opioids with supervised iOAT (
      • Strang L.
      • Taylor J.
      Heroin-assisted treatment and supervised drug consumption sites: Experience from four countries.
      ). The Netherlands, with an estimated population of 14,000 people who inject opioids (
      • Strang L.
      • Taylor J.
      Heroin-assisted treatment and supervised drug consumption sites: Experience from four countries.
      ), has 31 iOAT sites, with an estimated 3720 iOAT spots for 27% of the PWIO population. Finally, Switzerland, with an estimated population of less than 30,000 PWIO (
      • Strang L.
      • Taylor J.
      Heroin-assisted treatment and supervised drug consumption sites: Experience from four countries.
      ), has 12 iOAT sites, covering around 10% of the people who inject opioids population.
      Studies should examine the cost of each scenario in relation to the overdose and overdose deaths averted. In 2019, the Australian government estimates for the value of a statistical life were AUD 4.9 million, a statistical life year of AUD 213,000 (
      Australian Government
      Best practice regulation guidance note value of statistical life. Office of Best Practice Regulation: Australian Government.
      ). Scenarios 2 and 3 demonstrate cost per death averted (95% UI) of $7,774,172 (7,283,182–8,146,989) and $5,311,639 (4,951,842–5,638,807), respectively—both greater than the government valuation of life. That being said, scenario 4, which incorporates the most unsupervised iOAT in treatment, demonstrated a cost per death averted (95 % UI) of $3,723,340 (3,385,878–3,894,379), indicating that scenario 4 would be considered cost effective, in contrast to the other two scenarios.
      Sensitivity analysis modeling the decreased costs from unsupervised iOAT (estimate based on the ratio for cost from the literature estimate of OAT to Australian OAT costs) suggests that the cost per life saved would be much lower if unsupervised iOAT were implemented rather than supervised iOAT. This cost effectiveness may be further increased through a reduction in other costs associated with opioid dependence and use of illicit opioids, such as health care (including soft tissue injuries), judicial, and social costs, which our model did not include, but are well established as benefits of OAT.
      Countries such as the United States and Canada have much higher mortality rates compared to Australia (
      • Belzak L.
      • Halverson J.
      The opioid crisis in Canada: A national perspective. [La crise des opioïdes au Canada : une perspective nationale].
      ;
      • Centers for Disease Control
      QuickStats: Rates of drug overdose deaths involving heroin,* by selected age groups - United States, 2006–2015.
      ; ), due largely to increased prevalence of fentanyl and other high potency novel opioids within the illicit market (
      • Belzak L.
      • Halverson J.
      The opioid crisis in Canada: A national perspective. [La crise des opioïdes au Canada : une perspective nationale].
      ; ). This higher rate may mean that the introduction of supervised and unsupervised iOAT and subsequent increased treatment coverage would have a greater impact on mortality in these countries, compared with our findings. A greater number of lives saved would result in a lower cost per life saved, increasing the cost effectiveness in these settings.

