A Simulation Modeling Approach for Planning and Costing Jail Diversion Programs for Persons with Mental Illness

Conceptual Framework

The Mental Health/Jail Diversion Simulation Model is based on the Mental Health Simulation Model (Leff, Graves, Natkins, & Bryan, 1985; Leff, Hughes, Chow, Noyes, & Ostrow, 2010) that was developed for use in planning mental health services systems and has been in place for over two decades. The Mental Health Simulation Model has been used to plan for the introduction of evidence-based practices into ongoing systems, for estimating the costs and cost-effectiveness of transforming systems, and for identifying the implications of mental health initiatives on other systems such as criminal justice and social welfare. The model uses information collected from data systems (e.g., claims and encounter data) with gaps filled in by expert panels composed of system stakeholders. The general model seeks to describe an entire system of programs taken together and as such provides planners with the tools to explore the global effects and policy implications of local changes. A robust simulation performs numerous tasks such as forecasting capacity and budgets, conducting cost-effectiveness analysis, estimating the effects of initiating new or replacement services such as evidence-based practices, and serving as a pilot study for an actual experiment or quasi-experiment (Berk, Bond, Lu, Turco, & Weiss, 2000). Simulation simplifies the comparison of systems of care through mathematical modeling of services. It provides comparative data on budgets, consumer outcomes, cost-effectiveness, and requirements for capacity and staffing. The ability to anticipate and model such side effects via simulation and sensitivity analysis highlights the strength of the application.

The Mental Health/Jail Diversion Cost Simulation model was developed to help communities as they plan and budget for jail diversion programs. It is a strategic planning tool intended to provide program stakeholder groups with information for designing jail diversion programs and developing strategies for resource allocation across systems. This computerized model projects the costs, effectiveness, and potential cost offsets of implementing a jail diversion program for people with mental illness. The model application is implemented using Microsoft’s ASP.NET platform and is programmed in C Sharp (C#). The model uses the inputs (generated by local data and expert judgment) to generate each unique outcome scenario.

This model compares the service utilization, consumer outcomes, and costs for a group of individuals who are diverted into community-based services and supports to the costs for the same group of individuals in the absence of a jail diversion program. Program planners can use the model to explore the fiscal implications of implementing different jail diversion strategies, providing different services, and choosing different target populations.

The inputs to the model include mental health functional level of potential participants, mental health and substance abuse service needs, available or planned treatment services, mental health and criminal justice service unit costs, and probable service impacts. Data can be obtained from published reports, state and local mental health systems, criminal justice databases, or from instruments developed specifically for the model.

The approach takes advantage of operation research methods, sometimes called the “science of decision-making,” by using information technology, data, and other relevant sources to produce informed decisions (Pierskalla & Brailer, 1994). In the case of the intersection of the mental health and criminal justice systems, an operation research approach to planning requires a consideration of what happens when groups of consumers with differing disorders receive multiple services that vary in type and duration in response to the nature of the disorders, the effectiveness of treatments, and the impacts of the social environment (Leff, Dada, & Graves, 1986). Combined with the expected impacts of criminal justice involvement for a group that is not diverted, the model provides a comprehensive assessment of the service capacity needs for the desired system and the fiscal implications for different service systems.

The simulation model is outcomes-based, exploring the impact of diverse service configurations on the functional-level transition of consumers on a month-to-month basis. Functional level is measured using the Resource Associated Functional Level Scale (RAFLS), a measure uniquely developed for use with the simulation model by the HSRI (Leff et al., 1985). However, any measure of functioning can be translated into the RAFLS for use in the model.

The simulation model weighs needs and resources not only according to system constraints but also to stakeholder recommendations. Consumers, providers, and administrators may offer unique perspectives as to the impact of reducing certain services in support of others. The model can calculate the impact of those considerations simultaneously and therefore arrive at a system-level cost-effectiveness analysis. The simulation estimates service utilization and expenditures for a comprehensive, full-capacity service system, taking into account projected service needs and outcomes.

The next section explores data inputs required for the model. When describing model inputs and outputs, we provide data collected and analyzed as part of the beta test of the model in Travis County, Texas, from October 2006 to September 2007.

Method

In June 2006, the National GAINS Center solicited communities that were planning a postbooking jail diversion program to take part in a beta test of the model. In August 2006, the Mayor’s Mental Health Taskforce Monitoring Committee submitted an application on behalf of Travis County, Texas. At the time, their key policy question was how to build affordable residential services with a jail diversion program. They were also concerned with exploring if cost savings would accrue if only people charged with misdemeanors rather than low-level felons were the target group for jail diversion.

Over the next 12 months, the GAINS Center and HSRI worked with the Travis County Cost Simulation Planning Committee to collect cost, jail admission, criminal charges, criminal history, and service utilization data. Many county agencies participated in the data collection process, notably the Sheriff’s Office, the Criminal Justice Planning Department, the Community Supervision and Corrections Department, the Criminal Court Administration, the Indigent Care Commission, and the Planning and Budget Office. The committee was chaired by a representative from Austin Travis County Mental Health Mental Retardation and a judge from the County Courts at Law. Beginning in November 2006, a 3-month sample (n = 878) of jail admissions with a “mental health flag” who were administered the Texas Recommended Assessment Guidelines (TRAG) was collected and matched with current criminal charge data.

Criminal Justice Costs and Sentencing Estimates

The next step was to determine all key criminal justice costs including police, pre-trial services, courts (including indigent defense), jail days, and probation supervision. Table 1 summarizes the average costs and provides notes that indicate a more conservative approach in estimating criminal justice costs. For example, we did not inflate the average daily jail cost by factoring in higher upfront costs of processing an admission or for housing persons with mental health issues.

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Table 1:

Criminal Justice Unit Costs

Category	Unit Cost	Notes
Police time	$95 average per arrest	Includes wage and benefits of officer only
Pre-trial Services	$5.15 average daily cost	Average time in pre-trial services is 145 days
Court costs	Felony = $1,663Misdemeanor = $702	Combination of data collected from Criminal Courts, District Attorney, County Attorney, District Clerk and County Clerk
Jail	$45 per day	Does not factor in higher upfront costs of processing an admission to the jail
Probation	Regular Supervision = $1.09 per dayMental Health Caseload = $3.72 per day	Daily cost averaged over length of probation sentence

To calculate costs, we had to determine the expected sentences for the offenses, taking into account criminal justice history and highest charge level. For the purposes of the model, we wanted to compute an average of actual jail time and probation days across different users. For low-level felonies, the average sentence was 41 days and 1,456 probation days; for high-level misdemeanors, the average sentence was 10 days and 604 probation days; and for a mid-level misdemeanor, the average sentence was 5 days and 534 probation days.

Expert Panel Service Recommendation

Service packages were built by selecting available and planned services from the given service taxonomy to be provided to consumers in each health state or functional level. Service packages were determined by the expert panel of mental health and other relevant system stakeholders. Data provided to the expert panel include current utilization for services and service prescriptions made by other panels. They were also provided information on the scientific evidence for the effectiveness of candidate services. The group specified the percentage of consumers who would receive a given service (prescription rate) and the number of units of service prescribed (prescription amount) for each functional level. Once the percentage of consumers at each functional level was assigned, a recommended monthly penetration rate per service was calculated. This rate represents the average percentage of consumers at each functional level expected to receive a given service. After a penetration rate had been assigned, a monthly average amount of service per person was given to persons in each functional level.

Recommended penetration rates multiplied by recommended amounts of service yielded average utilization amounts for each service and functional level. Taken together the recommended utilization for a functional level constitutes a service package. The recommended service utilization multiplied by the estimated unit cost yields an estimated monthly cost for each service, which sums to an estimated monthly cost for the service package for each functional level. Both the recommended penetration rate and recommended amounts of service are critical inputs into the model. This helps quantify “the diversion to what” question that has been an issue in many diversion programs.

As an example, Table 2 provides a summary of one of three simulation scenarios that the planning committee wanted to explore. One problem that has been identified in communities that do not engage in this kind of planning is overestimating the number of persons who are eligible for diversion. For example, in the first test of the model, it was estimated that approximately 40 persons per month could be diverted. However, when the detailed criterion similar to Table 2 was applied, there were less than 10 on average per month who could be diverted. The form included in Table 2 helps communities clearly articulate the charges to be included and any conditions tied to the diversion, the clinical criteria, and any other important factors. This helps avoid any ambiguity for the diverse set of stakeholders that would be responsible for implementing any agreed upon interventions.

