Assessing the cost of managed behavioral care
Nicholas C. GEORGANTZAS, Matthew SEVER, and Frederick STELL
Management Systems ¢ GBA
Fordham University at Lincoln Center
113 West 60th Street * Suite LL617-D
New York, NY 10023-7471, USA
Abstract: Showing the important role feedback plays in managed
behavioral care is crucial because case management aggressiveness
determines the financial performance of health care programs. This study
shows how feedback affects the financial performance of a managed
mental health and substance abuse program which, not only reimburses
for treatment, but also guides the treatment plan for each patient’s case and
even determines how much treatment will be paid for.
The program is funded by a flat capitation rate received from its
members. Its expenses depend on the treatment authorized by its case
managers, who aim at authorizing the least treatment sessions while
keeping the treatment effective. In turn, the authorized treatment depends
on case management aggressiveness, which is relative to illness severity.
Our system dynamics modeling process aimed at evaluating exactly how
case management aggressiveness affects the program’s effectiveness and
efficiency.
Introduction
It is crucial for case managers to see the important role that feedback
plays in behavioral care. Given that inpatient care is more expensive than
outpatient care, intuitively, it often seems cost effective to case managers to
move patients into outpatient care as soon as possible. When inpatient care
is cut too short, however, patients that have not had enough time to
recover are re-admitted into hospitals and, consequently, the cost of
behavioral care rises despite the initial intent.
This essay describes the system dynamics simulation model built for a
managed mental health and substance abuse program. The study’s
purpose was to determine what level of case management aggressiveness
yields the best financial performance. The program under study not only
reimburses for treatment, but also guides the patient treatment plan, and
determines how much treatment will be paid for. The firm that oversees
the program receives a flat rate of income, its capitation rate, which is
based on its membership, while expenses depend on the amount of
treatment authorized for each patient's case. Together, case management
aggressiveness and the severity of illness determine how much care case
managers authorize.
The system dynamics modeling process used aimed at showing exactly
how case management aggressiveness affects the program’s cash position.
The modeling process entailed creating a set of rough-cut maps, or
influence diagrams (IDs), by analyzing the relationships among the
program’s membership, the care being authorized, and the resulting cash
flow. Throughout the modeling process, we assumed that we cannot
control directly neither the admission of patients from outpatient services
to inpatient services nor the admission of patients members to inpatient or
outpatient services. That is, when people from our membership population
become sick, then we provide them with the appropriate service. How
frequently our covered members use our services depends on their health,
but we what we can control is their length of stay in the hospital.
Our model depicts the relationships among program enrollment, case
management aggressiveness, behavioral care treatment, and cash flow.
Because case management aggressiveness affects everything else in this
program, we assess system performance by varying the aggressiveness of
managed behavioral care.
Model Description
Figure 1 shows the system dynamics simulation model resulting from
our modeling process. Although this is a rather small, four-level variable
structure, it has captured enough of the feedback loops that produce the
system’s dynamic behavior patterns. The «Membership», «Inpatient
Cases», and «Outpatient Cases» level variables, for example, are embedded
in thirteen (13), twenty-two (22), and nine (9) feedback loops, respectively.
Being a performance variable, the «Cash» stock on top of Fig. 1 entails
no feedback loops. This level variable is fed by daily revenue, which is the
product of «Membership» times the program’s flat «capitation» rate. The
«inpatient cost» and «outpatient cost» are the two outflows that deplete
Cash. The impatient cost per day is the sum of the inpatient variable cost
(Inpatient Cases x cost per day) plus the fixed overhead component of the
inpatient administrative cost or «inpatient adm cost» per day. Similarly, the
outpatient cost is the sum of the outpatient variable cost ((Outpatient Cases
/ 7) x cost per session)) per day plus the fixed overhead component of the
outpatient administrative cost or «outpatient adm cost» per day.
Fig. 1 Managed behavioral care model
inpatient cost
Cash
outpatient cost
ve)
eK
cost per day
inpatient adm cost
ie)
revenue
capitation
= fraction
cost per session
outpatient adm cost
graphic table function
enrollment f migration f
to inpatient care
n
to outpatient care
Inpatient Cases
634
admit inpatient
inpatient discharg:
admit inpatient fr
vg, inpatient care
T\O ratio
outpatient service
length of stay
case mgt
aggressiveness
readmit chance
Outpatient Cases
admit outpatient
outpatient discharge
admit outpatient fr
Figure 2 shows the model’s inpatient administrative cost (c) and
outpatient administrative cost (d) graphic table functions that contribute to
the inpatient
Fig. 2 The model's graphic table functions ( s )
(a) enrollment
120.00
102.46
84.92
67.38
49.84
32.30
0 2 4 6 8 10
perceived quality
(c) inpatient adm cost
1988
1740
1492
1244
996
0 4000 8000
Inpatient Cases
(e) outpatient service
106.0
93.8
81.6
69.4
57.2
45.0
cost and outpatient cost, respectively. The Appendix at the end of the essay
shows the model equations along with the detailed data underlying Fig. 2.
1 4 7 10
length of stay x
(1 - case mgt aggressiveness)
(b)
(d)
(f)
migration
0.0100
0.0067
0.0034
0.0001
0 3 6
©
perceived quality
outpatient adm cost
3585,
3176
2767
2358,
0 25000 50000
Outpatient Cases
readmit chance
0.700
0.514
0.328
0.142
1.0 75 14.0
avg inpatient care
The «enrollment» inflow feeds and the «migration» outflow depletes
the program’s Membership in the middle of Fig. 1. The enrollment inflow and
the migration outflow depend on the «enrollment f» and «migration f»
graphic table functions, respectively, both of which in turn depend on the
program’s «perceived quality» (computed by the same linear function the
program administrators use to assess it). Membership growth is crucial to
this mental health and substance abuse program because not only it
contributes directly to revenue, but also determines the program’s inpatient
and outpatient service utilization through Inpatient Cases and Outpatient
Cases. Among the thirteen (13) feedback loops than entail Membership,
twelve (12) run through either Inpatient Cases or Outpatient Cases or both.
The lower part of Fig. 1 shows how program members use its services.
First-stay Inpatient Cases are admitted to hospitals through the «admit
inpatient» inflow on the left, while first-time Outpatient Cases utilize the
service through the «admit outpatient» inflow on the right. How long
inpatients and outpatients use the program’s services depends on the
average «length of stay» and «outpatient service», respectively, both
measured in days.
The two outflows that deplete Inpatient Cases are: «inpatient discharge»
and «to outpatient care». The two outflows that deplete Outpatient Cases
are: «outpatient discharge» and «to inpatient care». This is where the policy
parameter «case mgt aggressiveness» comes into play. It affects both
inpatient discharge and to outpatient care outflows directly, and outpatient
discharge and to inpatient care outflows indirectly via outpatient service (Fig.
2e and Appendix).
The program’s case mgt aggressiveness reduces inpatient care either by
discharging Inpatient Cases or by transferring them to outpatient clinics. As
«avg inpatient care» declines, however, more patients get insufficient
treatment and need to be re-admitted into hospitals, thereby becoming
Inpatient Cases. This is what the «readmit chance» graph (Fig. 2f) shows.
Each case manager’s objective is to reduce the rather costly Inpatient
Cases by transforming them into Outpatient Cases. The rationale behind this
motive is that: if Inpatient Cases decline, then not only the utilization of
outpatient services will rise but, more importantly perhaps, the Cash
position of the mental health and substance abuse program will also
improve.
Inversely, by increasing avg inpatient care, the program’s case managers
expect to reduce their Outpatient Cases. Yet, when case managers increase
avg inpatient care, their outpatient utilization converges toward a minimum
value because no matter how long the inpatient treatment is, there is a
minimum of outpatient care needed.
Similarly, if case managers reduce the average length of outpatient
service (Fig. 2e), then the Inpatient Cases increase because there is an
increasing number of patients getting worse who need hospitalization.
Simulation Results
Because of its potential impact on the mental health and substance
abuse program’s financial performance, system behavior is assessed by
varying the case mgt aggressiveness policy parameter. The simulation output
time-series graphs of Fig. 3 for (a) Inpatient Cases, (b) Outpatient Cases, and
(c) Cash result from running the model from zero to ninety days, with a
computation interval dt=0.125, using the Runge-Kutta 4 integration method.
The four comparative runs of Fig. 3 show that as case mgt aggressiveness
increases from zero to 10 percent (from 0.0 to 0.1), both Inpatient Cases (a)
and Outpatient Cases (b) decrease, while the program’s Cash (c) position
improves—as the case managers expected.
Increasing case mgt aggressiveness more, however, from 10 to 20 percent
(from 0.1 to 0.2), has an inverse effect both on Inpatient Cases and on Cash.
