1. Israel David and Michal Moatty-Assa The Search for Compatible Organs – A Handy Aid

2. Supply-Demand Discrepancy Increasing shortage in kidneys for transplant 4,252 died waiting (2008)

3. (Kidney offers are thrown away) ~50% refuse 1 st kidney offered!

5. Main Parameters for Kidney Assignment Blood-group (ABO) compatibility Tissue match (HLA: A,B,DR) Level of antibodies in the patient body (PRA) Patient age Patient waiting time

6. Who waits the longest? Whom do I best fit? Who’s the youngest? Objectives: Clinical Efficiency: QALY, % survival. Equity: in waiting, across social groups. Matching Criteria: ABO, HLA, PRA, Age, Waiting

7. Donor-recipient ABO Compatibility O A B AB O A B AB + + + + — + — + — — + + — — — + “A gives A or AB” recipient

8. HLA: A protein-system (antigens) in the human cell, used by the immunological system for recognizing foreign substances. HLA constitution varies from one person to another. Tissue types The HLA antigen-sites which are presently considered most relevant to transplantation: A, B, and DR

9. Histocompatibility in the HLA (Human Leukocyte Antigen) System I = Number of antigens in the donor AND NOT in the recipient

10. pointsAgepointsPRA 418 – 0025% - 0% 240 – 19250% - 26% 160 – 41475% - 51% 0>606>75% points Waiting time (months) points HLA mismatches 0<244No MM 148 – 2531 MM 296 – 492No MM in DR 4>97 The Israeli “Point System” for kidney allocation

11. A continuous, time-dependent, full-info “Secretary”) ) The future arrival process How long do I wait? How good is this offer? my HLA, ABO population statistics by ABO, HLA donors arrival rate The decision of the single candidate

12. 0 t*=1.83t**=8.05 I=0,1I=0,1,2,3I=0,1,2 Match-Level Waiting-Time Projecting into TEMPORAL SETTING (An Example)

13. X: Offer Value T: Lifetime (Deterioration) 2. T ~ Gamma( ,  )  > 1 T is “IFR” (we take  = 2). 1. X is discrete, finite no. of values (e.g. by I = HLA-mm)

14. Defs. for the probs of the 7 possible HLA levels

16. OPTN/SRTR 2006 annual Report. (Table 5.10a: Unadjusted Graft Survival, Deceased Donor non-ECD Kidney Transplants, Survival at 3 Months, 1 Year, 3 Years, and 5 Years).

17. and the critical times

18. For a give region: