OPTIMAL LIVER ACCEPTANCE POLICIES FOR RISK-SENSITIVE PATIENTS

Purpose: It is believed that many living donor liver transplants, particularly the ones including healthier recipients, are occurring earlier than the time that would maximize life expectancy. We consider whether patient risk preferences can explain this discrepancy.

Method: We formulate a finite-horizon risk-sensitive Markov decision process (MDP) for the problem of determining the optimal liver acceptance policy for a risk-sensitive patient with any von Neumann-Morgenstern utility function. Our model maximizes the patient's total expected utility, which is composed of a pre-transplant expected utility and a post-transplant expected utility The model provides the optimal action (either transplant or wait) for each combination of patient health state and donor liver quality in each stage. We extend our model to the infinite-horizon case for patients who exhibit an exponential utility function, which provides good approximations for many other types of utility functions.

Result: We calibrated our model using data from national sources as well as a major liver transplant center. We considered 468 patients who received a living-donor liver transplant between the years 2001-2008. For each patient, we found the risk preferences under which her observed transplant decision is optimal. Only 61 patients are observed to exhibit risk-neutral behavior (indicating the transplant decision maximized life expectancy), and we are able to explain the observed decisions of 157 patients (among the remaining 407) by using a risk averse exponential utility function. However, risk aversion fails to explain the transplant timing decisions in the remaining 250 cases. In other words, more than half of our cohort requires risk-seeking behavior in order to render their observed decision optimal. Furthermore, we also conclude from our results that sicker patients tend to be more risk-averse, and this leads them to transplant at a higher MELD score than a risk-neutral patient under the same conditions would do.

Conclusion: Even though risk-sensitivity may have a notable impact on the liver acceptance decisions, it cannot fully explain the patient behavior in the timing of living-donor liver transplants.