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Modeling the Impact of School-Based Universal Depression Screening on Additional Service Capacity Needs: A System Dynamics Approach

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Abstract

Although it is widely known that the occurrence of depression increases over the course of adolescence, symptoms of mood disorders frequently go undetected. While schools are viable settings for conducting universal screening to systematically identify students in need of services for common health conditions, particularly those that adversely affect school performance, few school districts routinely screen their students for depression. Among the most commonly referenced barriers are concerns that the number of students identified may exceed schools’ service delivery capacities, but few studies have evaluated this concern systematically. System dynamics (SD) modeling may prove a useful approach for answering questions of this sort. The goal of the current paper is therefore to demonstrate how SD modeling can be applied to inform implementation decisions in communities. In our demonstration, we used SD modeling to estimate the additional service demand generated by universal depression screening in a typical high school. We then simulated the effects of implementing “compensatory approaches” designed to address anticipated increases in service need through (1) the allocation of additional staff time and (2) improvements in the effectiveness of mental health interventions. Results support the ability of screening to facilitate more rapid entry into services and suggest that improving the effectiveness of mental health services for students with depression via the implementation of an evidence-based treatment protocol may have a limited impact on overall recovery rates and service availability. In our example, the SD approach proved useful in informing systems’ decision-making about the adoption of a new school mental health service.

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Acknowledgments

This publication was made possible in part by funding from Grant Number K08 MH095939, awarded to the first author from the National Institute of Mental Health (NIMH). Dr. Lyon is an investigator with the Implementation Research Institute (IRI), at the George Warren Brown School of Social Work, Washington University in St. Louis; through an award from the National Institute of Mental Health (R25 MH080916) and the Department of Veterans Affairs, Health Services Research & Development Service, Quality Enhancement Research Initiative (QUERI) and grant number U54HD070725 from the Eunice Kennedy Shriver National Institute of Child Health & Human Development (NICHD), which is co-funded by the NICHD and the Office of Behavioral and Social Sciences Research (OBSSR). Dr. Pate’s work was conducted under postdoctoral fellowship support by grant number 5T32MH019545-20, awarded by the National Institute of Mental Health (NIMH) as part of a National Research Service Award Institutional Training Grant (NRSA, T32) at the Johns Hopkins Bloomberg School of Public Health.

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Appendix

Appendix

The details of the algorithm that underlies all of the SD models described in this paper are as follows:

  1. 1.

    In the beginning of the school year, the students are partitioned into three stocks (shown as three boxes at the left side of the figure) according to their mental health status.

    1. a.

      The depressed stock initially contains 139 students, according to data element a.

    2. b.

      The non-depressed use MH services stock is initialized with 142 students, according to data element b2.

    3. c.

      The do not need treatment stock is initialized with the remaining 719 students.

  2. 2.

    If there is no universal screening, then flows to the true positive stock will occur only through teacher or self-referrals. These referrals are assumed to begin after the first week and are constant throughout the remaining 35 weeks of the school year.

    1. a.

      The flow from stock b2 to the true positives stock is regulated by the valve labeled referral of others. The rate of flow is computed by dividing the 142 students in stock b2 at the beginning of the school year by the time duration of 35 weeks, yielding 4.06 students/week. (Since the SD model is mathematically represented in terms of continuous flows, flow quantities with fractions are permitted. In the results section, when we show the number of students in various queues and treatment states, we will round off to the nearest integer.)

    2. b.

      The upper double arrow between stock a and the true positives stock is for the portion of depressed students likely to use mental health services prior to introduction of the screening program, data element b1. As indicated in Table 1, there are 58 students in this category; hence the rate of flow is 58 students/35 weeks = 1.66 students/week.

  3. 3.

    If there is universal screening, then there would be additional flows to the true positive and false positive stocks. It is assumed that screening occurs during the first week and that the flows to the true positive and false positive stocks, representing referrals due to screening recommendations, occur during the second week. The rate of universal screening is set by data element c.

    1. a.

      The lower double arrow between stock a and the true positives stock is for depressed students who participate in universal screening, and are subsequently referred for mental health services according to the true positive rate. The flow rate is given by the number of students who are depressed and do not fall in category b1 (139 students in stock a minus 58 students characterized by b1) times the universal screening rate (data element c) times the true positive rate (data element d1) divided by the time duration of the flow, or (139 - 58) * 0.825 * 0.71 students/1 week = 47.4 students/week.

    2. b.

      The double arrow at the bottom of the figure between the do not need treatment and false positives stocks is for students who are not in need of mental health services and who participate in universal screening, and are subsequently referred to mental health services according to the false positive rate. The flow rate is given by the number of students who do not need treatment times the universal screening rate (data element c) times the false positive rate (data element d2) divided by the time duration of the flow, or 719 * 0.825 * 0.29 students/1 week = 172.0 students/week.

  4. 4.

    Students in the true positive and false positive stocks enter the MH assessment and initial assessment stocks when they are interviewed by the mental health service providers.

    1. a.

      The combined flow into these assessment stocks is given by the number of available interview slots that are available each week. The number of such slots is recomputed weekly, as explained in (8) below.

    2. b.

      The proportion of this flow that enter the MH assessment or initial assessment stock is set to be equal to the proportion of students in the true positive or false positive stocks.

  5. 5.

    After the students are assessed, they proceed to subsequent stocks in the system, as detailed in the following:

    1. a.

      All false positive students return to the do not need treatment stock.

    2. b.

      All students originating from stock b2 would flow from the MH assessment stock to the non-MH treatment stock.

    3. c.

      The remaining students, originating from stock a, would flow to the Level 1 treatment queue or non-MH treatment stock. The proportion of students entering the two stocks is given by data elements f1 and f2.

  6. 6.

    The students in the Level 1 treatment queue stock will flow to the Level 1 treatment stock when a slot becomes available, as determined by (8).

  7. 7.

    Students in the Level 1 treatment stock remain in this stock for 12 weeks (data element g). After 12 weeks, the students, having completed the Level 1 treatment, flow to one of the following stocks:

    1. a.

      The recovery proportion (data element h1) flows to the do not need treatment stock.

    2. b.

      The remission proportion (data element h2) flows back to the true positives stock.

    3. c.

      If evidence-based treatment is used, then the proportion in (7a) is given by data element i, and the proportion in (7b) is given by its complement.

  8. 8.

    The number of slots per week that are available for interviews and Level 1 treatment are determined as follows:

    1. a.

      The total number of slots per week is given by the number of mental health service providers multiplied by the staff capacity (data element e).

    2. b.

      Each service provider would allocate 15 % of all slots for interviews and the remaining 85 % for Level 1 treatment.

    3. c.

      Additional service personnel would allocate all of their slots for interviews.

    4. d.

      If the number of students filling interview slots is less than the total number of slots allocated for interviews, then students in the Level 1 queue can fill the unoccupied interview slots.

    5. e.

      If the number of students in the Level 1 queue is less than the number of Level 1 treatment slots, then any students waiting for interviews can fill the unoccupied Level 1 treatment slots.

The above nine-part description of the model constitutes the algorithm that completely governs the flow of students in the system shown in Fig. 1. While this algorithm could be implemented using Vensim equation models, we decided to use MATLAB (MathWorks, Natick, MA) because of its significantly faster computational speed.

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Lyon, A.R., Maras, M.A., Pate, C.M. et al. Modeling the Impact of School-Based Universal Depression Screening on Additional Service Capacity Needs: A System Dynamics Approach. Adm Policy Ment Health 43, 168–188 (2016). https://doi.org/10.1007/s10488-015-0628-y

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