Dynamic Simulation of Opioid Misuse Outcomes
Alexandra Nielsen and Wayne Wakeland
Systems Science Graduate Program, Portland State University, 1604 S.W. 10
th
Av., Portland, OR 97201, U.S.A.
Keywords: Prescription Drug Abuse, System Dynamics Modelling, Opioid Analgesics.
Abstract: The objective of the study was to develop a system dynamics model of the medical use of pharmaceutical
opioids, and the associated diversion and nonmedical use of these drugs. The model was used to test the
impact of simulated interventions in this complex system. The study relied on secondary data obtained from
the literature and from other public sources for the period 1995 to 2008. In addition, an expert panel
provided recommendations regarding model parameters and model structure. The behaviour of the resulting
systems-level model compared favourably with reference behaviour data (R
2
=.95). After the base model
was tested, logic to simulate interventions was added and the impact on overdose deaths was evaluated over
a seven-year period, 2008-2015. Principal findings were that the introduction of a tamper resistant
formulation unexpectedly increased total overdose deaths. This was due to increased prescribing which
counteracted the drop in the death rate. We conclude that it is important to choose metrics carefully, and
that the system dynamics modelling approach can help to evaluate interventions intended to ameliorate the
adverse outcomes in the complex system associated with treating pain via opioids.
1 INTRODUCTION
A dramatic rise in the nonmedical use of
pharmaceutical opioid pain medicine has presented
the United States with a substantial public health
problem (Compton and Volkow, 2006). Despite the
increasing prevalence of negative outcomes, such as
nonfatal and fatal overdoses, nonmedical use of
pharmaceutical opioids remains largely unabated by
current policies and regulations (see Fishman et al.,
2004). Resistance to policy interventions likely
stems from the complexity of medical and
nonmedical use of pharmaceutical opioids, as
evidenced by the confluence of the many factors that
play a role in medical treatment, diversion, and
abuse of these products in the United States.
Complex social systems are well known to resist
to policy interventions, often resulting in unintended
consequences or unanticipated sources of impedance
(Sterman, 2000). These undesirable outcomes can
result from our inability to simultaneously consider
a large number of interconnected variables,
feedback mechanisms, and complex chains of
causation (Hogarth, 1987). Prescription opioid use,
diversion, and nonmedical use constitute a complex
system with many interconnected components,
including prescribers, pharmacists, persons
obtaining opioids from prescribers for medical use,
persons obtaining drugs from illicit sources, and
people giving away or selling drugs. Interactions
among these actors result in chains of causal
relationships and feedback loops in the system. For
example, prescribing behaviours affect patients’
utilization of opioids; adverse consequences of
medical and nonmedical use influence physicians’
perceptions of the risks associated with prescribing
opioids; and physicians’ perception of risk affects
subsequent prescribing behaviours (Potter et al.,
2001); (Joranson et al., 2002).
This paper presents a system dynamics model
which simulates the system described above. The
model is designed to provide a more complete
understanding of how medical use, nonmedical use,
and trafficking are interrelated, and to identify
points of high leverage for policy interventions to
reduce the adverse consequences associated with the
epidemic of nonmedical use. An intervention
corresponding to the introduction of relatively less-
abusable, tamper-resistant formulation is simulated,
and possible downstream effects are highlighted.
397
Nielsen A. and Wakeland W..
Dynamic Simulation of Opioid Misuse Outcomes.
DOI: 10.5220/0004062103970408
In Proceedings of the 2nd International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH-2012),
pages 397-408
ISBN: 978-989-8565-20-4
Copyright
c
2012 SCITEPRESS (Science and Technology Publications, Lda.)
2 BACKGROUND
Between 1999 and 2006, the number of U. S.
overdose deaths attributed to opioids tripled–
increasing more than five-fold among youth aged 15
to 24 (Warner et al., 2009)–signalling the onset of a
major public health concern. Overdose deaths
involving opioid analgesics have outnumbered
cocaine and heroin overdoses since 2001 (CDC,
2010), and estimates from the 2009 National Survey
on Drug Use and Health (NSDUH) suggest that 5.3
million individuals (2.1% of the U.S. population
aged 12 and older) used opioids for nonmedical
purposes within the previous month (SAMHSA,
2010). Earlier data from NSDUH suggest that the
rate of initiating nonmedical usage increased
drastically from 1994 to 1999 (SAMHSA, 2006),
and has continued at high rates, with over 2 million
individuals reporting the initiation of nonmedical
use of pain relievers in 2009 (SAMHSA, 2010).
