Design concepts

ABS models tend to incorporate the design concepts below to some degree. This model is a more top down, probabilistic ABS model than many ABS models and as such does not fully employ some of the design concepts. Learning and prediction (by agents within the model) are not employed.

3.2.4.1 Emergence

The model is a top down, probabilistic model, so much of the dynamics are “built in” rather than emergent. However, the heterogeneous geography, placement of waivered providers, and patients’ willingness to travel do result in the emergence of groups of unserved individuals even in more urban locations with many providers. These emergent groups do not arise out of the actions and interaction of agents, but more due to a confluence of many random properties of geography, treatment seekers and

physician siting.

3.2.4.2 Adaptation

Again, as a top-down, probabilistic model the proposed model treats adaptation only lightly. Patients seek to establish treatment with the closest provider, and if this fails, seek to establish with referred providers, failing that, they will use diverted buprenorphine or wait. This could be construed as adaptive behavior in treatment seeking. Use of diverted buprenorphine could be construed as an adaptive behavior in prolonging treatment seeking through self-medication. Patients in treatment may be in treatment long enough to reach stable abstinence or reduced opioid use. Once this

threshold is reached, a patient no longer uses a provider’s OAT treatment spot. This could be construed as an adaptive behavior in recovery. Patients who cannot afford their treatment or who need money will divert some of their medicine to the street (presumably for money). This is an adaptive behavior in treatment retention.

3.2.4.3 Objectives

Treatment-seeking agents in the model want to get into treatment. Most people with opioid dependence do not want to enter treatment, their implied objective is to use opioids. As in actual treatment, attrition out of treatment is high, but retention in treatment and possibly reaching stable abstinence or reduced opioid use is also an objective of agents. While “success” per se is not modeled from the agent perspective, from the model observer perspective, an agent in treatment or stably abstinent is considered “successful.”

Providers in the model want to provide treatment but only up to patient limit levels or to the level that they are comfortable.

3.2.4.4 Sensing

Treatment-seeking agents do not have complete information on all providers within the radius they are willing to travel, but they are assumed to know the closest provider. They are able to query whether a provider has an open treatment spot and act according to this information. Agents are also aware of their own internal states,

such as how long they have been waiting for treatment, or how long they have been in treatment.

Providers know how many patients they have, what the patient limits are, and how many patients they are willing to treat. They also know how long they have been waivered. Providers know that patients have left treatment. If a provider is in a densely populated area, a provider has complete information on all providers within a given radius. If a provider is in a rural area, the provider may only know the closest provider.

For this model purpose—determining capacity and access, it is not necessary for providers to know patient details.

3.2.4.5 Interaction

Interaction between agents is simple, and much of it is indirect. Treatment-seeking agents and providers interact when patients take up provider treatment spots.

This results in indirect interaction among treatment-seeking agents. Indirect interaction occurs when a treatment spot is occupied and a potential patient is denied treatment, or when a treatment spot opens up and another patient can receive treatment.

3.2.4.6 Stochasticity

Stochasticity is the driving force behind this model. Providers and OTPs are placed on the map using a random process. A statistical distribution is fit to the actual population densities of the zip codes of waivered physicians and OTPs. Modeled providers select the density of their own practice location by drawing from this

probability distribution and matching their practice location population density to a close population density on the map. The location of agents with OUD is also randomly selected based on the percentage of NSDUH respondents with dependence in different metro area types. The proportion of large MSA, small MSA, and non-MSA are fixed at initialization, but the actual location of agents with OUD on the map is random. This is because the actual locations of people with dependence is protected information, and not known to modelers. The distance a patient is willing to travel for treatment is determined by 10 empirical probability distributions based on population density of patient zip code obtained from the NAABT patient locator data file (www.naabt.org), with a greater proportion of rural residents willing to travel large distances to receive treatment. Treatment retention is treated probabilistically based on retention in treatment studies.

To model capacity and access, I have chosen to fit certain variables to empirically observed distributions to be both general and empirically grounded, specifically

willingness to travel based on urban/rural designation. I have also chosen to simulate decisions as probabilities based on aggregate survey and study data because it is simple and more nuanced decision making logic is likely not necessary to address the research aims.

3.2.4.7 Collectives

While different agent types are aggregated into collectives for observation (see below), agents act as individuals and do not interact with groups of agents. For

example: there are no professional societies of providers that share a common desired cap level.

