Spatial inequities in access to medications for treatment of opioid use disorder highlight scarcity of methadone providers under counterfactual scenarios

The current study extends our previous work on simulating the PWID population in Chicago and the surrounding suburbs, Illinois, USA, including drug use and syringe sharing behaviors, and associated infection dynamics [2,31]. The demographic, behavioral, and social characteristics of the PWID population is generated using data from five empirical datasets on metropolitan Chicago (urban and suburban) area PWID that is previously described [31]. In brief, this includes data from a large syringe service program (SSP) enrollees (n = 6,000, 2006–13) [32], the IDU data collection cycles of the National HIV Behavioral Surveillance (NHBS) survey from 2009 (n = 545) [33] and 2012 (n = 209) [34], and a social network and geography study of young (ages 18–30) PWID (n = 164) [35]. Of note, profiles of PWID from these data sources were similar when grouped by age, gender and racial/ethnic groups. Data analyses from these sources is used to generate attributes for each of the estimated 32,000 PWID in the synthetic population for metropolitan Chicago [36] in the model and includes: age, age of initiation into injection drug use, gender, race/ethnicity, zip code of residence, HCV infection status, drug sharing network degree, parameters for daily injection and syringe sharing rates, and harm reduction/syringe service program (SSP) enrollment [31]. PWID agents may leave the population due to age-dependent death or drug use cessation and are replaced with new PWID sampled from the input data set to maintain a nearly constant population size of 32,000 for the entire course of the simulation.

Syringe sharing among PWID is modeled in HepCEP via dynamic syringe sharing networks. Network formation is determined by the probability of two PWID encountering each other in their neighborhood of residence and within the outdoor drug market areas in Chicago that attracts both urban and non-urban PWID for drug purchasing and utilization of SSPs that are also located in the same areas [37]. The methods used to calculate network encounter rates, establishment processes, and removal of networks have been described previously [31]. Each modeled individual has an estimated number of in-network PWID partners who give syringes to the individual and out-network PWID partners who receive syringes from the individual. The network edge direction determines the flow of contaminated syringes between individuals, and thus the direction of disease transmission. The network evolves over time, and during the course of the simulation some connections (ties) may be lost, while new ties form, resulting in an approximately constant network size.

PWID that receive MOUD treatment experience a reduction in the number of daily drug injections, which is determined by multiplying the PWID’s baseline pre-MOUD daily drug injection frequency by a reduction multiplier sampled from a uniform distribution from 0 to 0.25 [38]. Thus, the mean reduction in daily injection frequency is 87% when on MOUD treatment compared to when not on MOUD. Reduction in daily injection frequency reduces the number of syringe sharing episodes with other infected individuals.

Our approach to model the initiation and continuation of MOUD treatment incorporates multiple aspects of access to care: 1) the travel distance to the nearest methadone provider from the PWID place of residence, 2) the frequency of clinic visits, and 3) racial/ethnic inequalities to treatment as represented by the geospatial heterogeneity of the PWID population demographics. PWID first decide to enroll in MOUD treatment and then subsequently decide to continue treatment every 7 days, a duration chosen to reflect the average frequency of clinic visits for the treatment over time. Average treatment duration for methadone is obtained from literature to be 150 days [39] and the probability to start and continue treatment every 7 days is estimated using a random empirical distribution with mean of 150 days, resulting in some PWID having longer or shorter time on treatment. PWID who discontinue methadone treatment may reinitiate treatment later during the course of the simulation. Different urban and non-urban travel distance preferences to the nearest methadone provider are used by PWID to determine if they will or will not enroll in MOUD treatment (Table 1). The probability that a PWID will enroll in MOUD treatment is greater when the treatment travel distance is below the travel distance preference.

Table 1. Travel distance to methadone provider preferences used for reasonable geographic access assumptions.

