Opioid Epidemic Simulation

Abbreviations

Abbreviation	Definition
MOUD	Medications for Opioid Use Disorder
OUD	Opioid Use Disorder

1 Overview

This document outlines the concept model for simulating interventions that might reduce the burden of the opioid epidemic, such as Medications for Opioid Use Disorder (MOUD). The core of this model is a state-transition model representing opioid use disorder states and treatment dynamics. The model also includes a “quarters” component that captures the living conditions of individuals, including private residence, unhoused status, and incarceration.

2 Modeling aims and objectives

The primary goal of this OUD simulation modeling effort is to serve as a tool for evaluating the potential population-level impact of various interventions and combinations of interventions designed to mitigate the burden of the opioid epidemic. The model aims to explore how different strategies might affect key outcomes related to Opioid Use Disorder (OUD), including prevalence, treatment engagement, and potentially related harms.

A central objective is to simulate interventions grouped according to the U.S. Department of Health and Human Services (HHS) framework, which categorizes services into four key areas:

1. Enhanced Delivery of Evidence-Based Treatment: Simulating the expansion or improved delivery of Medications for Opioid Use Disorder (MOUD), such as methadone, buprenorphine, and naltrexone, potentially alongside integrated behavioral therapies and psychosocial support. This involves modeling changes in treatment initiation, adherence, and success rates.

2. Recovery Support: Modeling the impact of services that facilitate long-term recovery and wellness. This includes simulating the effects of increased access to recovery housing, peer recovery support services, employment assistance programs, and other wraparound services aimed at enhancing stabilization.

3. Integrated Harm Reduction: Evaluating strategies focused on reducing the immediate risks associated with drug use. This involves modeling the effects of interventions like naloxone distribution for overdose reversal, syringe services programs (SSPs) for preventing infectious disease, fentanyl test strip availability, and potentially low-barrier engagement points for healthcare access.

4. Data Monitoring and Primary Prevention: Exploring the potential effects of efforts aimed at preventing the initiation of OUD and improving surveillance. This could include modeling the impact of public awareness campaigns, safer prescribing initiatives, or early screening and intervention programs, informed by ongoing data monitoring.

By allowing the simulation of interventions individually and, crucially, in combination across these categories, the model is intended to help understand potential synergies or trade-offs between different approaches. The ultimate aim is to provide insights that can inform strategic planning and resource allocation for efforts addressing the opioid crisis.

3 Concept model and submodels

3.1 Core Disease Model

The core disease model represents opioid use disorder as a state machine with three states:

State Definitions

State	Definition
susceptible	Individual does not have opioid use disorder
with condition	Individual has opioid use disorder but is not receiving medication treatment
on treatment	Individual has opioid use disorder and is receiving medication treatment (MOUD)

Transition Rate Definitions

Symbol	Name	Definition
i	incidence rate	Rate at which individuals develop opioid use disorder
r	remission rate	Rate at which individuals with untreated OUD naturally recover
ti	treatment initiation rate	Rate at which individuals with OUD begin medication treatment
tf	treatment failure rate	Rate at which individuals on MOUD discontinue or fail treatment
ts	treatment success rate	Rate at which individuals on MOUD achieve sustained recovery/remission

Key features of the model include:

• The “with_condition” state can be used as a risk exposure

• Treatment state has no excess mortality or disability weight relative to susceptible

• State membership is determined by prevalence data and treatment ratios designed to be internally consistent and to match GBD 2021 estimates

3.2 Quarters Model

The simulation also includes a “Quarters Model” representing the living situation of each individual. This submodel tracks transitions between distinct states related to housing, homelessness, and incarceration.

This submodel uses a state machine with three states:

State Definitions

State	Definition
Private Residence	Individual resides in stable, private housing (e.g., house, apartment).
Unhoused	Individual lacks stable housing (e.g., living on streets, in shelters, temporary arrangements).
Incarcerated	Individual resides in a correctional facility (e.g., jail, prison).

Transitions between these states occur based on defined rates:

Transition Rate Definitions

Symbol	Name	Definition
pr_uh	Rate of becoming unhoused	Rate at which individuals transition from private residence to being unhoused.
pr_inc	Rate of incarceration (from residence)	Rate at which individuals transition from private residence to incarceration.
uh_pr	Rate of obtaining housing	Rate at which unhoused individuals transition to private residence.
uh_inc	Rate of incarceration (from unhoused)	Rate at which unhoused individuals transition to incarceration.
inc_pr	Rate of release to housing	Rate at which incarcerated individuals are released to private residence.
inc_uh	Rate of release to unhoused	Rate at which incarcerated individuals are released into unhoused status.

Key features and interactions of this submodel include:

• Interdependence with OUD Status: Transition rates within this Quarters Model (e.g., pr_uh, uh_inc) may be influenced by the individual’s state in the Core Disease Model (susceptible, with condition, on treatment). For example, individuals with untreated OUD might have a higher rate of becoming unhoused. See below for details on how this is implemented using the RiskEffect component.