Recent increases in prescribing opioids stem in part
from increases in chronic pain diagnosis and the
development of highly effective long-acting
pharmaceutical opioid analgesics.
One problem that arose with these new long-
acting formulations was the ease with which they
could be tampered with to enhance the effects when
used non-medically.
Policymakers striving to ameliorate the adverse
outcomes associated with opioids could benefit from
a systems-level model that reflects the complexity of
the system and incorporates the full range of
available data. Such a model could be used to study
the possible effectiveness of a tamper resistant drug.
3 SYSTEM DYNAMICS
SIMULATION MODEL
The current work features a system dynamics
simulation model that represents the fundamental
dynamics of opioids as they are prescribed,
trafficked, used medically and nonmedically, and
involved in overdose mortality. The model was
developed over a two-year period through
collaborative efforts of a modelling team and a panel
of pain care and policy experts. The SD modelling
approach uses a set of differential equations to
simulate system behaviour over time. SD models are
well suited to health policy analyses involving
complex chains of influence and feedback loops that
are beyond the capabilities of statistical models
(Sterman, 2006), and have been successfully applied
to the evaluation of policy alternatives for a variety
of public health problems (Cavana and Tobias,
2008; Homer, 1993; Jones et al., 2006; Milstein,
Homer, & Hirsch, 2010). The SD approach can help
identify points of high leverage for interventions, as
well as possible unanticipated negative
consequences of those interventions. This provides
policymakers with information that is not available
from research focused on individual aspects of a
system (Sterman, 2006).
Model development began with a thorough
literature review to locate empirical evidence to
support key model parameters. Literature sources
included a broad spectrum of data sources, survey
results, and scholarly articles covering data collect
between 1995 and 2009. Multiple data gaps were
identified that could not be adequately addressed by
existing literature (see Wakeland et al., 2010).
Expert panel members provided expert judgment to
help fill these data gaps.
The model was developed iteratively, starting
with a brainstorming session that included both
subject matter experts (SMEs) and computer
simulation team members. The system boundary for
the initial sketch model describing the various stocks
and flows was very broad and included populations
of people receiving opioid analgesics to treat pain,
people using these prescription drugs nonmedically,
people using illicit drugs, plus the overall demand
and supply for various drugs. The simulation team
then refined the diagram, searched for parameter
data, and specified possible equations. Model scope
was reduced and the model was simplified due to the
lack of data and requisite knowledge. The data and
model were reviewed again by the SMEs, and the
simulation team further refined the model and
sought additional data based on the SME feedback.
This process was repeated multiple times.
The model encompasses the dynamics of the
medical treatment of pain with opioids, the initiation
and prevalence of nonmedical usage; the diversion
of pharmaceutical opioids from medical to
nonmedical usage; and adverse outcomes such as
overdose fatalities. Discussion of each sector
includes a description of empirical support, a
narrative on model behaviour, and a causal loop
diagram showing model structure. Bracketed
numbers in the text correspond to specific points in
the diagrams. The model contains 40 parameters, 41
auxiliary variables, and 7 state variables, as well as
their associated equations and graphical functions.
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Figure 1: Causal loop diagram of the nonmedical use sector. Circled numbers correspond to bracketed notations in the text.
Numbers in boxes correspond to model parameters in the Appendix, Table 1.
Figure 2: Causal loop diagram of the medical use sector. Circled numbers correspond to bracketed notations in the text.
Numbers in boxes correspond to model parameters in the Appendix, table 2.
DynamicSimulationofOpioidMisuseOutcomes
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3.1 Nonmedical Use Sector
12%-14% of individuals who use opioids
nonmedically meet the criteria for opioid abuse or
dependence (Colliver et al., 2006), either of which is
associated with a high frequency of nonmedical use.
Extrapolation from heroin findings indicates that
higher frequency opioid use is associated with a
significantly higher mortality rate (WHO; see
Degenhardt et al., 2004); (Hser et al., 2001) and
supports a distinction between two subpopulations
of nonmedical users (low- and high-frequency) in
this model sector.
As illustrated in Figure 1 (with supporting data in
the Appendix, Table 1), a percentage of the US
population {1} is assumed to initiate nonmedical use
each year {2}, all of whom start out in a stock of
‘low-frequency nonmedical users,’ and a small
percentage of whom advance to a stock of ‘high-
frequency nonmedical users’ {3} during each
subsequent year. The total number of individuals
using opioids nonmedically {4} is divided by the
current number of individuals in the US who are
using other drugs nonmedically {5} to calculate the
relative popularity of opioids for nonmedical use
{6}. As the popularity of using opioids
nonmedically increases, the rate of initiation
increases, creating a positive feedback loop that
ceteris paribus would result in an exponential
increase in the rate of initiation.
Nonmedically used opioids are obtained through
many routes, but of key interest for the current
research is opioid ‘trafficking’ (i.e., buying or
selling) via persons who are receiving these products
ostensibly for treatment. Extrapolation of results
from the 2006 NSDUH survey (SAMHSA, 2007)
suggests around 25% of the nonmedical demand for
opioids is met via trafficking.
In the model, demand for opioids is calculated
from the number of individuals in low- and high-
frequency populations {7}. As noted above, 25% of
demand is assumed to be met by trafficking {8},
with the rest coming from sources not modelled
explicitly (mostly interpersonal sharing among
friends and relatives, per SAMHSA, 2007). When
the trafficking supply is ample relative to demand,
the rate of initiation {2} and the rate of advancement
from low-frequency to high-frequency use {3} are
assumed to be somewhat enhanced. When the
trafficking supply is limited, however, rates of
initiation and advancement are assumed to decrease
dramatically. The ratio of supply to demand {9}
indicates the degree to which opioids are accessible
for nonmedical use. As the populations of
nonmedical users increase beyond what trafficking
can support, accessibility becomes limited,
decreasing initiation and advancement. This creates
a negative feedback loop that eventually equilibrates
the otherwise exponential increase in nonmedical
use driven by the popularity feedback loop.
3.2 Medical Use Sector
Increases in opioid abuse and addiction have led to
regulatory policies which have lead many physicians
to avoid prescribing opioids to patients out of fear of
overzealous regulatory scrutiny (Joranson et al.,
2002). Or, they may decrease the amount of opioids
they prescribe, and shift their prescribing towards
short-acting opioid products because long-acting
opioids have been shown to have a higher rate of
abuse than immediate-release opioid analgesics
when abuse rates are normalized for the number of
individuals exposed (Cicero, Surratt, Inciardi, &
Munoz, 2007). Thus, physicians exhibit more
caution in prescribing long-acting opioids (Potter et
al., 2001).
As illustrated in Figure 2, the system model
assumes that a proportion of the US population is
diagnosed with a chronic pain condition each year
{1}. A fraction of these people are subsequently
treated with either short-acting {2} or long-acting
{3} opioid formulations, and become members of
one of the stocks (populations) of patients under
opioid treatment ostensibly for chronic pain. Patients
who begin treatment with short-acting formulations
may cease treatment if their condition improves, or
they may switch to long-acting formulations if their
pain conditions appear to worsen {4}.
Each year some individuals move from the
stocks of ‘individuals receiving opioids’ {2-3} to the
stocks of ‘individuals receiving opioids with abuse
or addiction’ {5-6}. The fraction of opioid-
prescribed individuals with abuse or addiction {7}
influences physicians’ perception of the risk
involved in opioid prescribing {8}, as does the total
number of overdose deaths among medical users
each year {9}. As physicians perceive higher levels
of risk {8} they become increasingly biased toward
prescribing short-acting formulations {10}, and their
overall rates of opioid prescribing decrease {11}.
Because of these balancing feedback loops, the
increase in the amount of abuse and addiction {7} is
slowed. Physicians’ responses to increasing rates of
abuse, addiction, and overdose effectively move the
model towards a state of dynamic equilibrium.
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Figure 3: Causal loop diagram of the trafficking sector. Circled numbers correspond to bracketed notations in the text.
Numbers in boxes correspond to the model parameters in the Appendix, Table 3.
