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Probabilistic Sensitivity Analysis for Decision Trees with Multiple Branches: Use of the Dirichlet Distribution in a Bayesian Framework

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  • Andrew H. Briggs
  • A. E. Ades
  • Martin J. Price

Abstract

In structuring decision models of medical interventions, it is commonly recommended that only 2 branches be used for each chance node to avoid logical inconsistencies that can arise during sensitivity analyses if the branching probabilities do not sum to 1. However, information may be naturally available in an unconditional form, and structuring a tree in conditional form may complicate rather than simplify the sensitivity analysis of the unconditional probabilities. Cur- rent guidance emphasizes using probabilistic sensitivity analysis, and a method is required to provide probabilistic probabilities over multiple branches that appropriately rep- resents uncertainty while satisfying the requirement that mutually exclusive event probabilities should sum to 1. The authors argue that the Dirichlet distribution, the multivariate equivalent of the beta distribution, is appropriate for this purpose and illustrate its use for generating a fully probabilistic transition matrix for a Markov model. Furthermore, they demonstrate that by adopting a Bayesian approach, the problem of observing zero counts for transitions of interest can be overcome.

Suggested Citation

  • Andrew H. Briggs & A. E. Ades & Martin J. Price, 2003. "Probabilistic Sensitivity Analysis for Decision Trees with Multiple Branches: Use of the Dirichlet Distribution in a Bayesian Framework," Medical Decision Making, , vol. 23(4), pages 341-350, July.
    • Handle: RePEc:sae:medema:v:23:y:2003:i:4:p:341-350
    DOI: 10.1177/0272989X03255922
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    4. Rachael DiSantostefano & Andrea Biddle & John Lavelle, 2006. "The Long-Term Cost Effectiveness of Treatments for Benign Prostatic Hyperplasia," PharmacoEconomics, Springer, vol. 24(2), pages 171-191, February.
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    7. Charles Christian Adarkwah & Afschin Gandjour & Maren Akkerman & Silvia M Evers, 2011. "Cost-Effectiveness of Angiotensin-Converting Enzyme Inhibitors for the Prevention of Diabetic Nephropathy in The Netherlands – A Markov Model," PLOS ONE, Public Library of Science, vol. 6(10), pages 1-10, October.
    8. Nick Bansback & Roberta Ara & Sue Ward & Aslam Anis & Hyon Choi, 2009. "Statin Therapy in Rheumatoid Arthritis," PharmacoEconomics, Springer, vol. 27(1), pages 25-37, January.
    9. Ankur Pandya & Ashley A Eggman & Hooman Kamel & Ajay Gupta & Bruce R Schackman & Pina C Sanelli, 2016. "Modeling the Cost Effectiveness of Neuroimaging-Based Treatment of Acute Wake-Up Stroke," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-13, February.
    10. Regina Rendas-Baum & Min Yang & Joseph Gricar & Gene Wallenstein, 2010. "Cost-effectiveness analysis of treatments for premenstrual dysphoric disorder," Applied Health Economics and Health Policy, Springer, vol. 8(2), pages 129-140, March.
    11. Ya-Chen Shih & Josephine Mauskopf & Rohit Borker, 2007. "A Cost-Effectiveness Analysis of First-Line Controller Therapies for Persistent Asthma," PharmacoEconomics, Springer, vol. 25(7), pages 577-590, July.
    12. Celine Johanna van de Laar & Carly A Janssen & Matthijs Janssen & Martijn A H Oude Voshaar & Maiwenn J AL & Mart A F J van de Laar, 2022. "Model-based cost-effectiveness analyses comparing combinations of urate lowering therapy and anti-inflammatory treatment in gout patients," PLOS ONE, Public Library of Science, vol. 17(1), pages 1-13, January.
    13. Yuanhui Zhang & Haipeng Wu & Brian T. Denton & James R. Wilson & Jennifer M. Lobo, 2019. "Probabilistic sensitivity analysis on Markov models with uncertain transition probabilities: an application in evaluating treatment decisions for type 2 diabetes," Health Care Management Science, Springer, vol. 22(1), pages 34-52, March.
    14. Laura McCullagh & Cathal Walsh & Michael Barry, 2012. "Value-of-Information Analysis to Reduce Decision Uncertainty Associated with the Choice of Thromboprophylaxis after Total Hip Replacement in the Irish Healthcare Setting," PharmacoEconomics, Springer, vol. 30(10), pages 941-959, October.
    15. Mylene Lagarde & John Cairns, 2012. "Modelling human resources policies with Markov models: an illustration with the South African nursing labour market," Health Care Management Science, Springer, vol. 15(3), pages 270-282, September.
    16. Bruce Wang & Joshua A Roth & Hiep Nguyen & Eugene Felber & Wes Furnback & Louis P Garrison, 2015. "The Short-Term Cost-Effectiveness of Once-Daily Liraglutide Versus Once-Weekly Exenatide for the Treatment of Type 2 Diabetes Mellitus in the United States," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-13, April.
    17. Kenneth J. Smith & Amber E. Barnato & Mark S. Roberts, 2006. "Teaching Medical Decision Modeling: A Qualitative Description of Student Errors and Curriculum Responses," Medical Decision Making, , vol. 26(6), pages 583-588, November.
    18. Naren Kumar Surendra & Mohd Rizal Abdul Manaf & Lai Seong Hooi & Sunita Bavanandan & Fariz Safhan Mohamad Nor & Shahnaz Shah Firdaus Khan & Ong Loke Meng & Abdul Halim Abdul Gafor, 2019. "Cost utility analysis of end stage renal disease treatment in Ministry of Health dialysis centres, Malaysia: Hemodialysis versus continuous ambulatory peritoneal dialysis," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-16, October.
    19. Edmund Jones & David Epstein & Leticia García-Mochón, 2017. "A Procedure for Deriving Formulas to Convert Transition Rates to Probabilities for Multistate Markov Models," Medical Decision Making, , vol. 37(7), pages 779-789, October.
    20. Rungskunroch, Panrawee & Jack, Anson & Kaewunruen, Sakdirat, 2021. "Benchmarking on railway safety performance using Bayesian inference, decision tree and petri-net techniques based on long-term accidental data sets," Reliability Engineering and System Safety, Elsevier, vol. 213(C).

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