Zhang Y, Wu H, Denton BT, Wilson JR, Lobo JM. Probabilistic sensitivity analysis on Markov models with uncertain transition probabilities: an application in evaluating treatment decisions for type 2 diabetes. Health Care Manag Sci. 2019 Mar;22(1):34-52. doi: 10.1007/s10729-017-9420-8.

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 the associated transition probability matrices (TPMs). This article describes two simulation-based approaches for conducting probabilistic sensitivity analysis of a given finite-state, finite-horizon, discrete-time Markov model with TPMs which may vary within specified uncertainty sets or according to appropriate or specified probability distributions. The first approach assumes no prior knowledge of the TPM's distribution, and each row is sampled uniformly over the corresponding uncertainty set. The second approach involves random sampling from the (truncated) multivariate normal distribution of the TPM's maximum likelihood estimator subject to the condition that each row has nonnegative elements, and sums to one. The proposed methods are easy to implement and have reasonable computation times. As an illustrative example, these two methods are applied to a medical decision-making problem involving the evaluation of treatment guidelines for glycemic control of patients with type 2 diabetes in which the natural variation in glycated hemoglobin (HbA1c) is modeled as a Markov chain, and the HbA1c transition probabilities are subject to uncertainty.

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