3.3 Trafficking Sector
Findings from Manchikanti et al. (2006) indicate
that 5% of chronic pain patients engage in doctor
shopping and around 4% engage in forgery. In the
model, forgery and doctor shopping by persons
interacting with prescribers are assumed to be
exhibited entirely by those with abuse or addiction,
which constitute around 7% of individuals receiving
opioid prescriptions for chronic pain. This would
imply that about 70% of persons with abuse or
addiction (5 out of 7) engage in doctor shopping and
over half (4 out of 7) engage in forgery. More
research is needed to support these parameters and
the associated logic.
As shown in Figure 3, a fixed fraction of persons
with abuse or addiction are assumed to engage in
trafficking each year, including doctor shopping {1}
and forgery {2}. The number of extra prescriptions
acquired {3} is calculated as a product of (a) the
total number of individuals engaging in trafficking
and (b) the number of extra prescriptions obtained
per trafficker {11}. Some proportion of these excess
prescriptions is assumed to be used by the traffickers
themselves, rather than diverted to other nonmedical
users {4}. This number is calculated as a product of
(a) the number of individuals with abuse or
addiction and (b) the average number of extra
prescriptions used per year by such individuals. The
number of prescriptions that are used “in excess” by
medical users is subtracted from the number of extra
prescriptions acquired. The remainder is converted
to dosage units {5} and assumed to be diverted to
nonmedical users {6}.
Trafficked opioids accumulate in a stock of
dosage units {7} that are consumed according to
DynamicSimulationofOpioidMisuseOutcomes
401
demand from the nonmedical use sector. Supply can
also be expressed as ‘months of supply available’
{8}, which indicates the extent to which the
trafficked supply is able to meet the demand at any
given time. When the supply of opioids becomes
limited, a profit motive emerges {9} and motivation
to forge and doctor shop increases. When supply is
large compared to demand, motivation to commit
fraud for the purpose of sale is small. As this
motivation fluctuates, the number of extra
prescriptions each trafficker would like to obtain
{10} also changes. But the number of prescriptions
that can be successfully trafficked is attenuated by
cautious dispensing when perceived risk is high
among physicians and pharmacies {11}, which
creates a balancing feedback loop that stabilizes the
amount of trafficking.
4 MODEL TESTING
The model was tested in detail to determine its
robustness and to gain an overall sense of its
validity. As is often the case with system dynamics
models, the empirical support for some of the
parameters was limited, as indicated in Tables 1-3 in
the Appendix. System Dynamics models are
generally more credible when their behaviour is not
overly sensitive to changes in the parameters that
have limited empirical support. Therefore, to
determine sensitivity of primary outcomes to
changes in parameter values, each parameter in turn
was increased by 30% and then decreased by 30%,
and the outcome was recorded in terms of
cumulative overdose deaths. One parameter with
limited empirical support which has a substantial
influence on model behaviour is the impact of
limited accessibility on the initiation rate. Another
parameter, the rate of initiation of nonmedical use,
also strongly influenced model behaviour but is less
worrisome because it does have sufficient empirical
support. Because model testing revealed a high
degree of sensitivity to certain parameters for which
empirical support is limited, study results should be
considered exploratory and viewed with caution.
In addition to sensitivity analyses, the model was
also carefully checked for dimensional consistency
and appropriate integration step-size, subjected to a
rigorous model walk through to uncover logical
flaws, and subjected to a variety of hypothesis tests.
The model walk-through revealed logical flaws that
required substantial model revision. Several
parameters with a high degree of sensitivity and
limited empirical support were replaced, and all tests
were re-run. The results of these tests were generally
favourable, indicating at least a preliminary degree
of model validity.
(a) Total overdose deaths (persons/yr.)
(b) Total nonmedical users (persons)
(c) Total new initiates (persons/yr.)
Figure 4: Model output versus reference behaviour. (a)
total prescription opioid overdose deaths per year, (b) total
nonmedical users of prescription opioids, (c) total number
of individuals initiating nonmedical opioid use per year.
When empirical support was available, model
outputs were validated against reference data for the
historical period. While this reference period is
relatively short, the model does fit the data well, as
shown in Figure 4.
Figure 4a shows the number of prescription
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opioid overdose deaths from a baseline model run
for the historical period overlaid on a plot of the
reported number of overdose deaths obtained from
the CDC multiple cause of death database.