Moreover, contrary to the case managers’ expectations, further reducing
avg inpatient care—either by discharging Inpatient Cases or by transferring
them to outpatient clinics via to outpatient care—does not improve the
program’s outpatient service utilization: Outpatient Cases continue to
decrease because there is an increasing number of patients getting worse
who need hospitalization (run #3, Fig. 3b). Impatient Cases increase more
drastically when case mgt aggressiveness reaches its 30 percent (0.3) mark
(run #4, Fig. 3a). One can also see the behavioral care system’s sensitivity to
large increases in case mgt aggressiveness in the Outpatient Cases decrease
(run #4, Fig. 3b), but this apparent sensitivity is most pronounced by the
dire-straights decrease in the program’s Cash position (run #4, Fig. 3c).
The dramatic increase in Outpatient Cases directly affects the inpatient
cost outflow that depletes Cash. And the decline in Outpatient Cases does
not seem sufficient enough to offset the large decrease in Cash. Recall the
rationale behind the case managers’ motive to increase case mgt
aggressiveness: If Inpatient Cases decline, then not only the utilization of
outpatient services will rise but also the Cash position of the mental health
and substance abuse program should improve. Their intuition works when
they increase case mgt aggressiveness from zero to 10 percent. Indeed, the
I\O ratio of Fig. 4a reaches its lowest threshold value at the 0.1 mark of case
met aggressiveness, where the program’s Cash position is maximized (run
#2, Fig. 3c and Fig. 4b), because the decrease in revenue caused by the
decrease in Membership growth (run #2, Fig. 4c) is more than offset by the
decrease in the inpatient cost outflow, which depletes Cash. The case
managers’ intuition breaks off, however, when they increase case mgt
aggressiveness to 30 percent.
Fig. 3 Simulation output time-series graphs
(a).
88.00 7
eee
et 1
Inpatient Cases 4 L ie al
P _ pee * case mgt
“a ee Run aggressiveness
44.00 4 LF 1 0.0
Oo 2 0.1
a 3 02
va 4 03
i:
0.00 r T T +—Days
0.00 18.00 36.00 54.00 72.00 90.00
(b). 2200.00. 4 5
13
of
1g
Outpatient Cases .4 Pe
2p et case mgt
ov" Run aggressiveness
4 _
1125.00. 4 wr 1 0.0
ic 2 01
/ 3 02
4 03.
50.00 T T T +—Days —,
18.00, 36.00 54.00 72.00, 90.00
c). 820000.00 -
(c) > a
~
4: SS
on 4.
Cash 4 1 LS
case mgt M4 WN
410000.00 Run aggressiveness
1 0.0
2 01
3 0.2
4 03 rn
0.00 t Days
0.00 18.00 36.00 54.00 72.00 90.00
Fig. 4 Simulation output phase graphs
(a) 007 4
1\O ratio
(Inpatient
to
Outpatient |
ratio)
0.05 | | | |
case mgt
0.03 T T T T , aggressiveness
(b) 820000.00 J
case mgt
Run aggressiveness
Cash |
0.0
01
0.2
410000.00 4 03
0.00 r r r r 5 NO ae
0.03 0.05 0.06
(c) 820000.00
case mgt
Run aggressiveness
Cash 4 a —
> 1 0.0
\ 2 0.1
13 02
410000.00 nl
Vo
ooo 4 | . , , , Membership
100000 104000 108000
At the 0.3 mark of case mgt aggressiveness (Fig. 4a), the I\O ratio shows a
high threshold limit, causing Cash to dive sharply (run #4, Fig. 4b) because
of the outpatient cost increase, coupled with a sharp decrease in Membership
growth (run #4, Fig. 4c). As case mgt aggressiveness increases, avg inpatient
care decreases. Outpatient Cases increase temporarily but, since more
patients are now getting worse and need hospitalization, the readmit chance
also increases, causing not only more Outpatient Cases to move to outpatient
care, but also perceived quality to decline. The decrease in perceived quality
causes Membership growth to decrease sharply because its enrollment inflow
decreases, while its migration out flow increases (middle of Fig. 1).
Conclusion
Indeed, it is crucial for case managers to see the important role that
feedback loops play in this mental health and substance abuse program.
The system dynamics modeling process we employed aimed at evaluating
exactly how case met aggressiveness affects the program’s effectiveness and
efficiency. The simulation results show that for small values of the case mgt
aggressiveness policy parameter (up to 0.1), the case managers’ intuition
becomes justified by the increase in the program’s Cash. Case managers
succeed in authorizing the least treatment while keeping the treatment
effective. Above the 10 percent case mgt aggressiveness mark (0.1), however,
the case managers’ intuition breaks off. Because more patients get worse
and need re-hospitalization when case mgt aggressiveness reaches values of
0.2 and 0.3, not only Inpatient Cases increase—thereby causing Cash to
decrease—but, more importantly perhaps, the program’s Membership
growth also declines. Therefore, managed care is recommended, but only
in small dosage.