The table represents six different possible combinations of low, medium, and high travel distance preferences considering three urban/suburban distance preference combinations for each low, medium, high distance preference pair with a maximum distance limit, and three corresponding low, medium, and high distance preference pairs with no maximum distance limit.

https://doi.org/10.1371/journal.pcbi.1012307.t001

We define six different possible combinations of low, medium, and high travel distance preferences considering three urban/suburban distance preference combinations for each low, medium, high travel distance preference pair with a maximum travel distance preference, and three corresponding low, medium, and high travel distance preferences pairs with no maximum distance preference (Table 1). In the cases with maximum preferences, the individuals will not be able to access treatment if the provider is farther away than the maximum preferred travel distance.

To approximate reasonable geographic access, the travel distance in miles from zip code centroid to the nearest methadone provider is calculated using the sf package in R (version 4.0.2) [40] which provides a Euclidean distance metric. Travel network routing is not modeled in this analysis. Methadone treatment requires frequency of visits comparable to that of people’s grocery shopping (daily or weekly) [41,42], and travel distances of 1 mile (urban) and 10 miles (suburban/rural) areas is reasonable for community members, respectively, to their grocery stores. Because of the scarcity of methadone providers, we extend the urban reasonable travel distance preference to 2 miles for urban areas. Published findings indicate that access to mental health treatment within 10 miles is associated with greater attendance in persons with OUD [43]. Accordingly, the travel distance preference of “reasonable geographic access” to methadone providers is set at 2 miles in urban areas, which approximates a 30-minute walking distance, and for suburban and rural areas, the travel distance preference is set at 10 miles (Table 1, Medium travel distance preference). We define Low and High travel distance preferences to further account for uncertainties around minimal and maximal travel distance preference.

As there is limited information on how geographic access affects individuals’ decision to seek treatment, an additional layer of uncertainty is introduced via penalties on individuals’ probability of getting treatment when the geographic travel distance exceeds the reasonable access distance preference but is below the maximum distance limit. If the travel distance exceeds the preference, the per-decision probability of treatment is lower (by a factor θ) than if the PWID is closer to the provider. Since θ is not easily estimated, values are chosen ranging from 60% to 90% for this study, which represents broad per-decision penalties for accessing locations beyond distance preferences. The base probabilities are calculated by using the distribution of the PWID agent population under the actual spatial distribution of methadone providers (see below) and under different preference scenarios to match the overall methadone treatment duration values. Each penalty level is combined with each of the six travel distance preference combinations in Table 1, resulting in 18 separate parameter combinations, or reasonable access assumptions.

Fig 1 provides a geographic illustration of whether each zip code minimum travel distance to a methadone provider is within the travel distance preference of reasonable geographic access (Table 1), underlying different assumptions of what is the ideal distance to ensure accessibility. The first, second, and third row in Fig 1 corresponds to the low, middle, and high travel distance preferences, respectively in Table 1. For each travel distance preference (each row in Fig 1), the four figures (columns in Fig 1) show each zip code’s accessibility to the nearest methadone provider under the actual spatial distribution of providers and three counterfactual spatial distributions.

Fig 1. Spatial access to methadone providers for the actual scenario and three counterfactual distribution scenarios, under varying travel distance preference assumptions.

Each dot represents the location of a single methadone provider. City of Chicago and collar county borders are indicated. Spatial access to methadone providers is calculated as distance to nearest provider to the center of each zip code area; thus in the low travel distance preference assumption, zip codes areas are not identified as accessible if there is no provider within a mile of its geographic center. Esri. “Light Gray Canvas” [basemap]. Scale Not Given. “Light Gray Canvas Base”. Oct 26, 2017. https://www.arcgis.com/home/item.html?id=291da5eab3a0412593b66d384379f89f. (October 1, 2023).

https://doi.org/10.1371/journal.pcbi.1012307.g001

Comparing the actual provider spatial distribution with the two need-based distributions (Fig 1, column-wise), we identify areas where the need for methadone providers is high while the spatial access to providers is limited. For example, some areas in Chicago have high need but few providers, and accessibility to methadone providers are improved in the two need-based counterfactual distributions.