The total opioid-related deaths resulting from all
types of medical and nonmedical use has been
reported to be 13,755 in 2006 and approximately
14,000 in 2007. The data suggest that the pattern
has been an S-shaped, with modest growth in the
late 90s and more rapid growth throughout the early
2000s before levelling off between 2006 and 2007
(Warner, Chen & Makuc, 2009). The baseline model
behaviour, also shown in Figure 4a, shows a similar
S-shaped growth curve, with the number of opioid
overdose deaths calculated to be approximately
13,200 in 2006 and 14,300 in 2007 (R
2
= .90).
While additional data are needed to validate these
results, the model behaviour does exhibit a
preliminary level of credibility for this metric.
Figure 4b shows the total number of individuals
using prescription opioids non-medically overlaid on
reference data for the historical time period. The
graph of historical data is not smooth, but again, the
general pattern of growth is S-shaped. The graphical
output from a baseline model run is a smooth S-
shaped curve that is a good fit for the limited time
series data available (R
2
= .95).
Figure 4c gives model output and reference data
for the number of individuals initiating nonmedical
use of prescription opioids. The reference behaviour
pattern here is highly non-linear with the number of
initiates more than doubling from 1995 to 2000, then
approximately no change between 2000 and 2004,
followed by a decrease and levelling from 2004 to
2007. The baseline model run matches the reference
behaviour pattern very closely (R
2
=.95).
Overall, model results closely track the complex
patterns graphs of empirical data despite exhibited.
Thus, baseline results were deemed sufficiently
plausible to proceed with intervention analysis.
5 RESULTS
To test the intervention, the model time horizon was
extended to 2015 and a baseline run was made. The
intervention was then formulated and tested.
5.1 Tamper Resistant Formulation
Logic representing the introduction of a tamper
resistant drug formulation was added to the model.
The model was run over a time period of twenty
years, which was divided into an historical period
from 1995 to 2008, and an evaluation period from
2008 to 2015. The intervention was represented as
simple toggle switch that doubled beneficial
parameters and/or halved harmful parameters. The
response of the model to this simulated intervention
is shown in Figure 5. This intervention of a new
drug formulation being introduced in 2008 was
implemented as a 50% decrease in: 1) the rate of
abuse or addiction among opioid-treated persons, 2)
the fraction of low-frequency nonmedical opioid
users who become high-frequency users per year, 3)
the rate of initiation of nonmedical opioid use, and
4) the perceived risk of opioid abuse amongst
prescribers (this increased the prescribing rates for
all opioids). Figure 5 shows that this change caused
an increase in the total number of overdose deaths
in the model, due to a sizable increase in deaths
among medical users and a small decrease in deaths
among nonmedical users. This was not expected.
Figure 6 explains why this happened. Subplot (a)
shows that the number of individuals receiving
treatment increased sharply, and this increase, even
when coupled with lower death rates, led to the net
increase in the total number of overdose deaths
compared to baseline (Figure 5). Figure 6, subplot
(b) shows the number of deaths divided by number
of individuals receiving opioid treatment (and then
divided by 10,000 to yield an indicator in the 0 to 10
range). This indicator, which was beginning to
increase as of 2008, declined as a result of the
intervention, especially in the nonmedical sector. So,
although the fraction of deaths among patients did
decrease as anticipated, the rise in patient
populations (due to the lower risk perception
associated with tamper resistant formulations
amongst prescribers) obscured the benefits of the
lower death fraction.
Figure 5: Projected total opioid deaths (top), nonmedical
(middle), and medical (bottom). Baseline is shown, plus
the impact of a tamper-resistant formulation introduced in
2008.
DynamicSimulationofOpioidMisuseOutcomes
403
(a) Total Number of Patients Receiving Opioid Therapy
(b) Deaths per 10,000 Patients, Medical, Nonmedical
Figure 6: A dramatic increase in (a) the number of patients
who receive opioids results in a smaller ratio (b) of the
overdose deaths divided by the number of patients
receiving opioid therapy/10000.
6 DISCUSSION
Results from the model indicate that SD modelling
holds promise as a tool for understanding the
complex challenges associated with the epidemic of
nonmedical use of opioids, and for evaluating the
potential impact (on overdose deaths) of
interventions to minimize the risks of opioid
analgesics. By deliberately exaggerating the direct
effects, downstream effects were also accentuated to
make as obvious as possible any unintended
consequences or counterintuitive results.
