ESTIMATING MARKOV CHAIN TRANSITION MATRICES IN LIMITED DATA SAMPLES- A MONTE CARLO EXPERIMENT

Author(s)

Tsang KP1, Wang BCM2, Garrison L31Virginia Tech, Blacksburg, VA, USA, 2Adjility Health, New York, NY, USA, 3University of Washington Department of Pharmacy, Seattle, WA, USA

OBJECTIVES: Markov models are often used in Health Economics to represent disease progression in Cost-Utility models.  The transition probabilities, however, may be difficult to populate when the data are limited. This note applies the Markov matrix approximation method using vector autoregression (VAR) to estimate the transition matrix when the sample size is small.    METHODS: We compare the performance of the standard (count) method versus the VAR method to estimate transition probabilities in small samples. For the count method, one counts the transitions from state  to any other state  in the data and then divides the counts by the number of occurrences for each . The VAR method follows Tauchen (1986) and Terry and Knotek (2011). We compare the two methods using Monte Carlo simulations by generating small samples from different data generating processes (DGPs) and comparing the mean squared errors made by each method versus the true transition matrix.  We employ two DGPs to populate the entries of our underlying transition probability matrices in our study: 1) A normal distribution with large variance (DPG1), and 2) a uniform distribution with small variance (DGP2). We then normalize each row so they sum to 1.  RESULTS: In DGP1, the VAR outperforms the count method in small samples (N = 10 or 30) and the count method marginally outperforms the VAR method in the large sample (N = 50). For DGP2, VAR outperforms in small samples and both methods perform similarly in the large sample.  We propose a combination of the two methods by increasing the weight on the count method when the sample size increases relative to the size of the matrix. CONCLUSIONS: By applying this methodology in Health Economics modeling, it allows the researcher to utilize Markov models in situations previously infeasible due to a paucity of data. 

Conference/Value in Health Info

2012-06, ISPOR 2012, Washington, D.C., USA

Value in Health, Vol. 15, No. 4 (June 2012)

Code

PRM34

Topic

Methodological & Statistical Research

Topic Subcategory

Modeling and simulation

Disease

Multiple Diseases

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