Modeling the population‐level impact of opioid agonist treatment on mortality among people accessing treatment between 2001 and 2020 in New South Wales, Australia

Abstract Background and Aims The individual‐level effectiveness of opioid agonist treatment (OAT) in reducing mortality is well established, but there is less evidence on population‐level benefits. We use modeling informed with linked data from the OAT program in New South Wales (NSW), Australia, to estimate the impact of OAT provision in the community and prisons on mortality and the impact of eliminating excess mortality during OAT initiation/discontinuation. Design Dynamic modeling. Setting and participants A cohort of 49 359 individuals who ever received OAT in NSW from 2001 to 2018. Measurements Receipt of OAT was represented through five stages: (i) first month on OAT, (ii) short (1–9 months) and (iii) longer (9+ months) duration on OAT, (iv) first month following OAT discontinuation and (v) rest of time following OAT discontinuation. Incarceration was represented as four strata: (i) never or not incarcerated in the past year, (ii) currently incarcerated, (iii) released from prison within the past month and (iv) released from prison 1–12 months ago. The model incorporated elevated mortality post‐release from prison and OAT impact on reducing mortality and incarceration. Findings Among the cohort, mortality was 0.9 per 100 person‐years, OAT coverage and retention remained high (> 50%, 1.74 years/episode). During 2001–20, we estimate that OAT provision reduced overdose and other cause mortality among the cohort by 52.8% [95% credible interval (CrI) = 49.4–56.9%] and 26.6% (95% CrI =22.1–30.5%), respectively. We estimate 1.2 deaths averted and 9.7 life‐years gained per 100 person‐years on OAT. Prison OAT with post‐release OAT‐linkage accounted for 12.4% (95% CrI = 11.5–13.5%) of all deaths averted by the OAT program, primarily through preventing deaths in the first month post‐release. Preventing elevated mortality during OAT initiation and discontinuation could have averted up to 1.4% (95% CrI =  0.8–2.0%) and 3.0% (95% CrI = 2.1–5.3%) of deaths, respectively. Conclusion The community and prison opioid agonist treatment program in New South Wales, Australia appears to have substantially reduced population‐level overdose and all‐cause mortality in the past 20 years, partially due to high retention.


INTRODUCTION
World-wide, nearly 500 000 deaths in 2019 were directly related to drug use, of which nearly 100 000 were caused by opioid use disorders (OUD) [1,2]. Opioid-related deaths have continued to steeply rise over the COVID-10 pandemic and represent a public health crisis in many countries [3,4].
Opioid agonist treatment (OAT), with medications such as methadone and buprenorphine, is an evidence-based treatment which individual-level analyses have shown reduces mortality due to opioid overdose and other causes [5,6] and prevents acquisition of HIV [7] and hepatitis C virus [8] among people who use opioids, especially if they inject drugs [9]. As a result, numerous public health agencies, such as the World Health Organization, recommend the provision of OAT [10][11][12][13]; methadone and buprenorphine are listed as WHO essential medicines for this indication.
While the individual-level efficacy of OAT on reducing mortality has been established and quantified in meta-analyses [5,6], demonstrating its effect at population-level has been more challenging. Such evidence is key to support and inform scale-up of OAT programs globally, which is urgently needed, as most programs reach only a small proportion of those in need [14]. Very few studies (mainly ecological) [15][16][17][18][19] have evaluated the impact of OAT provision on populationlevel mortality, with conflicting results. Ecological studies in Europe found that the number of OAT recipients were inversely associated with the number of overdose deaths [15,17]. In France, where since 1995 all registered physicians are allowed to prescribe bubprenorphie without speciality certification, the number of patients on OAT increased by more than 95% from 1995 to 1999 (from fewer than 2000 to more than 65 000 per year), and opiate-related overdose deaths declined by 79% during this period [17]. A similar ecological study in Baltimore found no association between number on OAT and number of heroin-related deaths from 1995 to 1999 (when purity of heroin was rising) but a significant inverse association from 2003 to 2009, which coincided with the scale-up of buprenorphine (a 13-fold increase during this period, while the number of overdose deaths decreased by nearly twofold [16]). In the United Kingdom, a cohort study found a low probability of impact of OAT on population mortality, suggesting that the observed duration of OAT is too short to achieve population benefit and reduce the number of overdose deaths [19]. In contrast to the statistical analyses above, dynamic modeling can be used to investigate the impact of OAT programs at the population level through mechanistically reproducing mortality dynamics through time [9,20]. Capturing the processes underlying mortality patterns as a function of OAT engagement and other key factors modulating mortality risk, such as incarceration, provides us with a solid framework to both retrospectively evaluate and predict OAT program impact. To date, dynamic modeling has not been used to evaluate historic OAT program impact, which is key to producing rigorous evidence of its population-level effectiveness and on the factors driving it needed to informing policy.
In the Australian state of New South Wales (NSW), OAT was scaled-up in the 1980s and has achieved a high coverage, with more than 40% of people who inject opioids reporting current use [21][22][23] (no estimates available among all people using opioids), thus providing a rich data source for understanding long-term impact at populationlevel. Additionally, OAT program data have been linked to public data sets on mortality and incarceration, thereby allowing a more comprehensive investigation of the effect of different life events (e.g. incarceration, hospitalization) on OAT engagement and the effectiveness of OAT on the risk of overdose and other cause mortality [24].
In this analysis, we use dynamic modeling to estimate the population-level impact of the NSW OAT program on opioid overdose and other cause mortality among those who ever received OAT from 2001 to 2020, incorporating OAT engagement patterns and incarceration effects on mortality. We also estimate the specific contribution of the prison OAT program to reducing mortality among this cohort and investigate the potential increased efficiency of the program if higher mortality on initiation and discontinuation of OAT was eliminated.