Since previous research has indicated that over
half of opioid overdose deaths are individuals who
have never been prescribed opioids directly (Hall et
al., 2008), it is important to consider distal effects of
medical sector-related interventions on nonmedical
use and overdose deaths. Results of the intervention
that simulated the introduction of tamper-resistant
formulations also show that it is important to be
aware of the metrics used to judge effectiveness.
When using the metric deaths per 10,000 treated
patients, tamper resistance appears to be effective at
reducing the rate of overdose deaths as proportion of
the medical users.
6.1 Limitations
Tamper resistance is only one possible intervention
in the system of opioid misuse. Other interventions
not referenced in this article include prescriber and
patient education interventions which affect
prescribing behavior and the onset of addiction
among patients, a prescription monitoring program,
which reduces fraud and nonmedical supply, and a
popularity intervention which disrupts the vicious
cycle of initiation, nonmedical use, and peer
pressure that drives up nonmedical use of opioids.
Tamper resistance is a pharmaceutical intervention,
and as such does not take into account the social
forces that influence health behavior or drug use.
Despite great efforts to find empirical support for
all model parameters, parameter validity remains a
primary limitation in the study (see Wakeland, et al.
2010). Several parameters have weak empirical
support, and a number of potentially important
factors have been excluded. For example, the model
is limited because it focuses on chronic pain, and
ignores the vastly-larger number of persons who
receive opioids to treat acute pain. The prescribing
of opioids to treat acute pain accounts for a much
larger fraction of the opioids dispensed annually, so
it is likely to contribute the supply of opioids for the
nonmedical use sector, as well as to physician’s
perception of risk in the medical use sector.
The model may also be exaggerating the notion
of profit as a motive for trafficking. Since the
fraction of demand met by interpersonal sharing is
large, it may be necessary to model this mechanism
in a more detailed fashion.
Additionally, poly-drug use and abuse, opioid
treatment programs, alternative treatments, and
institutional factors that impact opioid use, such as
payer policies and formularies, can all influence
rates of medical and nonmedical use of opioids and
the outcomes associated with such use. The
exclusion of these factors imposes limitations on the
model’s ability to provide conclusive inferences.
7 CONCLUSIONS
The principal strength of this study is its system-
level perspective and deliberate recognition of the
complex interconnections and feedback loops
associated with the use of opioids to treat pain and
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the associated adverse outcomes. From a systems
perspective it is clear that interventions focused on
prescribing behaviour can have implications beyond
the medical aspects of the system, and that a
multifaceted approach which also addresses illicit
use is warranted. The present study serves well to
demonstrate how a systems-level model may help to
evaluate the relative potential efficacy of
interventions to reduce opioid-related overdose
deaths.
ACKNOWLEDGEMENTS
Funding was provided by Purdue Pharma L.P., and
NIDA grant number 1R21DA031361-01A1. The
authors also gratefully acknowledge support from J.
David Haddox, John Fitzgerald, Jack Homer, Lewis
Lee, Louis Macovsky, Dennis McCarty, Lynn R.
Webster, and Aaron Gilson.
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APPENDIX
Table 1: References of support for model parameters in the nonmedical use sector.
Parameter Value Support
1 Base Level of Abuse Potential of Opioids 1.3 Panel Consensus
2 Fraction of Demand Met from Chronic Pain Trafficking .25 Extrapolation from NSDUH (SAMHSA, 2007)
3 Fraction of Low-Freq Users who switch to High-Freq 0.06
Extrapolated from MTF data (Johnston et al.,
2007) and results (Mack et al., 2003)
4 High-Frequency User All-Cause Mortality Rate 0.02
Extrapolated from heroin research findings (WHO;
Degenhard et al., 2004; Hser et al., 2001)
5 High-Frequency User Cessation Rate 0.08 Imputation from NSDUH SAMHSA 2009b)
6 Low-Frequency User All-Cause Mortality Rate 0.012 Extrapolated from (Rehm et al., 2005)
7 Low-Frequency User Cessation Rate 0.15 Imputation from NSDUH data (SAMHSA 2009b)
8
Number of Days of Nonmedical Use Among High-Freq
Users
220
Extrapolation from NSDUH 2007 results (Lee et
al., 2010)
9 Nbr. of Days of Nonmedical Use Among Low-Freq Users 30 Extrapolated from NSDUH 2007 (Lee et al., 2010)
10 Number of Dosage Units Taken per Day 2 Modeling Team Judgment, reviewed by Panel
11
Overdose Mortality Rate for High-Freq Nonmedical
Users
0.002
Extrapolated from Fisher et al., 2004; Warner et
al., 2009; Warner-Smith et al., 2000
12
Overdose Mortality Rate for Low-Freq Nonmedical
Users
0.0002
Extrapolated from Fisher et al., 2004; Warner et
al., 2009; Warner-Smith et al., 2000
13 Rate of Initiation of Nonmedical Opioid Use 0.006 Imputed from NDUHS (SAMHSA, 1996)
14
Table Function for the Impact of Limited Accessibility
on Initiation and Increasing Use
[(0,0)-(5,2)] Modeling Team Judgment, reviewed by Panel
15
Table Function for the Number of Individuals Using
Illicit Drugs Excluding Marijuana and Opioids
6.7M to 8.6M
Calculated from NSDUH 2006 results (SAMHSA,
2007)
16 US Population Ages 12 and Older 211M to 357M Imputed from NSDUH (SAMHSA, 1996, 2002)
Table 2: References of support for model parameters in the medical sector.