Comparing across rows in Fig 1, more zip codes have better spatial access to methadone providers as we assume a higher travel distance preference (i.e., people are able and willing to travel longer distances). This preference does not account for transit barriers such as travel time and access to public transit infrastructures, vehicles, as well as the financial cost of transit. Under the low travel distance preference that likely reflects real-world barriers to transit, few areas have reasonable geographical access to methadone providers. Therefore, simply redistributing methadone providers spatially may not provide better access when the number of individual providers is limited.

Since the total number of methadone providers are fixed in this analysis, redistributing provider locations in the counterfactual distributions relative to the actual distribution leads to some areas having a higher reduction in syringe sharing events than others. The reduction in the number of annual syringe sharing events (relative to baseline) in each zip code for the actual provider distribution (Fig 2, columns 1 and 5), under each reasonable access assumption reflect the zip code provider spatial accessibility in Fig 1. The change in syringe sharing reduction by zip code, relative to the actual distribution, highlights the effects of spatially redistributing methadone providers in each of the three counterfactual distributions (Fig 2, columns 2–3 and 6–8). Blue colored zip codes indicate a larger reduction in annual syringe sharing events than the actual distribution, while red colored zip codes indicate a lesser reduction in syringe sharing than the actual distribution.

Fig 2. Effects of reasonable access to methadone assumptions on syringe sharing events by zip code for each scenario in Cook County IL and surrounding counties.

Columns 1 and 5 represent the reduction in syringe sharing events for the actual spatial distribution of methadone providers, relative to the baseline scenario without methadone. In the other columns, blue colored zip codes indicate a greater reduction in syringe sharing events relative to the actual scenario, while red colored zip codes indicate a lesser reduction in syringe sharing events relative to the actual scenario. Zip code polygons shapefile obtained from the 2010 U.S. Census Datasets [44].

https://doi.org/10.1371/journal.pcbi.1012307.g002

Simulation scenarios across a range of methadone provider location distributions and spanning the spectrum from least optimistic reasonable access assumptions (Fig 2, upper rows, low travel distance preference, maximum travel distance, and a penalty of 0.6.) to the most optimistic access assumptions (Fig 2, lower rows, high travel distance preference, no travel distance maximum, and a penalty of 0.9) demonstrate a high degree of spatial heterogeneity in the expected reduction in syringe sharing events among PWID in Chicago, IL and surrounding suburbs.

The spatial variation of syringe sharing reduction across reasonable access assumptions (Fig 2) reflects heterogeneity in the PWID population both in terms of local population density, and in terms of drug use behaviors and co-injection risks reflected in the underling empirical population data used in the model. Since the underlying individual PWID behaviors are difficult to observe in reality, optimizing provider spatial distributions to reduce the number of syringe sharing events may not be an appropriate goal; rather, the robustness of spatial distributions that perform well over a wide range of possible ground truths and decision-making uncertainties are examined.

Fig 3 provides a visual representation of the regret scores for the annual reduction in syringe sharing events for each of the 18 reasonable access assumptions, grouped by the four spatial distributions of methadone providers (Tables A and B in S1 Supporting Information). Each point in Fig 3 represents the regret score for each of the reasonable access assumptions, color coded by travel distance preference (Table 1). Given the definition of regret scores, lower values represent a more ideal outcome (less regret) for a particular reasonable access assumption, i.e., values of zero indicate that the spatial provider distribution had the largest reduction in syringe sharing events for the indicated reasonable access assumption. Vertical box plots for each spatial provider distribution in Fig 3 provide the median, 25^th and 75^th percentiles for regret score.

Fig 3. Regret score of annual reduction in needle sharing by travel distance preference and spatial distribution of methadone providers.