METHODS
We designed a simulation model of fatal overdose and other cause mortality among people who ever received OAT in NSW. The model tracks changes in opioid use, OAT engagement and incarceration, incorporating heterogeneity in overdose and other mortality risks during these periods. Data from the literature and the NSW OAT cohort were used to inform the model's parameters. The model was calibrated using Bayesian methods to time-series data on OAT engagement, incarceration and mortality patterns from the NSW OAT cohort to reproduce the observed dynamics and to both quantify and more clearly understand the impact of the OAT program. Full detail on the model assumptions and data used are provided in the Supporting information, but key information is provided below. The analysis was not pre-registered and the results should therefore be considered exploratory.

Model description
We developed a dynamic, deterministic mathematical model of fatal overdose and other cause mortality among people who ever received OAT in NSW from 2001 to 2020, incorporating incarceration patterns and OAT receipt. While the NSW OAT program started systematically collecting data in 1985 [25] we chose 2001 as our start date, as linked-incarceration data are available from 2000 and the model incorporated past-year incarceration.
Receipt of OAT was represented through five stages: (i) first month on OAT, (ii) short (1-9 months) and (iii) longer (9+ months) duration on OAT, (iv) first month following OAT discontinuation and (v) rest of time following OAT discontinuation ( Figure 1 and Supporting information, S1.2, 'OAT cessation'). This disaggregation aimed to capture the impact of OAT on reducing overdose and other cause mortality, as well as the increased risk of overdose death in the first month of OAT initiation (compared to rest of time on OAT) or discontinuation (compared to rest of time off OAT) [5,26,27]. Additionally, as implemented by others [28], it incorporated heterogeneity in OAT durations, representing two main patterns of OAT engagement (rapid turnover and stable treatment), leading to more and less frequent exposure to the risks associated with OAT initiation and discontinuation [29].
Given the high risk of overdose upon release from prison during the first month and up to the first year post-release, and differential access to OAT in prison, the population was stratified into (i) never or not incarcerated in the past year, (ii) currently incarcerated, (iii) released from prison within the past month and (iv) released from prison 1-12 months ago. The increased risk of overdose and other cause mortality was high during the first month post-release, and a lower residual increased risk of fatal overdose (but not other cause mortality) was maintained during the remaining 11 months. Mortality from overdose and other causes during incarceration was lower than found outside prison (see Table 1 in the 'Model parameterization' section).
Individuals newly entered the model into the 'first month on OAT' compartment and were distributed into the four incarceration status groups described above. Once they had discontinued OAT they could be re-enrolled multiple times, either in the community or in prison. Individuals either left the model through fatal overdose, other cause mortality or progressed to a 'no opioid use' compartment (through ceasing both OAT and illicit opioid use), in which they were only exposed to other cause mortality. Individuals could relapse by transitioning back into opioid use off OAT, and could be re-enrolled onto OAT. Both overdose and other cause mortality were assumed to increase linearly to reproduce observed increases in these rates over time (see Supporting information, Table S1 and 'Sensitivity and uncertainty analyses' section). Larney et al. on mortality among people who use opioids [30], OAT effect on mortality through different periods of risk [5,31] and OAT effect in reducing incarceration [32][33][34]. Incarceration data represented all incarceration episodes, including on remand (i.e. pre-sentence) and custodial sentences of any duration. The majority of parameters were sampled from prior uncertainty distributions (Table 1 for key parameters and Supporting information, Table S1 for full list), with the exception of initial conditions and yearly cohort entries, which were directly based on observed data (Supporting information, Table S2).