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Table 2:

Sample Summary of Planned Jail Diversion Intervention

Diversion Alternative	Nonresidential Treatment for Defendants With Housing Stability and Co-Occurring Disorders–Scenario 2
Criminal justice status	Track 1–Misdemeanors: - Release on bond - Divert within 5 days of jail admission - Pretrial services, 6 months - Dismiss charges at 6 months Track 2–Felonies: - Condition of probation - Divert within 10 days of jail admission Consider waiving indictment as a requirement of admission Probation, 2 to 5 years
Clinical criteria	Priority population: Diagnosis of bipolar disorder, major depression, schizoaffective disorder, or schizophrenia Co-occurring substance use disorder Priority services include: - Forensic intensive case management (FICM) - Supported housing - Supported employment Counseling
Legal criteria	Eligible offense categories: Misdemeanor A, Misdemeanor B, state jail felony, Felony 3 2 or more prior arrests
Other criteria	Not homeless or does not have significant housing instability

Results

The results from the simulation model produce a variety of outputs that allow the determination of the cost to different systems over time and ensure that the appropriate community-based services are available for people who are diverted. The model results quickly allow a comparison of diverted and not diverted groups on several key variables, including costs to mental health and substance abuse systems, costs to the criminal justice agencies, jail days, and individual outcomes (i.e., functional-level improvement).

The model produces additional outputs that can be helpful in comparing the diverted and not diverted groups and/or planning a system of care for a diverted population including hospital days, emergency room use, units and costs for all services, total cost and population by month, total reimbursement (can include reimbursement rates for each service and percentage of population covered by Medicaid or other funding source), reimbursement by type of service (e.g., residential) and by individual service category (e.g., group therapy), and total costs less reimbursement (e.g., Medicaid).

The cost examples from the Travis County case study demonstrate how to interpret model outputs.

Total Costs

The outputs from the model directly compare a cohort of diverted and nondiverted individuals and compare the costs for the two groups. Figure 1 shows simulated costs at the end of Year 1 of the intervention and the costs of Year 1 and Year 2 of the program. The Year 1 chart shows that for the first year of a jail diversion program, the diverted group is more expensive. Comparing costs for Years 1 and 2 of the program, the diverted group becomes less expensive and, for the entire cohort, was over $2 million less costly than the nondiverted group. There are two main reasons for the shift. First, reduced recidivism for the diverted group results in additional criminal justice savings over time. Second, the transition rates to higher functioning states are slower for the nondiverted group as a result of less efficient, more expensive service packages and more inappropriate use of hospital and emergency services. The other diversion scenarios in Travis County and in the first test of the model (Pennsylvania General Assembly, 2007) showed similar trends; the first year was comparatively more expensive, but these costs are recouped by the end of the second year after diversion. Cost reductions typically begin accruing within approximately 14 months.

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Figure 1:

Total Costs to All Systems at Year 1 and Combined Years 1 and 2

Postbooking jail diversion, as modeled in this simulation, does not necessarily result in immediate public-level savings, but at a minimum frees funds to be used for other purposes. To determine whether there will be overall public-level system savings requires more community context. Additional cost savings opportunities include current and future public-level savings. To examine current public-level savings, the model outputs units of service (e.g., therapist hours) required for the diverted and not diverted groups. A community can use this information to determine whether the units saved will be enough to close institutions or reduce staff overtime, for example. For assessing future public-level savings, communities can make projections based on the number of jail days saved to determine if it is possible, as a result of jail diversion programming, to avoid new jail construction.

Cost by System

Figure 2 provides an example of the total cost for each group broken out by resources for mental health services in the community, criminal justice costs, and mental health services in jail. The chart illustrates the resource distribution and cost differentiation between the diverted and nondiverted groups. For the diverted group, 73% of the costs are for mental health services in the community. The criminal justice costs, which include supervision, pre-trial jail days, and costs associated with subsequent arrests, account for just over one quarter of the total costs for the diverted group.

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Figure 2.

Resource Distribution Under Different Scenarios

For the nondiverted group, the criminal justice costs are 77%. Although the nondiverted group spends more time in jail than the diverted group, members of the nondiverted group also seek out services during their time at risk in the community. Instead of receiving coordinated care, members of the nondiverted group are more likely to use expensive hospital and emergency room services. The use of expensive, uncoordinated services accounts for the proportion of total costs represented by mental health services (19%) despite limited time in the community. The nondiverted group also uses more jail mental health services as a function of more time spent incarcerated compared with the diverted group.

Discussion

There were two key findings from the simulations that produced a net savings. First, unless the people charged with the most serious misdemeanors and low-level felonies are included for diversion, there will be no cost savings since there are too few jail days avoided. This is not an inappropriate target population for jail diversion. A study by Naples and Steadman (2003) found no significant differences between divertees with violent as opposed to nonviolent target offenses. The simulations also suggest that the most significant cost savings are associated with postbooking jail diversion programs that serve individuals who have more severe clinical diagnoses and more serious criminal charges, and who spend more time in the diversion program. Second, the cost burden was shifted from the criminal justice system to the community-based service system, which is already strained for resources. However, the cost of community treatment can be shared with the federal government assuming the divertees are enrolled in Medicaid. It is likely, then, that cost shifting from the criminal justice system to community mental health services may result in early cost savings as a result of the burden of Medicaid being shared across levels of government. Given that the impacts of expanded Medicaid eligibility and financing changes on the delivery of mental health services, as a result of the Patient Protection and Affordable Care Act (Public Law 111-148), have yet to take shape, it is impossible to determine what the law’s effect will be on the cost shifting observed in this model. In general, diversion results in an overall cost shift from the criminal justice system to the mental health system, although criminal justice costs remain a sizable proportion of the total costs (Ridgely, Engberg, Greenberg, Turner, DeMartini, & Dembosky, 2007).

