Projected Estimates of Opioid Mortality After Community-Level Interventions

Key Points Question Using simulated urban and rural communities, what evidence-based practices are associated with a reduction in opioid overdose mortality of at least 40% by 2022? Findings In this decision analytical model using simulated urban and rural communities, no single intervention or approach was associated with a 40% reduction in overdose mortality in any community. Achieving a 40% reduction required increasing capacity for treating with medications for opioid use disorder, improving retention on medications, and increased naloxone distribution. Meaning These findings suggest that reducing opioid overdose may require substantial, coordinated effort with a focus on improving initiation with medications, retention in care, and increased naloxone distribution.


INTRODUCTION
The growing prevalence of Opioid Use Disorder (OUD) has resulted in an increase in opioid overdoses in the United States. Overdose is the leading cause of premature death among Americans under the age of 50 and has increased by more than 2.5 times between 1999 and 2015. Although evidence-based treatments are available for treating OUD, these treatments are under-utilized, thus the impact of opioids on the United States' population persists.
Researchers and policy makers have made efforts to create feasible action plans for reducing the prevalence of OUD. Unfortunately, most policy makers do not have the evidence needed for informing and implementing system-level change. System-level thinking investigates how systems operate and how they can be modified to produce desired outcomes. At this time, data on system-level interventions for OUD are limited and inconsistent.
In an effort to fill the knowledge gap, simulation modeling can be used to integrate data from multiple sources to translate outcomes from clinical studies to policy-relevant data about population health and cost. By simulating state-level behaviors and practices related to OUD, we can project and evaluate the impact of relevant interventions and policies on public health outcomes and costs, hence informing practice and policy decisions to combat OUD.
The Researching Effective Strategies to Prevent Opioid Death (RESPOND) model is a state-transition, cohort-based model that simulates populations with high-risk opioid use in a state, including the natural history of opioid use disorder, movement on and off of opioid treatment, and overdose. The model provides outputs and projections that decision-makers can use to evaluate and modify care delivery systems to match their local epidemics and available resources.
Model inputs and parameters are adaptable to users' needs, namely to represent heterogeneous populations, different dynamics of the drug overdose epidemic, and the effectiveness of intervention strategies in the prevention of opioid-related harms. The user, for example, can customize among other things, the demographics, time in each cycle, transition probabilities between health statuses and treatment states, and the number of health states included in the model in order to represent different structure and disease dynamics of the underlying population.

MODEL STRUCTURE
Overview RESPOND is a state-transition, cohort-based [1,2] model that simulates the population living within a jurisdiction and who have high-risk opioid use. Typically, RESPOND simulates the population of a state, but it can also simulate a smaller area, such as a town or rural community, depending on the model parameter values. The model employs a Markov process with a weekly cycle length to accurately reflect population dynamics, clinical progression, and treatment of opioid use disorder.
The model structure comprises four main components; 1) population dynamics, 2) natural history of OUD, 3) care delivery, and 4) mortality.
The first part of the model pertains to simulating the epidemiology and demography of the opioid epidemic assuming either an open or closed cohort, namely allowing or not allowing new individuals to enter ("arrivals") the simulation process at each cycle respectively. When simulating an open cohort, the arrival rate represents both the development of new opioid use disorder, and migration into the state among those with existing opioid use. RESPOND does not directly simulate the development of opioid use disorder. Instead, the population "arrives" in each time step as an exogenous rate without simulating the specific steps in the development of opioid use. The input values for arrivals are calibrated to match observed, state-level OUD estimates stratified by age and sex.
The second part (core simulation - Figure 1) of the RESPOND model involves the simulation of the natural history of opioid use disorder as a relapsing and remitting disease over a lifetime. RESPOND simulates OUD as a series of transitions between four health states of opioid use: 1) active, non-injection, 2) nonactive, non-injection, 3) active injection, and 4) non-active, injection opioid use. In each time-step of the simulation, population fractions move between opioid use states. The definitions of "active" and "injection" opioid use can vary (but must be pre-specified) depending on the users' needs and available information. In the RESPOND Massachusetts base case, "active" opioid use is defined as any reported use in the previous seven days. "Injection" opioid use reflects any injection in the preceding seven days (a person who is both injecting and using oral opioids would be categorized as "injection" in RESPOND).
The third part of RESPOND is related to care delivery, and currently includes four "treatment episodes": 1) outpatient buprenorphine (Bup), 2) outpatient injectable naltrexone (Ntx), 3) outpatient methadone (Mmt) maintenance, and 4) inpatient acute drug detoxification center. The model is adaptable to additional intervention types to better reflect local conditions and evolutions in the treatment field. In general, treatment episodes tend to decrease movement into active drug use, increase movement into non-active drug use, and have an independent effect on overdose rates conditional on active drug use.
The fourth part of the model is mortality. RESPOND simulates overdose-related mortality, and competing causes of death. RESPOND simulates overdose mortality by first simulating overdose incidence as a function of age and type of drug use (injection vs. non-injection use). Next, the model simulates a probability of death conditional on having had an opioid overdose. The model simulates competing causes of death through the use of standardized mortality ratios that are a function of age, sex, and type of opioid use (injection vs. non-injection).
The primary model outputs are: 1) All-cause mortality, 2) Overdose mortality, and 3) Number of people on treatment.
The simulation process is as follows: At simulation start, the model initiates a cohort of people currently living with OUD in the jurisdiction of interest. Based on data from that jurisdiction, the model assigns the current population to a drug use state, as well as a treatment block, such that the simulated population, including the prevalence of OUD treatment, reflects the status quo. Moving forward through simulated time, the sequence of simulation steps are: 1) aging of the population, 2) arrival of new population, 3) transition between OUD drug use states, 4) transitions into and out of treatment, 5) overdose, and 6) death.
At the end of this sequence of processes, the model advances simulated time by one cycle (week) and repeats the process. The simulation continues until a time horizon assigned by the user. to the hospital, and overdose events [3]. RESPOND uses the MA PHD dataset to estimate parameters such as OUD epidemiology in MA and rates of transition onto treatments assuming the status quo.