Model parameterization
Full details are provided in the Supporting information.

Model calibration
We used an approximate Bayesian computation sequential Monte Carlo approach [35] for calibration to incorporate parameter uncertainty. The model was calibrated by minimizing the sum of least squares to the following data normalized to the same scale  Table S1) and perturbed over multiple generations, improving model fits at each generation, until successive iterations did not sufficiently improve the model fits. This generated 1000 calibrated model fits, which were used to produce model projections and associated credible intervals (corresponding to the 2.5 and 97.5 percentiles and noted '95% CrI' hereafter).

Analyses
We implemented a series of analyses to estimate the impact of the OAT program and of specific periods of heightened risk (i.e. OAT initiation, discontinuation and prison release) on opioid overdose and other cause mortality from 2001 to 2020 within the cohort of individuals who ever received OAT during this time-period (Table 2).
To estimate the impact of the community and prison OAT program, we compared mortality (overdose and all cause) for the calibrated scenario with OAT from 2001 to 2020 ('baseline scenario') to a scenario assuming no OAT effect on mortality, implemented through setting the OAT overdose and other cause mortality risks in the first month on and off and during treatment equal to 1, and the relative risk of incarceration on OAT to 1. The latter was implemented to account for the fact that through reducing incarceration risk, OAT also reduces exposure to heightened mortality risk during the post-release period.
We then assessed the specific contribution of the prison OAT program to the overall OAT program impact by comparing the baseline scenario to a scenario assuming no OAT program in prison, implemented through moving people in prison OAT to off OAT, interrupting OAT upon incarceration and stopping OAT enrollment while in prison. Importantly, through removing prison OAT provision, more people are exposed to the increased mortality risk in the first year fol- We additionally estimated the contribution (i.e. population attributable fraction) of three high-risk periods (first month post-incarceration release and first month of OAT initiation and discontinuation) to overdose and other cause mortality from 2001 to 2020. We assessed the contribution of first month post-incarceration release by comparing the baseline scenario to a scenario where the relative risks of death associated with the first month post-incarceration release were set to 1. We assessed the contribution of increased risk upon the first month of OAT initiation and discontinuation by comparing the baseline scenario to a scenario where the relative risk of increased overdose and other cause mortality during the first month of OAT initiation or discontinuation, respectively, were set to 1.

Sensitivity and uncertainty analyses
We implemented two sensitivity analyses to investigate the impact of assumptions on predicted proportion of deaths averted through the OAT program. First, both linear and exponential functions fitted the observed overdose data trends. In our main analyses we conservatively assumed a linearly increasing trend, therefore we also implemented a sensitivity analysis assuming an exponentially increasing overdose mortality rate. Secondly, we performed an analysis assuming no relapse to opioid use after prolonged cessation. We implemented an analysis of covariance to identify parameters that   person-years and 0.6/100 person-years, respectively) [30].

Model comparison to data
Our model successfully reproduced the cohort data, suggesting that it captured the primary mechanisms underlying these observations.

Impact of OAT program on overdose and other cause mortality
The baseline model scenario estimated that there were 2020 (95%

Population-attributable fraction of OAT initiation and discontinuation
We estimated the increased risk in the first month following OAT initia-   Figure S4 for relative change in death due to incarceration and OAT initiation/discontinuation on overdose and other cause mortality in NSW from 2001 to 2020 F I G U R E 3 Percentage of overdose and other cause deaths averted among the cohort of people who received opioid agonist treatment (OAT) in NSW between 2001 and 2020 through the full OAT program and the OAT program in prison. See also Supporting information, Figure  S4 for relative change in deaths through the full OAT program and the OAT program in prison compared to no OAT provision from 2001 to 2020 Interventions addressing the excess risk during OAT initiation and cessation could have prevented up to 1.4% (95% CrI = 0.8-2.0) and 3.0% (95% CrI = 2.1-5.3) of all deaths, respectively (Table 3 and Figure 4).

Sensitivity analyses
Assuming an exponentially increasing overdose mortality rate resulted in a marginally higher impact of the OAT program on overdose deaths ( and (3) increased mortality in the first month on OAT (9.2% of variance) (Supporting information, Table S7).

