This document describes a study that used a multi-state Markov model to analyze patterns of use of three opioid dependence treatments: methadone, buprenorphine, and other drug-free outpatient treatments. The study followed 30,080 Medicaid patients diagnosed with opioid dependence from 2003 to 2007. The model estimated transition probabilities between the three treatment states and discontinuation over time. Results found the probability of discontinuing methadone treatment was 20% after 6 months, while survival probabilities on each treatment after 30 months were 30% for methadone, 9% for buprenorphine, and 5% for other treatments. The study concluded multi-state Markov models are useful for investigating treatment switching and compliance over long
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A Multi State Markov Model for Analyzing Patterns of Use of Opiod Treatments FOUAYZI
1. A multi-state Markov model for analyzing
patterns of use of Opioid treatments
Hassan Fouayzi, MS; Robin Clark, PhD; and Jeffrey Baxter, MD
Hassan Fouayzi, MS, Meyers Primary Care Institute (Reliant Medical Group, Fallon Community Health Plan,
and University of Massachusetts Medical School), Worcester, MA, USA
Robin E. Clark, PhD, Center for Health Policy and Research, University of Massachusetts Medical School,
Worcester, MA, USA
Jeffrey D. Baxter, MD, Center for Health Policy and Research, University of Massachusetts Medical School,
Worcester, MA, USA
1
2. Acknowledgements and Conflict of Interest statement
No conflicts of interest to disclose.
Preparation of this study was assisted by grant #64752 from
the Robert Wood Johnson Foundation’s Substance Abuse
Policy Research Program (SAPRP).
Acknowledgements:
Meyers Primary Care Institute (Reliant Medical Group, Fallon
Community Health Plan, and University of Massachusetts
Medical School), Worcester, MA, USA
Center for Health Policy and Research at University of
Massachusetts Medical School, Worcester, MA, USA
3. Introduction
A multi-state model (MSM) is a stochastic model that allows individuals to
move among a finite number of states
In medical studies, multi-state models (MSM) are mainly used to investigate
clinical symptoms , biological markers, scales of a disease, or complications
of the course of an illness (1)
In pharmacoepidemiology studies, survival analysis methods are usually
used to investigate use of medications using 2 states only:
Adherence vs non adherence, persistence vs discontinuation...
MSM models can be used to evaluate multiple states simultaneously,
accommodate more information from censored subjects, and can also be
used to analyze competing risks.
1 Luís Meira-Machado et al (2009) .”Multi-state models for the analysis of time-to-event data”. Stat Methods Med Res;18(2):3195–
4. The multi-state Markov model
Markov modeling is a form of stochastic modeling that
describes a process as a series of probable transitions
between states.
Composed of mutually exclusive set of health states (e.g.,
alive or dead)
Transitions among states occur at regular intervals or cycles
(e.g., monthly) based on transition probabilities.
The process is memoryless (one state depends only on
preceding state but independent of all former states).
4
5. Objective of the study
The aim of this study was to highlight the
importance of using multi-state Markov
models to assess use and switching patterns
of three leading treatments for opioid
dependence
5
6. Background
In 2009, over 1.7 million people in the US abused or were
dependent on prescription opioids and 399,000 on heroin
(1)
Methadone and buprenorphine have been shown to be
effective in retaining patients in treatment and decreasing
opioid use (2,3).
Drug-free outpatient psychosocial behavioral health
interventions alone are also sometimes used although they
appear less effective than pharmacological therapy
1 NSDUH 2009
2 Mattick, R., J. Kimber, et al. (2009). "Buprenorphine maintenance versus placebo or methadone maintenance for opioid
dependence." Cochrane Database of Systematic Reviews.
3 Connock, M., A. Juarez-Garcia, et al. (2007). "Methadone and buprenorphine for the management of opioid dependence: a
systematic review and economic evaluation." Health Technology Assessment 11(9). 6
7. Study population and design
Retrospective longitudinal study using
Massachusetts Medicaid Enrollment and Claims
data.
30,080 Medicaid beneficiaries aged between 16 and
65 years old and diagnosed with opioid dependence
between 2003 and 2007 were followed until
discontinuation of opioid treatment or end of
observation, whatever comes first.
41.6 % women
mean age= 33.4, SD=9.8
mean follow up =11.1 months, SD=12.2 7
10. Results (Cont.)
Frequency table of pairs of consecutive states: for each state p and
q, the number of times a patient was in state p followed by a state
q. For instance, there were 600 transitions from the transient state
methadone to the transient state buprenorphine.
10
11. Results (Cont.)
The probabilities of being in any one state after 6 months and 24
months of follow up are reported here. A typical patient in state
methadone has a probability of 0.20 of discontinuing therapy after
6 months. 11
14. Results (Cont.)
Figure 2 shows the predicted probability of survival (staying on therapy) for opioid users
for monthly times in the future. For instance, the 30 months survival probability of being
on Methadone is 0.3, on Buprenorphine is 0.09, and on other treatments is 0.05. 14
15. Next steps
Tests such as exponential sojourn times assumption
test
Model comparison using likelihoods / AIC for a
parsimonious final model and to potentially gain
more power
Goodness of fit assessment
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16. Conclusion
Results of this study describe the dynamics of
opioid therapy enrollment and the effects of
several covariates on the transition intensities.
In addition to other methods for assessing
compliance to and persistence with treatments,
Markov Multi-state models are very helpful for
investigating patterns of use and switching
between treatments over a long time period .
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