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A Stylistic Queueing-Like Model for the Allocation of Organs on the Public List

Israel David and Michal Moatty-Assa. A Stylistic Queueing-Like Model for the Allocation of Organs on the Public List. Supply-Demand Discrepancy. Increasing shortage in kidneys for transplant 4,252 died waiting (2008). (Kidney offers are thrown away) ~50% refuse 1 st kidney offered!.

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A Stylistic Queueing-Like Model for the Allocation of Organs on the Public List

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  1. Israel David and Michal Moatty-Assa A Stylistic Queueing-Like Model for the Allocation of Organs on the Public List

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

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

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

  5. The Israeli “Point System” for kidney allocation

  6. First In First OfferedFIFOf – Decision rule Allocation rule FIFO sorting for Offering simplifying assumptions, “stylistic” moel

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

  8. Model Assumptions Constant lifetime under dialysis (T) Poisson arrival of donor kidneys (rate l) Poisson arrival of patients "Aggregate HLA " – only one relevant genetic quality What is the compromising t?

  9. n = 1, basics – פונקציית המטרה, הרווח האופטימלי מהצעת כליה ברגע - מ"מ, רווח (שנות חיים) מהשתלת הכליה - תוחלת הרווח הצפויה מדחיית ההצעהברגע t X – Offer random value; x = E[X] = Rp +r(1-p) U(t) – expected optimal value assuming that at t an offer is pending V(t) – optimal value from t onwards (exclusive of t if an offer is pending); V(T) = 0. l, T, R, r, p, ant1

  10. Dynamic Programming • U(t , x) = max{x, V(t)} • U(t) = EX[U(t , X)] • V(t) =

  11. n = 1, depiction of V and U

  12. n = 1, Explicit t* x = E[X] = Rp +r(1-p)

  13. n = 1, Explicit solution of V(t), U(t) .

  14. (A solvable Volterra)

  15. 0 n = 2, (approx.) outlook for the second candidate Non-hom.-Poisson stream with 3 stages effective l

  16. n = 2, conditional expected gains

  17. n = 2, Explicit t*

  18. n > 1, general input output specifics of cand. n optimization optimal decision rule (tn*) for cand. n specifics of cand.(n - 1) and t*n-1

  19. still… n = 3 0 effective l

  20. n = 3 0 effective l

  21. The l-recursion per sub-intervals where where for all Except for intersections with or

  22. leftmost Vn(t)’s for sub-intervals • - optimal value for cand. n in rejecting at the beginning of sub-val l • - arrival probability of an offer during sub-val l • - conditional expected gain if during sub-val l

  23. (explicit expressions for )

  24. The critical subinterval and determining tn* is taken to be such that t is substituted for the beginning of subinterval

  25. blocking and releasing of simultaneous antigen currents 0

  26. Simulation Measures • Long-run proportion of "good" transplants • Long-run death-rate • Long-run Waiting Time for allocated candidate

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