Each dot represents the regret score for each of the 18 reasonable access assumptions (three travel distance preferences with and without maximum distance plus three distance penalty values). Vertical box plots for each spatial provider distribution provide the median, 25^th and 75^th percentiles. Whisker lines indicate minimum and maximum regret values. The regret score represents the difference in syringe sharing reduction for each of the four spatial provider distributions, relative to the spatial distribution with the largest reduction in syringe sharing, for all combinations of reasonable access assumptions. A decision regret score of zero represents an ideal outcome in that the spatial distribution was best at reducing syringe sharing for a given reasonable access assumption. Conversely, a high regret score means that the scenario had a significantly larger number of syringe sharing episodes relative to the best scenario with the fewest number of syringe sharing episodes.

https://doi.org/10.1371/journal.pcbi.1012307.g003

Fig 3 therefore helps to provide insight as to how reasonable access assumptions impact individuals’ decisions to initiate and continue methadone treatment. The need-based 2 distribution (PWID density) performs better than the need-based 1 (total population density) and actual distributions when spatial access to providers is important (i.e., low travel distance preference and higher barriers to travel, represented as orange dots). The need-based 1 distribution performs better than the need-based 2 and actual distributions under medium and high travel distance preference (e.g. willingness to travel further and lesser barriers to travel, represented as blue and green dots).

Across the actual, spatially random, and need-based 1 provider distributions, the regret scores tend to rank from highest for the low travel distance preferences (Fig 3, orange dots), with the next highest for the medium travel distance preference (Fig 3, blue dots), and lowest for the high travel distance preference (green dots) due to the fact that more PWID chose to initiate and continue MOUD treatment when travel distance preferences are greater and therefore allow for more access to providers based on the locations shown in Fig 1. Low travel distance preference access assumptions result in the lowest regret for the need-based 2 distribution because providers are located closest to areas of highest PWID density, resulting in better access compared to other distributions.

The actual provider distribution results in a greater reduction in syringe sharing events than the need-based 2 distribution (PWID density) only when assuming a high travel distance preference (green dots), while it performs much worse than both need-based distributions when assuming low travel distance preference (orange dots). Notably, the actual provider distribution does not achieve a zero (best) regret score for any combination of reasonable access assumptions (Fig 3). In all cases, the spatially random distribution generates the worst result (Fig 3).

Based on a 75^th percentile regret metric for each of the four spatial provider distributions, the Need-based 2 spatial distribution (PWID density) represents a more robust distribution of methadone providers with respect to reducing annual syringe sharing events, across the uncertainties around all reasonable access assumptions and travel distance preferences (Fig 3, fourth column).

Our current results report reductions in annual syringe sharing events for all combinations of reasonable access assumption and provider spatial distributions. Downstream health sequelae such as hepatitis C and HIV have been examined in previous work [2,51] in the PWID population; however, the current study did not investigate associated reductions in HCV. The current study also did not implement HCV treatment or other harm reduction services (e.g., sterile syringe and equipment provision). Simply reducing the syringe sharing frequency in a highly connected PWID network may not be sufficient to eliminate new HCV infection without also reducing the disease incidence.

The reported results include the annual reduction in syringe sharing for only a single simulation year (2030). Time-varying trends in syringe sharing metrics were not investigated. Further, the PWID population is maintained at a constant size of 32,000 individuals for the course of the simulation. Although we model transient changes in PWID demographics as in previous studies [2,31], we believe that the PWID population size may be somewhat close to constant given that people who transition to MOUDs is balanced out by new initiates into injection drug use entering the population.

The model has several limitations around practical access to methadone treatment. First, laws around access to methadone and OTP services can vary greatly by state, with some states like Illinois requiring a government issued ID for access to services [52]. The HepCEP model does not account for inequity in access to OTPs based on an individual’s possession of a valid government issued ID card. Minoritized groups, especially those who are unhoused, recently released from carceral settings, or undocumented, may face additional barriers to obtaining methadone treatment for OUD due to lack of government issued ID documents. Second, the model assumes that there is no treatment capacity constraint on individual providers, e.g. every PWID who seeks methadone treatment is able to do so. OTPs across the US have experienced constraints in providing care due in part to governmental regulations and lack of coverage via private health insurance for methadone treatment [53]. In light of this, our results may overestimate access to methadone treatment based on the study locale.

Synthetic model population data used in this analysis predominantly represent minoritized community members. The authors acknowledge that including social phenomena such as degree of medical mistrust, racism and stigma towards treatment are all important factors in urban MOUD induction and adherence [54], but are beyond the scope of this analysis. These unmeasured, potentially impactful forces may further moderate the findings described.