Robust Control of Liver Transplant Timing
Department of Industrial Engineering, University of Pittsburgh, davidlk@engr.pitt.edu
Department of Industrial Engineering, University of Pittsburgh, schaefer@engr.pitt.edu
Division of General Internal Medicine, University of Pittsburgh, robertsm@upmc.edu
Markov decision process (MDP) models for the optimal timing of organ transplants require the estimation of underlying transition probabilities from clinical data. Such estimation may be a source of
ambiguity due to
- the lack of data for some states (MELD scores) that are seldom visited and
- the use of general population data to provide estimates for more specific disease groups.
Such ambiguity is inherent in many medical decision-making problems. In this paper we incorporate the ambiguity in a robust MDP formulation of the living-donor model (LDM) for optimal transplant timing. The robust model is a max/min sequential game where the decision-maker plays against nature. The decision-maker decides when to wait and when to transplant in order to maximize total expected adjusted quality of life years, while nature seeks to minimize the reward by choosing worst case transition probabilities from a limited set of transition measures determined by relative entropy bounds. We first provide new structural results for the traditional model, without ambiguity. We then show how the optimal actions are affected by the ambiguity of robust model. These results not only provide insight into the problem but also stand to simplify computation. Finally, we provide the results of a numerical study analyzing the impact of the robust model with clinically obtained data.
