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Decision Analysis with Cumulative Prospect Theory

Address correspondence and reprint requests to Dr. Bayoumi Inner City Health Research Unit, 2-024 Shuter Wing, St. Michael's Hospital, 30 Bond Street, Toronto, ON, Canada M5B 1W8; telephone (416) 864-5728; fax: (416) 864-5485; e-mail: (ahmed bayoumi{at}utoronto.ca)

Donald A. Redelmeier, MD, MSc

Address correspondence and reprint requests to Dr. Bayoumi Inner City Health Research Unit, 2-024 Shuter Wing, St. Michael's Hospital, 30 Bond Street, Toronto, ON, Canada M5B 1W8; telephone (416) 864-5728; fax: (416) 864-5485; e-mail: (ahmed bayoumi{at}utoronto.ca)

Background. Individuals sometimes express preferences that do not follow expected utility theory. Cumulative prospect theory adjusts for some phenomena by using decision weights rather than probabilities when analyzing a decision tree. Methods. The authors examined how probability transformations from cumulative prospect theory might alter a decision analysis of a prophylactic therapy in AIDS, eliciting utilities from patients with HIV infection (n = 75) and calculating expected outcomes using an established Markov model. They next focused on transformations of three sets of probabilities : 1) the probabilities used in calculating standard-gamble utility scores; 2) the probabilities of being in discrete Markov states; 3) the probabilities of transitioning between Markov states. Results. The same prophylaxis strategy yielded the highest quality-adjusted survival under all transformations. For the average patient, prophylaxis appeared relatively less advantageous when standard-gamble utilities were transformed. Prophylaxis appeared relatively more advantageous when state probabilities were transformed and relatively less advantageous when transition probabilities were transformed. Transforming standard-gamble and transition probabilities simultaneously decreased the gain from prophylaxis by almost half. Sensitivity analysis indicated that even near-linear probability weighting transformations could substantially alter quality-adjusted survival estimates. Conclusion. The magnitude of benefit estimated in a decision-analytic model can change significantly after using cumulative prospect theory. Incorporating cumulative prospect theory into decision analysis can provide a form of sensitivity analysis and may help describe when people deviate from expected utility theory. Key words: decision analysis; cumulative prospect theory; expected utility theory ; standard gamble. (Med Decis Making 2000;20:404-412)

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