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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

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

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): 195–222. 3

The multi-state Markov model

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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).

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

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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 20092 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).

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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

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The multi-state Markov model

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Results

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Results (Cont.)

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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.

Results (Cont.)

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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.

Results (Cont.)

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Results (Cont.)

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Results (Cont.)

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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.

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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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 . 16

Thank You

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