#PharmEconFriday: The Markov Model

Over the next few years, my career will shift focus to pharmacoeconomics (#PharmEcon) research and further away from pharmacy management and operations.  As I learn in this field, I would like to share my thoughts and “lessons learned” along the way and hopefully teach a little through a new series of posts that I’ll try to release on Fridays.  Although it can be a very complex field, I think breaking down each concept in ways that the general public can learn from could be valuable to both the student and the teacher.

Introducing the Markov ModelMarkov Model

One of the most commonly used models in economic analyses is a Markov Model, named after Russian mathematician Andrey Markov.  In this framework, the researcher divides a disease into different mutually exclusive states, called Markov states, to represent the different events in the progression of the disease.  Markov Models are ran through cycles, typically defined as one year.  Temporary states are states visited in sequence until they ultimately end up an an absorbing state, to which there is no going out.  Hypothetical patients put in the model move from state to state based on predefined model inputs called transition probabilities.  As the name implies, these are the probability that a patient would advance to a different Markov state or remain in the current temporary state.

Since I’m beginning most of my economic work in the area of Hepatitis C virus (HCV) infections, I’ll use the progression of this liver disease to help explain these definitions (see Figure 1 below).

Markov model example-hepatitis c

Figure 1: Example Markov states for chronic HCV infection.

In the example of chronic HCV infection, one might construct a basic model using the METAVIR scoring system to describe different states of the disease progression.  Each arrow represents the options a patient in the current state has and the researcher would assign probabilities (based on previous studies or expert opinion) to each arrow.  The little circular arrows that loop back to the same state would represent the probability that a patient would stay in the current state.  Notice how “Transplant” doesn’t have a loopy arrow?  That is because in this model framework, transplant is considered a tunnel state, or one where a patient is forced to move out after 1 cycle.  If you think about it, a patient that receives a liver transplant would transition to a “post transplant” state after the transplant.  This model doesn’t show a path for multiple transplants, but that could be added.  The absorbing state in this model is death, which makes sense as long as you aren’t trying to build a model for zombies.

If you want to learn more…

These posts are meant to be basic introductions to these concepts which will hopefully draw more interest to a field that I find extremely fascinating.  If you would like to learn more on the topic, please feel free to contact me or if you prefer to do a little independent reading on Markov models please check out the following papers:

  • Briggs A, Sculpher M. An introduction to Markov Modelling for Economic Evaluation. Pharmacoeconomics. 1998;13(4):397-409.
  • Sonnenberg FA, Beck JR. Markov Models in Medical Decision Making: A Practical Guide. Medical Decision Making. 1993;13:322-338.
  • Stahl JE. Modelling Methods for Pharmacoeconomic and Health Technology Assessment. Pharmacoeconomics. 2008;26(2):131-148.
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Joey
Joey Mattingly, PharmD, MBA is an assistant professor at the University of Maryland School of Pharmacy located in Baltimore, Maryland. Joey has managed retail and long-term care pharmacy operations in Kentucky, Illinois and Indiana. Leading Over The Counter is a blog of Joey's views and opinions on the topics of pharmacy leadership and management and do not represent the University of Maryland, Baltimore. Joey can be followed on Twitter @joeymattingly.

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