DISCUSSION
In this study, we presented the first dynamic model assessing the

Comparison with other studies
Our study updates an earlier statistical analysis that estimated a 29% reduction in mortality among people on OAT from 1985 to 2006 [31] in NSW by applying the observed crude mortality rate among those off OAT to the total number of person-years in the cohort. Instead, our dynamic modeling simulated system dynamics of OAT engagement, incarceration, opioid use cessation and relapse. In particular, different patterns of OAT engagement affect mortality risk, with frequent OAT interruptions and re-initiations leading to higher mortality compared to long/stable treatment duration [26]. Effective overdose prevention interventions during the induction and discontinuation periods could have prevented up to 2.1% and 4.2% of overdose deaths, respectively. Peer, social worker [37] and telehealth interventions [38,39] to support patients during the induction period, as well as distress tolerance interventions [40] and novel regimens such as microdosing [41][42][43] to prevent precipitated withdrawal are being investigated and could potentially reduce overdose risk during this period. For some patients, residential treatment [44] during the first week(s) of treatment will be warranted to prevent early dropout associated with withdrawal symptoms. Preventing overdose during the first month following OAT discontinuation is more challenging, given that discontinuation is often related to relapse as a result of difficult and chaotic life events. Regular overdose education and naloxone distribution (OEND) among patients, but also their family members, partners and friends delivered as part of OAT programs, could help to prevent fatal overdoses during relapse. Contact with emergency services, law enforcement and penitentiary institutions is high during OAT discontinuation [45] and is predictive of non-fatal and fatal overdose [46], highlighting the importance of strong overdose prevention programs in these settings.
Generally, our findings are consistent with other dynamic model projections predicting the potential impact of scaling-up OAT (particularly if long duration) on overdose mortality among people who inject drugs (PWID) in Russia, Mexico, United States and Iran [9,[47][48][49], and also support previous ecological analyses which found associations between expansion of OAT programs and reduced mortality [15][16][17]19]. A recent dynamic modeling study using US Veteran Health Administration data found that treatment duration had to be more than 6 months to ensure a net mortality benefit of OAT across nearly all model projections, with longer treatment durations leading to increased impact [50]. In contrast, estimates in the United Kingdom suggested that an average duration of OAT of more than 1 year may be required to reduce overdose deaths in the population, and showed substantially poorer retention in England compared to NSW (1.74 years in NSW versus 1 and 0.47 years for methadone and buprenorphine, respectively, in England [19,26]). OAT discontinuation has been associated with more severe OUD (i.e. higher frequency of opioid use), polysubstance use and younger age, as well as precarious living conditions, including homelessness, incarceration and lack of social income assistance [51][52][53]. Both type of OAT medication and dose [51,54] must be well adapted to patients' OUD severity.
While buprenorphine and buprenorphine-naloxone prescription have been associated with higher rates of discontinuation versus methadone prescription [52], others have reported contrasting findings [55] and large-scale studies are being implemented to guide clinical practice [24,56,57]. Interventions to improve medication regimen choice through better assessment of symptoms have been proposed [58], and strategies to increase retention through counselling, therapeutic drug monitoring [59] and contingency management are being tested [59,60] and have shown promise [61]. Providing stable housing and employment opportunities support the recovery process beyond OAT retention through promoting personal satisfaction and social integration. In addition, addressing fear of health-system or medication dependence as well as stigma [62,63] towards long-term OAT, especially methadone, is also key to improving OAT retention.
The mortality risk among people with OUD is heterogeneous and higher upon release from incarceration. Our estimates of the proportion of overdose deaths during the first month following prison are lower than other estimates-i.e. < 4% in NSW compared to more than 7% in Scotland [64], probably due to high OAT coverage in NSW  Table S2C and Figure S2). The increase in post-release fatal overdoses could also be due to changes in the postrelease environment, such as higher prevalence of unstable housing [66,67], leading to engagement in higher-risk behaviors or changes in drug markets linked to more dangerous polydrug use. In both cases, this points towards the need for more radical interventions to address the excess risk during post-incarceration release [68,69]. Fortunately, depot buprenorphine is currently been scaled-up in NSW prisons [70] and might revert this trend. Indeed, OAT provision in prison has been shown to be highly effective at reducing fatal overdose post-release [6] and should be made available in correctional settings where it currently is not [71]. In addition, providing support during the month preceding release through engagement with recovery mentors and connection with community OAT services [72] has proved successful in facilitating treatment continuity, and findings from the impact evaluation of the 'Connections' program in NSW prisons on reducing mortality, recidivism and improving parenting outcomes will shed further light on these interventions [73]. OEND in correctional settings has been shown to be acceptable and feasible and to increase trainees' self-efficacy to respond to an overdose [74].