Regardless of cost-shifting strategies, little in the way of improved public health or safety outcomes can be achieved in the absence of community-based services. A recent report by the National Leadership Forum on Behavioral Health/Criminal Justice Services (2009) identified eight core services as an “Essential System of Care,” with four practices being the most basic (forensic intensive case management, supportive housing, peer support, and accessible and appropriate medication) and four required as a comprehensive system is developed (integrated dual disorders treatment, supported employment, assertive community treatment/forensic assertive community treatment, and cognitive behavioral interventions targeted to risk factors). The simulation model demonstrated here is but one tool to help communities most efficiently use scarce resources so that they can move toward an Essential System of Care.

One advantage of simulation is the opportunity to apply various configurations of eligibility criteria over the sample. Stakeholders can explore their options using a sample drawn from the jail, as we did in this study, or from another point in the criminal justice system (e.g., probation violators), without having to first establish the infrastructure to pilot a program. However, simulation bypasses the compromises and negotiations that stakeholders face to arrive at a set of eligibility criteria for a program. Eligibility criteria often represent a compromise among stakeholders with different agency missions, political realities, and operating standards. For example, a behavioral health service provider may only be able to serve individuals with illnesses that fall within state priority populations (i.e., schizophrenia spectrum, bipolar, and major depressive disorders). Programs supported with grant funds may be limited to individuals charged with nonviolent or misdemeanor offenses, such as the Bureau of Justice Assistance’s Justice and Mental Health Collaboration Program. Even individuals who meet the eligibility criteria may not be accepted into the program. As found by Naples, Morris, and Steadman (2007) in a study of the eligibility determination and program acceptance process in postbooking jail diversion programs, courts rejected 35% of cases recommended for diversion by program staff. Many of these negotiations and compromises took place over the course of the Travis County simulation planning process. The different sets of eligibility criteria were not agreed upon until 6 months into the project.

The study could have been bolstered by testing the model in multiple counties, drawing the Travis County sample over a longer period, or evaluating the costs of the implemented jail diversion program against the simulation’s projections. However, a cost study of a jail diversion program documented cost trajectories and cost shifting similar to the projections reported in this article (Ridgely et al., 2007), as did the first test of the model (Pennsylvania General Assembly, 2007). For this reason, we feel that while the costs may vary from place to place, the model is a useful tool for projecting the fiscal impact and resources required to implement a postbooking jail diversion program. As the model has not been tested in different criminal justice settings, such as prisoner reentry or law enforcement-based approaches, it is not possible to draw conclusions for those settings.

The model was designed to help mental health system administrators advocate for the use of jail diversion programs by providing detailed cost, service utilization, and anticipated service outcomes. The information collected for the model provides valuable insight into the ways the system works with justice-involved individuals with mental illness. Even if the actual simulations were not run, the exercise of collecting this information and thinking through the system issues has shown to be an effective planning strategy for communities anticipating the implementation of a jail diversion program. In addition, the results from the simulation allow users to justify the expense to funders and provide standards for assessing program performance to administrators and providers responsible for the implementation of the program. At the same time, users need to be prepared to have services available for divertees immediately upon release into the community.

In the future, we would like to validate the model in communities that used the planning model to test assumptions and refine inputs for future use. We would track model predictions versus actual results along a number of variables including service utilization, mental health outcome improvement, and recidivism rates. As part of the service utilization assessment we would also want to do an assessment of fidelity to any of the evidence-based practices included in the service packages.

The Mental Health/Jail Diversion Simulation Model provides a tool for communities to inform the process of planning a jail diversion program with a fiscal impact assessment. The model addresses an important public policy consideration related to diversion; specifically, whether and to what extent jail diversion achieves current and future public-level cost savings. Through the application of the model in Travis County, Texas, we confirmed the pattern of cost shifting from the criminal justice to the mental health system observed in prior studies. Moreover, the results of the simulations provide stakeholders responsible for designing jail diversion programs with insight as to how eligibility criteria affect the pool of individuals who can be intercepted and the overall fiscal impact.