3.2.4.8 Observation

Observation refers to what data are collected from the model. The following metrics are recorded at the end of a model year:

 Total population in the modeled environment

 Number of people who received BUP treatment in the past year per 100,000 population

 Number of people who received ANY OAT treatment in the past year per 100,000 population

 Milligrams of diverted buprenorphine in the region

 The number of opioid overdose deaths in the past year per 100,000 population

 Spatial Potential Access Gini Indices (see Section 3.5 for derivation of these measures)

3.3 Data

3.3.1 Initialization

Initialization varies from one simulation run to the next as described above in Section 3.3.1. Initialization consists of 4 steps: geography, OTPs, providers, and agents with OUD are each initialized in turn.

Geography is initialized by importing population density maps into the simulation environment and by assigning densities to 1 square mile “patches”

accordingly. Similarly, a map of medically underserved areas (MUAs) is imported and overlaid on the population map to determine for which patches the “medically

underserved area” variable is “true.” MUAs maps are generated by the HRSA to identify regions which have a shortage of primary care health services and are publicly available for GIS analysis (Health Resources and Services Administration, 2018). Figure 3-2 shows the initial population density and MUA maps. The model is initialized with nine other sets of maps to explore the effect of geographic variation on outcomes and measures.

This is described in Section 3.4.4.3.

Figure 3-2: Population density (left) and Medically Underserved Area (right) maps. Blue-grey regions represent MUAs.

OTPs are initialized with the following random and calculated parameters:

Table 3-4: OTP initial parameter values and empirical support

Parameter Value Support Comment

Number of OTPs 1368 * total model Location of OTPs Random:

Lognormal the OTP directory.

Model OTPs select a population density from the distribution and then are sited on a patch with a similar population density.

methadone spots Mean 103 sd 89 2011 OTP Survey number of

accepts public

methadone spots Mean 362 sd 469 2011 OTP Survey number of

methadone spots Mean 235 sd 213 2011 OTP Survey number of

physicians

Random: 1 or 2 2011 OTP Survey Private For-Profit

accepts cash 100% 2011 OTP Survey

accepts private

methadone spots Mean 255 sd 204 2011 OTP Survey number of

physicians

Random: 1 or 2 2011 OTP Survey

Providers are initialized with the following random and calculated parameters:

Table 3-5: Provider initial parameter values and empirical support

Parameter Value Support Comment

Number of years the physician provider has had a waiver

Random: Uniform distribution [0, 15]

SAMHSA list of all waivered

SAMHSA list of all waivered with density < 20.

Otherwise with a urban in the model and in the US. suggested by the PA expert.

3 A full de-identified list of providers with a DATA 2000 waivers was provided directly by SAMHSA in 2014.

4 Data obtained from a representative of Reckitt Benckiser in personal communication.

prescribing, could treat a very large number of treat more than the high patient limit,

Number of

SAMHSA list of all waivered physicians are in adult primary care or psychiatric visit costs less than

$60.

Initial visit is double the maintenance office visit. Costs vary considerably from provider to provider and region to region. The random function

allows for a large range of visit costs.

Cost of NP or PA office visit

70% * cost of physician office visit

Assumed. Primary care NPs are often reimbursed at a lower rate than primary care physicians by managed care payers (Hansen-Turton, Ware, Bond, Doria, &

Cunningham, 2013).

Agents with OUD are initialized with the following random and calculated parameters:

Table 3-6: Agent initial parameters and empirical support

Parameter Value Support Comment

Number of people is defined as opioid abuse or to travel based on zip code

Analytics Retail live in small towns while 48% live in

5 Data obtained from a representative of Reckitt Benckiser in personal communication.

Agents with waiting times less than 1 week will seek treatment in the given week, but will relapse if they Richard G. Soper, &

Michael M. Miller,

of patients listing “I needed it to afford my treatment” as a

35% per year Calibrated to fit buprenorphine

of patients listing “I was pressured to divert by a friend or because someone else needed it more than I did” as

a reason for analysis of full data set analysis of full data set analysis of full data set analysis of full data set

Coinsurance 0 for public insurance,

2011 OTP survey The SAMHSA OTP survey gives ranges of doses. For simplicity, doses were rounded up

to the highest dose in the range

Figure 3-3: Graphical display of the simulation after model initialization. Maroon squares represent OTPs;

large red triangles are OB BUP providers; small triangles represent people seeking OAT.