Appendix: Model Equations
Level Variables
Cash(t) = Cash(t - dt) + (revenue - outpatient_cost - inpatient_cost) * dt
INIT Cash = Membership * capitation {$}
Membership(t) = Membership(t - dt) + (enrollment - migration) * dt
INIT Membership = 100000 {people}
Inpatient_Cases(t) = Inpatient_Cases(t - dt) + (admit_inpatient + to_inpatient_care -
to_outpatient_care - inpatient_discharge) * dt
INIT Inpatient_Cases = Membership * admit_inpatient_fr {people}
Outpatient_Cases(t) = Outpatient_Cases(t - dt) + (to_outpatient_care +
admit_outpatient - to_inpatient_care - outpatient_discharge) * dt
INIT Outpatient_Cases = Membership * admit_outpatient_fr {people}
Rate Variables
admit_inpatient = admit_inpatient_fr * Membership + readmit_chance *
inpatient_discharge {people per day}
admit_outpatient = admit_outpatient_fr * Membership {people per day}
enrollment = enrollment_f {people per day}
inpatient_cost = (Inpatient_Cases * cost_per_day) + inpatient_adm_cost {$ per day}
inpatient_discharge = Inpatient_Cases / (length_of_stay * (1 -
case_mgt_aggressiveness))
migration = migration_f * Membership {people per day}
outpatient_cost = ((Outpatient_Cases / 7) * cost_per_session) + outpatient_adm_cost {$
per day; the division of Membership by seven (7) here reflects the program's extant
policy to authorize only one (1) outpatient session per patient per week (7 days)}
outpatient_discharge = (Outpatient_Cases) / outpatient_service
revenue = capitation * Membership {$ per member per day}
to_inpatient_care = readmit_chance * Outpatient_Cases / outpatient_service {people
per day}
to_outpatient_care = Inpatient_Cases / (length_of_stay * (1 - case_mgt_aggressiveness))
{people per day}
Auxiliary Variables
avg_inpatient_care = ((Inpatient_Cases / to_outpatient_care) + (Inpatient_Cases /
inpatient_discharge)) / 2 {days}
I\O_ratio = Inpatient_Cases / Outpatient_Cases {dimensionless}
length_of_stay = NORMAL(14, 0, 123) {days (6 =0 for smooth simulation output)}
perceived_quality = 10 - (10 * (readmit_chance - 0.142) / 0.7) {dimensionless}
Constant Parameters
admit_inpatient_fr = 1 / 30000
admit_outpatient_fr = 16 / 30000
capitation = 15/30 {$ per person per day}
case_mgt_aggressiveness = 0 {dimensionless}
cost_per_day = 550 {$ per person per day}
cost_per_session = 75 {$ per person per day}
Graphic Table Functions
enrollment_f = GRAPH(perceived_quality)
(0.00, 32.3), (1.00, 52.0), (2.00, 62.9), (3.00, 70.5), (4.00, 75.0), (5.00, 77.3), (6.00, 79.1),
(7.00, 82.7), (8.00, 90.8), (9.00, 107), (10.0, 120)
inpatient_adm_cost = GRAPH(Inpatient_Cases)
(0.00, 996), (800, 996), (1600, 1244), (2400, 1244), (3200, 1492), (4000, 1492), (4800,
1740), (5600, 1740), (6400, 1988), (7200, 1988), (8000, 1988)
migration_f = GRAPH(perceived_quality)
(0.00, 0.01), (1.00, 0.0091), (2.00, 0.0075), (3.00, 0.00515), (4.00, 0.0035), (5.00, 0.0025),
(6.00, 0.00175), (7.00, 0.0012), (8.00, 0.00075), (9.00, 0.00035), (10.0, 0.0001)
outpatient_adm_cost = GRAPH(Outpatient_Cases)
(0.00, 2358), (5000, 2658), (10000, 2658), (15000, 2985), (20000, 2985), (25000, 2985),
(30000, 3285), (35000, 3285), (40000, 3285), (45000, 3585), (50000, 3585)
outpatient_service = GRAPH(length_of_stay * (1 - case_mgt_aggressiveness))
(1.00, 106), (2.50, 90.1), (4.00, 76.8), (5.50, 66.0), (7.00, 56.3), (8.50, 50.0), (10.0, 45.0)
readmit_chance = GRAPH(avg_inpatient_care)
(1.00, 0.7), (2.30, 0.69), (3.60, 0.682), (4.90, 0.658), (6.20, 0.604), (7.50, 0.521), (8.80,
0.367), (10.1, 0.245), (11.4, 0.189), (12.7, 0.159), (14.0, 0.142)
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