Living-Donor Liver Transplantation Timing under Ambiguous Health State Transition Probabilities

45 Pages Posted: 20 Jul 2017

See all articles by David Kaufman

David Kaufman

University of Michigan at Dearborn - College of Business

Andrew J. Schaefer

University of Pittsburgh

Mark S. Roberts

University of Pittsburgh

Date Written: June 28, 2017

Abstract

Markov decision process (MDP) models for the optimal time to initial a medical therapy, such as an organ transplantation, require the estimation of health state transition probabilities from physiological data. Such estimation may be a source of probabilistic ambiguity when, for example, some critical health states are seldom visited historically. For MDP models in general, robust dynamic programming has been proposed as an approach to mitigate the effects of ambiguity on optimal decisions. However, very few realworld studies examining the usefulness of robust MDP policies have been reported. We present a robust MDP model for medical therapy initiation in which worst-case transition probabilities are chosen from a set of probability measures constructed using relative entropy bounds. For this model, we prove that therapy is initiated sooner, in additional states, as the ambiguity increases. We apply the methodology to the problem of deciding when to undergo a living-donor liver transplantation, and present the results of a case study using clinical data. We propose a novel implied confidence level measure that maps the robust solutions to historical transplant decisions, and find that in some cases the robust policies are closer to decisions that have been made in practice.

Keywords: Markov Decision Processes, Medical Decision-Making, Robust Optimization, Dynamic Programming

JEL Classification: C61, I19

Suggested Citation

Kaufman, David and Schaefer, Andrew J. and Roberts, Mark S., Living-Donor Liver Transplantation Timing under Ambiguous Health State Transition Probabilities (June 28, 2017). Available at SSRN: https://ssrn.com/abstract=3003590 or http://dx.doi.org/10.2139/ssrn.3003590

David Kaufman (Contact Author)

University of Michigan at Dearborn - College of Business ( email )

Fairlane Center South
19000 Hubbard Drive
Dearborn, MI 48126-2638
United States

Andrew J. Schaefer

University of Pittsburgh ( email )

135 N Bellefield Ave
Pittsburgh, PA 15260
United States

Mark S. Roberts

University of Pittsburgh ( email )

200 Meyran Avenue
Suite 200
Pittsburgh, PA 15213
United States

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