• Influence on OUD Transitions: Conversely, an individual’s state in the Quarters Model can affect transition rates within the Core Disease Model. For instance, being unhoused or incarcerated might increase OUD incidence risk (i), decrease treatment initiation rates (ti), or increase treatment failure rates (tf). See below for details on how this is implemented using the RiskEffect component.

• Parameterization: Rates need to be parameterized using available data sources on housing instability, homelessness, incarceration, and release patterns, potentially stratified by relevant demographic factors and OUD status where data permits.

4 Data Notes

Parameterizing the MOUD simulation requires integrating data from various sources to define initial population states and the transition rates governing movement between states in both the Core Disease Model and the Quarters Model. Key data requirements and methodologies include:

4.1 Core Disease Model Parameters

The Core Disease Model requires estimates for:

• Overall OUD Prevalence: Sourced from the most recent Global Burden of Disease (GBD) Study, specifying the relevant year and location.

• Treatment Coverage Ratios: Data on the proportion of individuals with OUD who are receiving MOUD. Sources may include national surveys (e.g., NSDUH), jail healthcare system data, and HIV surveillance studies.

• Transition Rates: Estimates for disease incidence (i), untreated remission (r), treatment initiation (ti), treatment failure (tf), and treatment success (ts).

A significant challenge is that not all required transition rates (particularly untreated remission, r, as well as all treatment-related rates) are directly available from GBD. We want these rates, and we want them to be be internally consistent over time.

To address this, we have used a novel NumPyro implementation of a DisMod-AT-like model. DisMod-AT (Disease Model – Age-and-Time) is a Bayesian meta-analytic tool designed to synthesize diverse epidemiological data (e.g., prevalence, incidence, remission, excess mortality/relative risk) to produce a consistent set of transition rates for compartmental disease models.

• Process: The NumPyro/DisMod-AT tool is configured with the OUD state model structure (Susceptible, With Condition, On Treatment). Inputs include location-specific data on OUD prevalence, treatment coverage, and GBD estimates of incidence, prevalence, and excess mortality for OUD, as well as data or assumptions about remission and treatment-related rates.

• Output: The tool solves for a full set of internally consistent prevalence and transition rates (p, i, r, f, ti, tf, ts) that best fit the input data constraints according to Bayesian principles. This provides a robust estimate for parameters like the untreated remission rate (r).

4.2 Quarters Model Parameters

The Quarters Model requires data on the distribution of the population across the three states (Private Residence, Unhoused, Incarcerated) and the transition rates between them (pr_uh, pr_inc, uh_pr, uh_inc, inc_pr, inc_uh).

• Population Distribution:

  • Private Residence: Baseline population estimates, potentially stratified by age and sex, are typically derived from U.S. Census Bureau data, particularly the American Community Survey (ACS) which provides detailed yearly housing characteristics.

  • Unhoused: Estimates often rely on annual Point-in-Time (PIT) counts conducted by Continuums of Care (CoCs) and reported to HUD. These provide a snapshot but may undercount the true population. Local Homelessness Management Information System (HMIS) data, where available (e.g., for Seattle/King County), can offer more detailed longitudinal information but may have coverage limitations. Specific research studies on local unhoused populations are also valuable.

  • Incarcerated: Data on jail and prison populations can be obtained from the Bureau of Justice Statistics (BJS) and state/local sources like the Washington State Department of Corrections or county jail dashboards/reports.

• Transition Rates: Estimating the rates of movement between these states is complex and often requires synthesizing multiple data sources and making assumptions:

  • Incarceration/Release Dynamics (``pr_inc``, ``uh_inc``, ``inc_pr``, ``inc_uh``): BJS and local corrections data provide information on entries and releases. Determining the housing status upon release (to stable housing vs. homelessness) often requires specialized reports or research studies.

  • Housing Instability (``pr_uh``): Data on eviction rates, housing loss, or entries into homelessness from stable housing can be sourced from local housing authorities, HMIS data, or specific surveys/studies.

  • Exits from Homelessness (``uh_pr``, ``uh_inc``): HMIS data and longitudinal studies of unhoused individuals are key sources for estimating transitions back to private residence or into incarceration.

• Stratification and Interaction: A critical step involves estimating how these population distributions and transition rates differ based on OUD status (from the Core Disease Model) and demographic factors (age, sex). This often requires analyzing linked data sources (if available), applying relative risks derived from literature, or making informed assumptions due to data scarcity linking OUD directly to housing/incarceration transitions at a population level.

4.3 General Considerations

Data from different sources must be reconciled for the specific simulation timeframe, location (e.g., Seattle, King County, Washington State), and population demographics. Significant data processing, harmonization, and potentially imputation may be necessary, particularly for deriving transition rates and stratifying them appropriately. Assumptions made due to data limitations should be clearly documented alongside the model specifications.

5 Model Runs

Model runs

Run	Description	Scenarios	Specification modifications	Stratificaction modifications	Note
1	MOUD cause model	Baseline	–	–	Demonstrate that calibration is possible

6 Limitations

TK - Discussion of model limitations and assumptions

7 References/Other