israel david and michal moatty-assa the search for compatible organs – a handy aid
TRANSCRIPT
Israel David and Michal Moatty-Assa
The Search for Compatible Organs – A Handy Aid
Supply-Demand Discrepancy
• Increasing shortage in kidneys for transplant
• 4,252 died waiting (2008)
• (Kidney offers are thrown away)
• ~50% refuse 1st kidney offered!
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
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
Donor-recipient ABO Compatibility
O A B AB
O
A
B
AB
+ + + +
— + — +
— — + +
— — — +
“A gives A or AB”
recipient
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
Histocompatibility in the HLA (Human Leukocyte Antigen) System
I = Number of antigens in the donor AND NOT in the recipient
PRApointsAgepoints
25% - 0%018 – 04
50% - 26%240 – 192
75% - 51%460 – 411
>75%6>600
HLA mismatches
pointsWaiting time
)months(points
No MM4<240
1 MM348 – 251
No MM in DR296 – 492
<974
The Israeli “Point System” for kidney allocation
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
0 t*=1.83 t**=8.05
I=0,1 I=0,1,2,3
I=0,1,2
Match-Level
Waiting-Time
Projecting into TEMPORAL SETTING
)An Example)
X: Offer ValueT: Lifetime (Deterioration)
2. T ~ Gamma(, )
> 1 T is “IFR”
(we take = 2).
( )
( )( )
g tr t t
G t
1 .X is discrete, finite no. of values )e.g. by I = HLA-mm(
Defs. for the probs of the 7 possible HLA levels
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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).
and the critical times
( , ) , ( )V t X max X t
λ t
( )
( ) ( ) ( ) ( )t
t r t t F x dx
For a give region:
2( )
(1 ) 1
AtB B Det
A A t t
A c ( ( ))c F t
( )
c ( ) ( )t
t B F x dx
( )( )
tF x dx