      4.1 Limitations

      Our study has several limitations to consider. We based our model estimate on current literature, which shows 19.3 overdose deaths per 10,000 people who inject opioids per annum within scenario 1, equating to 0.19% (95% UI: 0.18–0.20). However, recent estimates of drug-related mortality from a cohort of people who inject opioids from metropolitan Melbourne were higher (approximately 50 deaths per 10,000 people who inject opioids) (
      • Nambiar D.
      • Agius P.A.
      • Stoové M.
      • Hickman M.
      • Dietze P.
      Mortality in the Melbourne injecting drug user cohort study (MIX).
      ). Higher overdose may mean that the estimated lives saved in this analysis may represent an underestimate (i.e., our findings relating to cost and lives saved are conservative).
      We modeled our scenario on the assumption of attendance at a clinic multiple times per day, and it is most applicable to metropolitan settings. Time and costs for individuals traveling from rural regions to access these dispensing facilities may represent a barrier to access, and due to the lower density of populations in regional and rural areas, delivering supervised services cost effectively may be challenging. For this reason, specific modeling of scenarios based on local data may be required to inform likely costs and impacts for services outside metropolitan settings.
      Although using other sedatives while on OAT and iOAT will result in increased risk of overdose, our model was unable to accurately model this increased risk due to the lack of current literature reporting relative risks. Sensitivity analysis conducted for scenarios 3 and 4 showed that co-use of other sedative drugs was the variable that had the largest influence in additional overdose and overdose deaths per 10,000 people who inject opioids per annum, suggesting that better estimates of this risk are important to inform future work. The ability to quantify the increased risks associated with co-use of other sedatives in future studies would inform the need to prioritize clients with co-use, treatment type, and accessibility to treatment in the scenario that has limited treatment spots (
      • Jones J.D.
      • Mogali S.
      • Comer S.D.
      Polydrug abuse: A review of opioid and benzodiazepine combination use.
      ;
      • Lintzeris N.
      • Nielsen S.
      Benzodiazepines, methadone and buprenorphine: Interactions and clinical management.
      ).
      Similarly, a lack of available data meant that we assumed that the mortality probability from a non–witnessed overdose was equivalent to a witnessed overdose with no naloxone available. However, the survival probability for a witnessed overdose will likely be higher, as witnesses can take actions, such as performing rescue breathing, that are known to improve overdose outcomes (
      • Dietze P.
      • Cantwell K.
      • Burgess S.
      Bystander resuscitation attempts at heroin overdose: Does it improve outcomes?.
      ).
      We were unable to model potential diversion and related harms with unsupervised iOAT, as no studies to date have reported on this. Studies on opioid access have shown that diversion of OAT often takes place in the grey treatment market for those who may not be on treatment, and can reflect inadequate treatment coverage (
      • Cicero T.J.
      • Ellis M.S.
      • Chilcoat H.D.
      Understanding the use of diverted buprenorphine.
      ;
      • Mravčík V.
      • Janíková B.
      • Drbohlavová B.
      • Popov P.
      • Pirona A.
      The complex relation between access to opioid agonist therapy and diversion of opioid medications: A case example of large-scale misuse of buprenorphine in the Czech Republic.
      ). Increases in coverage through unsupervised iOAT as seen in scenarios 2–4 may allow for a reduction in diversion of OAT medications, including unsupervised iOAT medications. The relative safety of hydromorphone in known doses compared to illicit opioids of unknown composition and purity may still be safer than illicit opioid use if doses are diverted, though diversion to opioid naïve individuals would still present a meaningful overdose risk.
      Furthermore, given the lack of Australian iOAT parameters, the risks of overdose were parameterized through international studies, which may not be directly transferable to Australian contexts. While we were able to parameterize those new and stable to treatment, exiting treatment carries a risk (
      • Burns L.
      • Gisev N.
      • Larney S.
      • Dobbins T.
      • Gibson A.
      • Kimber J.
      • Degenhardt L.
      A longitudinal comparison of retention in buprenorphine and methadone treatment for opioid dependence in New South Wales, Australia.
      ), which this modeling study does not reflect. We modeled a single overdose event for each participant, meaning multiple overdoses are also unaccounted for, but the median incidence of overdose per year among those who experience overdose is one, with multiple overdoses per annum an exception in studies used to inform this study (Unpublished analysis of 2019 Illicit Drug Reporting System).
      Finally, the costs of unsupervised iOAT and OAT estimates were dated to 2003 and 2013, underpinning the importance of future studies that investigate the cost-effectiveness as a main outcome to better inform and validate future modeling studies. Assumptions for the cost of unsupervised iOAT could only be derived from current estimates of supervised iOAT without the clinic costs, and the costs for iOAT were based on UK estimates without including the cost of building new facilities. This cost may mean that the cost of establishing iOAT may initially be higher than that included here. The cost of OAT in private pharmacies often includes additional dispensing costs—included in the cost estimate for OAT paid for by patients themselves—not associated with those in iOAT. And when considering the cost for patients and government during implementation, the cost difference between OAT and iOAT may be small. That being said, the model does not consider additional benefits that treating opioid dependence has on health and crime in the cost-effectiveness analysis and the study did not estimate costs of new iOAT facilities. The models are limited to representing ongoing costs related directly to treatment, and the value of lives lost, but do not reflect the additional value of treatment on improving health, reducing crime, and reducing the impact of substance use on the community, all of which have well recognized value (
      • Byford S.
      • Barrett B.
      • Metrebian N.
      • Groshkova T.
      • Cary M.
      • Charles V.
      • Strang J.
      Cost-effectiveness of injectable opioid treatment v. oral methadone for chronic heroin addiction.
      ;
      • Doran C.M.
      • Shanahan M.
      • Mattick R.P.
      • Ali R.
      • White J.
      • Bell J.
      Buprenorphine versus methadone maintenance: A cost-effectiveness analysis.
      ;
      • Kelly S.M.
      • Schwartz R.P.
      • O'Grady K.E.
      • Mitchell S.G.
      • Duren T.
      • Sharma A.
      • Jaffe J.H.
      Impact of methadone treatment initiated in jail on subsequent arrest.
      ;
      • Rose-Jacobs R.
      • Trevino-Talbot M.
      • Vibbert M.
      • Lloyd-Travaglini C.
      • Cabral H.J.
      Pregnant women in treatment for opioid use disorder: Material hardships and psychosocial factors.
      ).

      5. Conclusion

      Modeling the provision of a mix of OAT, supervised iOAT, and unsupervised iOAT suggests that the incorporation of iOAT for people who do not respond to conventional OAT treatment may decrease the number of overdoses and overdose deaths compared to maintaining the status quo in treatment provision. Our model suggests that benefits could be achieved with lower costs if a greater proportion of unsupervised iOAT is used relative to supervised iOAT, without increased overall harm.

      CRediT authorship contribution statement

      Wai Chung Tse: Conceptualization, Methodology, Formal Analysis, Original draft preparation, Writing- Reviewing and Editing, Visualization.
      Nick Scott: Conceptualization, Methodology, Validation, Writing- Reviewing and Editing.
      Paul Dietze: Conceptualization, Methodology, Writing- Reviewing and Editing.
      Suzanne Nielsen: Conceptualization, Methodology, Original draft preparation, Writing- Reviewing and Editing, Visualization, Supervision.

      Declaration of competing interest

      SN and PD have received funding from Indivior. SN has received research funding from Seqirus, and PD has received an investigator-driven grant from Gilead Sciences for unrelated work on Hepatitis C and an untied educational grant from Reckitt Benckiser for unrelated work on the introduction of buprenorphine-naloxone into Australia. PD and SN and have served as unpaid members of an Advisory Board for an intranasal naloxone product.

      Acknowledgements

      Suzanne Nielsen (1163961) and Paul Dietze (1136908) hold National Health and Medical Research Council Research Fellowships. No other funding was received to support this work.

      Appendix A. Supplementary data

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