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

2220 uuu hgfIP

,112112

121112

121121

1212123

22222222

22222222

22222222

222

mu

uumu

uumu

umu

uuu

mu

uumu

uuumu

umu

uh

mu

uuumu

uumu

uumu

u

mu

uumu

uumu

uh

hhgfffhhgggf

hhhggfhggfff

hhhgffhgggff

hhhgggfffIP

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