Probabilistic sensitivity analysis on Markov models with uncertain transition probabilities: an application in evaluating treatment decisions for type 2 diabetes

Yuanhui Zhang (), Haipeng Wu (), Brian T. Denton (), James R. Wilson () and Jennifer M. Lobo ()
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Yuanhui Zhang: North Carolina State University
Haipeng Wu: Google Inc.
Brian T. Denton: University of Michigan
James R. Wilson: North Carolina State University
Jennifer M. Lobo: University of Virginia

Health Care Management Science, 2019, vol. 22, issue 1, No 3, 34-52

Abstract: Abstract Markov models are commonly used for decision-making studies in many application domains; however, there are no widely adopted methods for performing sensitivity analysis on such models with uncertain transition probability matrices (TPMs). This article describes two simulation-based approaches for conducting probabilistic sensitivity analysis on a given discrete-time, finite-horizon, finite-state Markov model using TPMs that are sampled over a specified uncertainty set according to a relevant probability distribution. The first approach assumes no prior knowledge of the probability distribution, and each row of a TPM is independently sampled from the uniform distribution on the row’s uncertainty set. The second approach involves random sampling from the (truncated) multivariate normal distribution of the TPM’s maximum likelihood estimators for its rows subject to the condition that each row has nonnegative elements and sums to one. The two sampling methods are easily implemented and have reasonable computation times. A case study illustrates the application of these methods to a medical decision-making problem involving the evaluation of treatment guidelines for glycemic control of patients with type 2 diabetes, where natural variation in a patient’s glycated hemoglobin (HbA1c) is modeled as a Markov chain, and the associated TPMs are subject to uncertainty.

Keywords: Robustness and sensitivity analysis; Markov model; Transition probability matrices; Medical decision-making; Monte Carlo simulation (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10729-017-9420-8

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