Cost-effectiveness Analysis with Influence Diagrams^[*]

Summary

Background: Cost-effectiveness analysis (CEA) is used increasingly in medicine to determine whether the health benefit of an intervention is worth the economic cost. Decision trees, the standard decision modeling technique for non-temporal domains, can only perform CEA for very small problems.

Objective: To develop a method for CEA in problems involving several dozen variables.

Methods: We explain how to build influence diagrams (IDs) that explicitly represent cost and effectiveness. We propose an algorithm for evaluating cost-effectiveness IDs directly, i.e., without expanding an equivalent decision tree.

Results: The evaluation of an ID returns a set of intervals for the willingness to pay – separated by cost-effectiveness thresholds – and, for each interval, the cost, the effectiveness, and the optimal intervention. The algorithm that evaluates the ID directly is in general much more efficient than the brute-force method, which is in turn more efficient than the expansion of an equivalent decision tree. Using OpenMarkov, an open-source software tool that implements this algorithm, we have been able to perform CEAs on several IDs whose equivalent decision trees contain millions of branches.

Conclusion: IDs can perform CEA on large problems that cannot be analyzed with decision trees.

Keywords

Cost-benefit analysis - cost-effectiveness analysis - decision trees - influence diagrams

^* Supplementary material published on our web-site www.methods-online.com

• References

• 1 Drummond MF, Sculpher MJ, Torrance GW, O’Brien BJ, Stoddart GL. Methods for the Economic Evaluation of Health Care Programmes. 3rd ed. Oxford University Press; 2005
• 2 Gold MR, Siegel JE, Russell LB, Weinstein MC. Cost-Effectiveness in Health and Medicine. New York: Oxford University Press; 1996
• 3 Stinnett AA, Mullahy J. Net health benefit: A new framework for the analysis of uncertainty in cost-effectiveness analysis. Medical Decision Making 1998; 18: S68-S80.
• 4 Weinstein MC, Torrance G, McGuire A. QALYs: The basics. Value in Health 2009; 12: S5-S9.
• 5 Pauker S, Wong J. The influence of influence diagrams in medicine. Decision Analysis 2005; 2: 238-244.
• 6 Arias M, Díez FJ. Cost-effectiveness analysis with sequential decisions. Madrid, Spain: UNED; 2011
• 7 Howard RA, Matheson JE. Influence diagrams. In Howard RA, Matheson JE. editors Readings on the Principles and Applications of Decision Analysis. Menlo Park, CA: Strategic Decisions Group; 1984: 719-762.
• 8 León D. A Probabilistic Graphical Model for Total Knee Arthroplasty. Master’s thesis. Dept. Artificial Intelligence, UNED; Madrid, Spain: 2011
• 9 Luque M. Probabilistic Graphical Models for Decision Making in Medicine. PhD thesis. UNED. Madrid: 2009
• 10 Luque M, Díez FJ, Disdier C. A decision support system for the mediastinal staging of non-small cell lung cancer. In: 31st Annual Meeting of the Society for Medical Decision Making. Los Angeles; CA: 2009
• 11 Kuntz KM, Weinstein MC. Modelling in economic evaluation. In Drummond MF, McGuire A. editors Economic Evaluation in Health Care. New York: Oxford University Press; 2001: 141-171.
• 12 Arias M, Díez FJ. The problem of embedded decision nodes in cost-effectiveness decision trees. Pharmacoeconomics 2014; 32: 1141-1145.
• 13 Olmsted SM. On Representing and Solving Decision Problems. PhD thesis. Dept. Engineering and Economic Systems. Stanford University; CA: 1983
• 14 Shachter RD. Evaluating influence diagrams. Operations Research 1986; 34: 871-882.
• 15 Jensen FV, Nielsen TD. Bayesian Networks and Decision Graphs. 2nd ed. New York: Springer Verlag; 2007
• 16 Weinstein MC, Stason WB. Foundations of cost-effectiveness analysis for health and medical practices. New England Journal of Medicine 1977; 296: 716-721.
• 17 Weinstein MC, Fineberg HV, Elstein AS. et al. Clinical Decision Analysis. Philadelphia, PA: Saunders; 1980
• 18 Sox HC, Blatt MA, Higgins MC, Marton I K. Medical Decision Making. Woburn, MA: Butterworth Heinemann; 1988
• 19 Cooper GF. The computational complexity of probabilistic inference using Bayesian belief networks. Artificial Intelligence 1990; 42: 393-405.
• 20 Jensen F, Jensen FV, Dittmer SL. From influence diagrams to junction trees. In de Mantaras RL, Poole D. editors Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI’94). San Francisco, CA: Morgan Kauffmann; 1994: 367-373.
• 21 Chavira M, Darwiche A. Compiling Bayesian networks using variable elimination. In Veloso MM. editor Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI’07). Hyderabad, India: Morgan Kauffmann; 2007: 2443-2449.
• 22 Darwiche A. Recursive conditioning. Artificial Intelligence 2001; 126: 5-41.
• 23 Koller D, Friedman N. Probabilistic Graphical Models: Principles and Techniques. Cambridge, MA: The MIT Press; 2009
• 24 Kwisthout J, Bodlaender H, van der Gaag L. The necessity of bounded treewidth for efficient in- ference in Bayesian networks. In: Proceedings of the 19th European Conference on Artificial In- telligence (ECAI’10). Lisbon, Portugal: 2010: 237-242.
• 25 Nielsen SH, Nielsen TD, Jensen FV. Multi- currency influence diagrams. In Salmerón A, Gámez JA. editors Advances in Probabilistic Graphical Models. Berlin, Germany: Springer; 2007: 275-294.
• 26 Díez FJ, Luque M, König C. Decision analysis networks. In Cano A, Gómez M, Nielsen TD. editors Proceedings of the Sixth European Workshop on Probabilistic Graphical Models (PGM’12). Granada, Spain: 2012: 83-90.