NIDA Clinical Trial Network Protocols 0051 (CTN)
The National Institute on Drug Abuse administers a large clinical trials network for evaluation of treatments for substance use disorders. The Clinical Trial Network (CTN) 0051 protocol was a head to head comparative effectiveness trial of sub-lingual buprenorphine and injectable naltrexone for individuals with opioid use disorder who were accessing acute opioid detoxification services. RESPOND uses urine toxicology data from the trial to estimate transitions between substance use states while taking buprenorphine or naltrexone, as well as health care utilization among patients with OUD [1]. [4][5][6] Medical Literature In addition to the primary data sources listed above, RESPOND estimates many model parameters from the medical literature. The detailed explanation of model parameters below provides references to the relevant publications.

Initial Cohort
To simulate the demography and OUD epidemiology in the underlying population, RESPOND requires the initial cohort to be specified as follows: 1) age and sex distributions of people with opioid use disorder, 2) proportion of people beginning in each drug-use state, and 3) proportion of people within each treatment episode.
Structural Assumptions: • No population begins the simulation in a post-treatment block.
• RESPOND does not characterize the population by race or ethnicity.
Methodological Notes: Table 1 presents the key parameters related to cohort initialization.
To estimate the prevalence of both identified and unidentified OUD in Massachusetts, we employed a capture-recapture methodology to the Massachusetts Public Health Data Repository (MA PHD) to estimate the prevalence of OUD in Massachusetts during calendar years 2012 to 2015 stratified by age and sex [7]. The capture-recapture approach provides a method to estimate the total population with high-risk opioid use, including those who have not been identified as being an opioid user and do not appear in medical claims or prevalence surveys. To make population estimates beyond 2015, we combined data sources to extend the MA PHD. First, we used the National Survey on Drug Use and Health (NSDUH) to estimate the longitudinal trend in OUD in the United States 2015-2018. Next, we applied the trend line from NSDUH to the MA PHD OUD prevalence measurements. This approach assumes that the trend in prevalence in MA is similar to the trend nationally, but it provides an estimate of total population count that is informed by MA data. Aging RESPOND simulates discrete time steps (rather than continuous time) and categorical age groups or "brackets" over the lifetime. The user can define the bounds of age groups so as to match the structure of the underlying population. Aging occurs as the population progresses to the next age group after a number of cycles that is determined by the size of the age brackets. The model employs a half-cycle correction and aging occurs in discrete steps, namely only at multiples of the age group size.
Structural Assumptions: • The entire population of the last age bracket (95 to 100-year-olds) is removed from the simulation at each aging cycle and replaced by the population from the previous age bracket. Structural Assumptions:

Entering Cohort
• All new populations enter the first block ("No Treatment" episode) and the first OUD state (currently active, non-injection).
• All new arrivals enter the simulation as active non-injectors under the "No Treatment" block but can transition to other feasible OUD states in the OUD transition module.