Parameter Value Support
1
All-Cause Mortality Rate for those receiving Long-
acting Opioids
0.012
US Population mortality data, adjusted by panel
consensus
2
All-Cause Mortality Rate for those receiving Short-
acting Opioids
0.01
US Population mortality data, adjusted by panel
consensus
3
All-Cause Mortality Rate for those with
Abuse/Addiction
0.015
US Population mortality data, adjusted by panel
consensus
4 Average Long-acting Treatment Duration 7 yrs. Panel Consensus
5 Average Short-acting Treatment Duration 5 yrs. Panel Consensus
6 Base Level of Abuse Potential for Opioids 1.3 Modeling Team Judgment, reviewed by Panel
7 Base Rate for Adding or Switching (to Long-acting) 0.03
Extrapolation from outcome data: Verispan, LLC,
SDI Vector One®: National (Governale, 2008a)
8 Base Rate of Treatment .05 to .23 Panel Consensus, informed by Potter et al., 2001
9
Base Risk Factor (degree Tx reduced in 1995 due to
perceived risk)
1.3 Modeling Team Judgment, reviewed by panel
10 Diagnosis Rate for Chronic Pain .05 to .15 Panel Consensus & Gureje et al., 2001
11 Overdose Mortality Rate if Abusing Opioids 0.0015 Extrapolation from Heroin data (Sullivan, 2007)
12 Overdose Mortality Rate if on Long-acting 0.0025 CONSORT study (Potter et al., 2001)
13 Overdose Mortality Rate if on Short-acting 0.00005 CONSORT study (Potter et al., 2001)
14 Rate of Addiction for those on Long-acting 0.05
Meta-Analyses (Dunn et al., 2010; Højsted &
Sjøgren, 2007)
15 Rate of Addiction for those on Short-acting 0.02 VISN16 data (Fishbain et al., 2008)
16
Table Function
1
for Short-acting Bias (as function of
perceived risk)
[(1,0)-(4,1)] Modeling Team Judgment, reviewed by panel
17 Tamper Resistance (baseline value) 1 Policy variable (1=status quo)
DynamicSimulationofOpioidMisuseOutcomes
407
Table 3: References of support for model parameters in the trafficking sector.
Parameter Value Support
1 Avg. Nbr. of Dosage Units Per Opioid Prescription 86 Extrapolation from VONA (Governale, 2008)
2
Avg. Nbr. of Extra Dosage Units taken per Day Among
those with Abuse or Addiction
1.5 Panel Consensus
3 Fract. of Abuse/Addicted who Engage in Dr Shopping .5 Extrapolated from (Manchikanti et al., 2006)
4 Fraction of Abuse/Addiction who Engage in Forgery .4 Extrapolated from (Manchikanti et al., 2006)
5
Number of Days of Extra Opioid Usage Among those
with Abuse/Addiction
50
Generalized from NSDUH 2002, 2003, & 2004
(Table 2.18B in Colliver et al., 2006)
6 Profit Multiplier 15 Modeling team judgment
7
Table Function for the Effect of Rec Risk on Extra Rx
Obtained
[(0,0) – (2,1)] Modeling team judgment
SIMULTECH2012-2ndInternationalConferenceonSimulationandModelingMethodologies,Technologiesand
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