A Matching Algorithm for

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A Matching Algorithm for Paired Living Kidney
Donation in the UK
Joanne Allen Senior Statistician NHS Blood and
Transplant
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Background
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Paired living kidney donation
Blood group and tissue type incompatibility
prevent many potential living donor kidney
transplants A simple exchange of suitable donor
kidneys is one possible solution Couple
1 Couple 2 Recipient 1 Recipient 2
Donor 1 Donor 2
Human Tissue Act made this possible in the UK
from Sept 2006
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Background

• The British Transplantation Society and NHS Blood
  and Transplant worked together to develop
  arrangements for paired donation in the UK
  working party
• Diverse range of views
• A national scheme
• is required by the HTA
• will maximise the potential of paired donation -
  although a local bias is preferred
• will be regularly reviewed
• should be limited to paired rather than pooled
  donation initially

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Stages involved in the UK paired donation scheme
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Matching process Stage 1 Identify all possible
2-way exchanges
Say we have 5 couples and couple 1 can swap with
any other and couple 4 can swap with couples 3 5
Each circle represents one incompatible
donor-recipient couple
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Matching process Stage 2 Determine all
combinations of exchanges
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Matching process Stage 2 Determine all
combinations of exchanges
1
1
2
2
5
5
3
4
3
4
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Matching process Stage 2 Determine all
combinations of exchanges
1
1
2
2
5
5
1
3
4
3
4
2
5
3
4
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Matching process Stage 2 Determine all
combinations of exchanges
1
1
2
2
5
5
1
3
4
3
4
2
5
1
3
4
2
5
3
4
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Matching process Stage 2 Determine all
combinations of exchanges
1
1
2
2
5
5
1
3
4
3
4
2
5
1
1
3
4
2
5
2
5
3
4
3
4
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Matching process Stage 3 Optimum combination
1
1
X
2
2
5
5
1
X
X
3
4
3
4
2
5
1
1
X
X
X
3
4
2
5
2
5
X
3
4
3
4
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Matching process Stage 3 Optimum combination
1
X
2
5
1
X
3
4
2
5
3
4
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Prioritisation factors
To determine who is transplanted and who donates
to whom Blood group match Local
exchange Sensitisation Tissue type match Age
difference between the 2 donors
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Simulations
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Simulations

• Having identified relevant factors, simulations
  were written in SAS and were used to inform
  decision-making on
• effective waiting list sizes
• appropriate weights for prioritisation factors
• likely chance of transplant for different types
  of patient
• Simulations based on real data from 20 centres
• 400 transplants that could not proceed over
  2-year period due to blood group and/or tissue
  type incompatibility

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Simulations

• The SAS simulation program
• selects a stratified random sample, ensuring an
  even mix of blood group and tissue type
  incompatible couples
• Identifies all possible two-way exchanges,
  ensuring that the donors and recipients are blood
  group and tissue type compatible in both sides of
  the exchange
• Determines the priority score for each of the
  two-way exchanges, based on weights specific to
  each simulation
• Determines all combinations of exchanges (or a
  subset of combinations when dealing with large
  pool sizes)
• Determines the optimum combination of exchanges
  (highest overall priority score), ensuring that
  each donor and recipient is not involved in more
  than one exchange
• 10 simulations for each scoring system and pool
  size

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How many couples are needed?
Maximum transplanted
10 simulations were run for each pool size, using
a stratified random sample
No. of couples on list
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Prioritisation factors

• How many points for
• Local exchange (based on 5 areas of the UK)
• HLA match (4 levels)
• Sensitisation ( of blood group identical donors
  having antigens which are declared unacceptable
  for the recipient pool of 10,000)
• Age difference between the 2 donors
• Blood group match consider restricting use of O
  donors
• Identify combination of transplants with highest
  sum of point scores for individual transplants

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Proposed scheme - results
Based on single factor scoring
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Proposed scheme - results
Based on single factor scoring
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Proposed scheme - results
Based on single factor scoring
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Proposed scheme - results
Based on single factor scoring
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Proposed scheme - results
Based on single factor scoring
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Agreed national matching scheme

• Points for each possible transplant in a
  combination -
• Local exchange 20 points
• Sensitised patient 0-50 points for 0-100
  sensitised
• HLA matched transplant 015 points for levels 4
  to 1, respectively
• Small donor-donor age difference 3 points if
  lt20 years
• Also - restrict use of group O donors to group O
  recipients only
• The highest scoring combination is identified
• The maximum possible number of transplants will
  be achieved
• Note at registration, HLA match and donor age
  requirements can be specified

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Who is most likely to find a match?
Based on 200 simulations of 30 couples, average
transplant rates in the first matching run are
- 23 blood group incompatible 34 HLA
incompatible Among HLA incompatibles
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Who is most likely to find a match?
Blood group incompatible
Tissue type incompatible
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Where are we now?
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Matching run summary
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Matching run summary
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Matching run summary
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Matching run summary
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Matching run summary
3-way exchanges considered in April 2008 run
onwards, following agreement from the Kidney
Advisory Group
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Pooled donation
2-way exchange 3-way exchange
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Matching run summary
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Matching run summary
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Matching run summary
Transplants did not proceed for various reasons
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Blood group composition of October 2008 list
Many more A donors than A, AB recipients
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Degree of sensitisation for patients on October
2008 list
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Future development
Domino paired/pooled donation
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www.uktransplant.org.uk

• joanne.allen_at_nhsbt.nhs.uk

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Thank You