Methodological Notes:
Error! Reference source not found. and Table 2 present the key parameters related to cohort initialization.
• The size of the entering cohort (Nenter,t) at each cycle (week) is defined as: where NOUD,t is the estimated OUD population in year t, NFOD,t-1 is the estimated number of fatal overdoses, and ND_other,t is the estimated total number of deaths from other causes, in the previous year (t-1).   Natural History of OUD RESPOND simulates opioid use as a series of transitions through four opioid use health states: 1) Non-Active and 2) Active non-injection use, as well as 3) Non-Active and 4) Active injection use (Figure 1).
Throughout the simulation, there is a multi-directional movement between OUD states.
Transitions between drug use compartments impact four important outcomes: 1) risk of overdose, 2) risk of death from competing causes, 3) health care utilization (cost), and 4) quality of life.
The primary sources of data for substance use transitions are studies from the medical literature.
Structural Assumptions: • OUD is a remitting and relapsing process over a lifetime. There is no health state of OUD cure or permanent recovery.
• Transitions between OUD health states are not time updated.
Methodological Notes: Table 3 presents the key parameters related to OUD transitions for no treatment.
• CIs for proportions pE, pF, pB, pH, and pD are calculated using the normal approximation to binomial proportions.
• CIs for rates RA, RC, and RD are provided from the manuscript and calculated assuming Poisson distribution.
• Weekly rates and proportions, calculated from the respective overall estimates, are converted to weekly transition probabilities as indicated in .   Bailey et al. [11] p * G Proportion of non-active injection to active injection PC Probability of non-active non-injection to active non-injection 0.2308 Calculated from p: 1-exp(x) where x = ln(1-p)/4 PG Probability of non-active injection to active injection • p * C and p * G indicate the percentage of people relapsed within a month of discharge (after inpatient detoxification).
• The denominators for calculating weekly probabilities depend on whether the respective available proportion or rate estimates are yearly or monthly.
Care Delivery RESPOND models OUD while engaged with treatment using the same 4-state opioid use simulation that it uses to model OUD without treatment. The 4-state OUD simulation is embedded within all treatment episodes (blocks), such that individuals may both remain engaged with treatment, but also experience periods of drug use relapse. Each treatment type has its own bi-directional transition probabilities between active and non-active use. The net movement between active and non-active use while engaged with treatment favors movement to non-active use over time.
RESPOND simulates treatment using the following parameters: 1. Probability of movement onto treatment from no treatment 2. Treatment initiation effect -the probability of ceasing active opioid use immediately after initiating treatment 3. Bi-directional movements between active and non-active opioid use while engaged with treatment

Probability of loss to follow-up
The population that is lost to follow-up (disengages from care) must pass through a "post-treatment period" before rejoining the simulation of OUD. The post-treatment period is a four-week time, immediately following discontinuation of a treatment, during which the risk of relapse to drug use is high, as is the risk of overdose. Population that survives the post-treatment period transitions back to the simulation of OUD without treatment.

Movement From no Treatment to Treatment Episodes
Structural Assumptions: • Only population in active opioid use states seeks OUD treatment. Population that is not currently using opioids does not seek treatment.
The main source of data to inform the probability of transition from no treatment to a treatment episode is the MA PHD. The weekly transition probability from no-treatment to treatment is calculated as: where N Obs,NoTrt → Trt .q : the observed number of people with OUD who transitioned from no-treatment to treatment q in January 2013 N Total,NoTrt → Trt .q : the total number of people with OUD "at risk" of transitioning from no-treatment to treatment q in January 2013 The weekly transition probability P NoTrt → Trt .q is estimated using data from the MA PHD repository 1 , and is stratified by age (16 groups: 5-year age-groups from 10-85, and >85years old), sex, and treatment (q= Detox, Residential, Mmt, Ntx, and Bup) ( Table 4).

Block Initiation Effect
The main source of data for the treatment initiation effect and for substance use transitions while engaged with buprenorphine, naltrexone, or methadone is the NIDA CTN urine toxicology data. The CTN trials collected routine periodic urine toxicology from all participants. While the published clinical trials results censored participants at the first relapse to drug use (the primary outcome of that trial), the trials continued to collect data from patients who experienced a relapse, such that the database includes longitudinal urine toxicology from patients who relapsed to active use, as well as some who remitted back to non-active use over the course of the trial. We are able to analyze those data in an "as treated" manner, such that RESPOND is able to estimate realistic movements between active and non-active drug use states among people who are taking a medication. In addition, while engaged with treatment, the population faces a risk of disengaging from care (loss to follow-up).
Methodological Notes: Upon entering treatment, a proportion of the population immediately transitions from active to nonactive opioid use. This proportion pInit_Act →NonAct is stratified by treatment episode as follows: We assume a binomial distribution and we use the Wald's method to calculate 95% CIs for the proportion pAct →NonAct representing the block initiation effect. ** There is no block initiation effect for population that is not currently using opioids, because only population that is currently using opioids seeks care in the model.

