148 The UMAP Journal 28. 2(2007) Table 5 Averaged results of repeated simulations of multiple-pair transplant exchange nationwide (extrapolated from Region 9 data). Kind of match Transplants Percentage 2-way no mismatch 2-way non-perfect 9646 0 3-way non-perfect otal transplants 9656 h willing b 10497 Another option is to consider multiple exchanges for all donor-recipient pairs in a particular center. This minimizes the travel time required for the patients, while improving the computational power of the search algorithm. A center has on average 259 candidates, of whom 39 have willing but incompat- ible donors available. For this sample size, we get on average 25 transplants (65%), compared to 92% under exchange at the regional level. Furthermore, the proportion of high-quality transplants is also smaller. The benefits of a center- only exchange system are personal and psychological: Patients live close to the surgery location, which means better support from both family and familiar physicians Task 4: Patient Choice Theory Suppose a patient is offered a barely compatible kidney from the cadaver queue. There are two options: take the bad-match kidney immediately, or ● wait for a better match from the cadaver queue or We consider two cases: without paired exchange and with it. Model 1: Decision Scenario without Paired Exchange Of transplants with poorly matched kidneys, 50% fail after 5-7 years. So we assume that the lifetime after a poorly matched kidney transplant is expo. nentially distributed with mean 6 years[Norman 2005, 458 ables with mean X by solving P(survive t years)=edes to exponential vari- We translate data of Table 6 on survival probabilitic148 T77e UMAP Journal 28.2 (2007) Table S. Averaged results of repeated simulations of multiple-pair transplant exchange nationwide (extrapolated from Region 9 data). Kind of match Transplants Percentage 2-way no mismatch 2 2-way non-perfect 9,646 3-way no mismatch 0 3-way non-perfect 8 Total transplants 9,656 92% Candidates with willing but incompatible donor 10,497 Another option is to consider multiple exchanges for all donor-recipient pairs in a particular center. This minimizes the travel time required for the patients, while improving the computational power of the search algorithm. A center has on average 259 candidates, of whom 39 have willing but incompat￾ible donors available. For this sample size, we get on average 25 transplants (65%), compared to 92% under exchange at the regional level. Furthermore, the proportion of high-quality transplants is also smaller. The benefits of a center￾only exchange system are personal and psychological: Patients live close to the surgery location, which means better support from both family and familiar physicians. Task 4: Patient Choice Theory Suppose a patient is offered a barely compatible kidney from the cadaver queue. There are two options: "o take the bad-match kidney immediately, or "* wait for a better match, - from the cadaver queue or - from a paired exchange. We consider two'cases: without paired exchange and with it. Model 1: Decision Scenario without Paired Exchange Of transplants with poorly matched kidneys, 50% fail after 5-7 years. So we assume that the lifetime after a poorly matched kidney transplant is expo￾nentially distributed with mean 6 years [Norman 2005, 458]. We translate data of Table 6 on survival probabilities to exponential vari￾ables with mean A by solving P(survive t years) = e-At