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Health Care Management Science

, Volume 22, Issue 1, pp 34–52 | Cite as

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

  • Yuanhui ZhangEmail author
  • Haipeng Wu
  • Brian T. Denton
  • James R. Wilson
  • Jennifer M. Lobo
Article

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 

Notes

Acknowledgments

This material is based upon work supported in part by the National Science Foundation through Grant Number CMMI 1462060. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Operations Research Graduate ProgramNorth Carolina State UniversityRaleighUSA
  2. 2.Google Inc.Mountain ViewUSA
  3. 3.Department of Industrial and Operations EngineeringUniversity of MichiganAnn ArborUSA
  4. 4.Edward P. Fitts Department of Industrial and Systems EngineeringNorth Carolina State UniversityRaleighUSA
  5. 5.Department of Public Health SciencesUniversity of VirginiaCharlottesvilleUSA

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