Transitions Between Active and Non-Active Opioid Use While Engaged With Treatment
We estimated Weekly OUD transition probabilities pTrt_Act →NonAct using Multi-State Models (MSMs) [13].
We fit separate models for each treatment: buprenorphine (Bup), naltrexone (Ntx), and methadone Structural Assumptions: • Population engaged with treatment may move between active and non-active opioid use, but the population engaged with treatment does not change the route of administration of their opioid use. In other words, population that entered treatment using non-injection opioids will not escalate to injection drug use while still engaged with treatment (Core Simulation within OUD treatment episodes (blocks) - Figure 2).
Transition probabilities between active and non-active states are the same for both injection and noninjection drug use. This structural assumption is confirmed by the MSM estimates for buprenorphine and methadone models, in which route was included as a model covariate, but was not a significant predictor of transition rates Methodological Notes: • Each MSM includes age and sex as covariates.
• Age is included as a continuous covariate in the MSM model, thus allowing estimation of the transition probabilities for age bins in which data are not available. We consider five 5 age groups: 10-19, 20-24, 25-34, 35-49, and 50-99 years old.
• OUD transition for Buprenorphine and Methadone: We keep all the weekly MSM estimates of OUD transition probabilities except week 1, which is considered as block initiation.
• OUD transition for Naltrexone: We delete the estimates for the first 4 weeks due to the inaccurate results from detoxification. Week 5 is also excluded from the analysis, as it is considered as block initiation.

Probability of Loss to Follow-Up
In the RESPOND model, every treatment episode has a corresponding post-treatment episode. The posttreatment block represents the period of time immediately following discontinuation of a medication or release from an abstinence-based setting (acute drug detoxification center, residential drug treatment, or jail), when opioid tolerance is low and the risk of overdose is higher than that of a person who never initiated treatment.
The main source of data for estimating the probability of loss to follow-up is Market Scan, a large insurance claims database containing millions of individuals who have commercial insurance coverage.
As a randomized controlled trial, the CTN data cannot provide estimates of retention in care or loss to follow-up in the real world. We have previously published rates of loss to follow-up from buprenorphine and naltrexone treatment [14]. We therefore turn to Market Scan, which is nationally representative and reflects real-world practice in the U.S.
Structural Assumptions: • In RESPOND, the only way to transition into a post-treatment episode is from a corresponding treatment episode.
• The "No Treatment" block does not have a post-treatment episode.
• RESPOND also considers the probability of immediate relapse to active opioid use upon being lost to follow-up from treatment: Methodological Notes: The weekly transition probability from treatment to post-treatment is calculated as: where rq = log{1-(1-pq)} and pq: the retention probability for treatment q. Table 7 presents estimates of the weekly transition probabilities P Trt → Post−Trt .q based on data from Morgan et al. [14], stratified by treatment. where ROD,t is the no-treatment overdose rate at time t. Morgan et al. [15] Sordo et al. [16] Overdose During the Post-Treatment Period During the post-treatment period, individuals faces a risk of overdose higher than that of people who never initiated a treatment.
The post-treatment rates of overdose at time t are calculated as: ROD, t, post-trt = R FOD,t P FOD,t  Pact_inj (6) where RFOD,t and PFOD,t are the post-detoxification fatal overdose rates and proportions respectively at time t (t=2013, 2014, 2015), Pact_inj is the proportion of active injectors, and 1-Pact_inj is the proportion of active non-injectors. We assume P act_inj = 0.329. Table 11 presents the fatal overdose rates and probabilities by age group and sex. Mortality RESPOND simulates mortality through two independent mechanisms, fatal opioid overdose and nonoverdose death.

Fatal Overdose
The population that experiences overdose then faces a probability of death conditional on having had an overdose. This conditional probability of death, given an opioid overdose, is generalizable to all overdose cases and is therefore not stratified by age, sex, or OUD status. The population that survives an overdose does not change substance use as a result of the overdose.
The probability PFOD,t of fatal overdose at year t is calculated as: where NFOD,t is the total number of fatal overdoses, and NOD,t is the total number of all-type overdoses.

Non-overdose mortality
Non-overdose mortality reflects sex and type of OUD stratified competing risks of death among people who use drugs. Competing risks include mortality from conditions such as infectious endocarditis and sepsis, as well as medical comorbidities that accrue over a lifetime. The general approach to estimating competing risks of death is to apply standardized mortality ratios (SMRs) to actuarial lifetables for the U.S. reflecting elevated mortality among drug users.