Kidney Exchange

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Kidney Exchange

• Based on Al Roths notes for
• ASSA, January 2008

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Kidneys as commodities

• There are over 70,000 patients on the waiting
  list for cadaver kidneys in the U.S.
• Each human being has 2 kidneys and healthy
  individuals can live with just one kidney.
• How much are you willing to receive for one of
  your kidneys?
• There is a potential market herebut
• Section 301 of the National Organ Transplant Act
  (NOTA), 42 U.S.C. 274e 1984 states
• it shall be unlawful for any person to knowingly
  acquire, receive or otherwise transfer any human
  organ for valuable consideration for use in human
  transplantation.

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Kidney exchange

• Who can give a kidney?
• Two genetic characteristics play key roles
• Blood type and 2) Tissue type or HLA type
• This is a matching market (like houses,
  roommates, partners, employees, etc.) but
• Money is not allowed!!!!

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Compatibility I

• Type O kidneys can be transplanted into any
  patient
• Type A (B) kidneys can be transplanted into type
  A (B) or type AB patients
• Type AB kidneys can only be transplanted into
  type AB patients.
• Type O patients are at a disadvantage in finding
  compatible kidneys.
• And type O donors will be in short supply.

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Compatibility II

• Tissue type or HLA type
• Combination of six proteins, two of type A, two
  of type B, and two of type DR.
• Prior to transplantation, the potential recipient
  is tested for the presence of antibodies against
  HLA in the donor kidney
• The presence of antibodies, known as a positive
  crossmatch, significantly increases the
  likelihood of graft rejection by the recipient
  and makes the transplant infeasible.

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Kidney exchange--background

• In 2006 there were 10,659 transplants of cadaver
  kidneys performed in the U.S.
• In the same year, 3,875 patients died while on
  the waiting list (and more than 1,000 others were
  removed from the list as Too Sick to
  Transplant.
• In 2006 there were also 6,428 transplants of
  kidneys from living donors in the US.
• Families and Friends but
• Sometimes donors are incompatible with their
  intended recipient.
• This opens the possibility of exchange by
  matching another pair with and incompatible
  donorbut

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Incentives and congestion

• For incentives and other reasons, such exchanges
  have been done simultaneously.
• That means two surgeries happening at the same
  time.
• Usually also in the same hospital
• Why stopping at only two simultaneous surgeries?
• Logistically is very difficult to perform more
  than two at the same time
• Is there a big gain in doing more than two?

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Incompatible patient-donor pairs

• Long side of the market
• Pairs (patient-donor) that are hard to match
  looking for a harder to find kidney than they are
  offering
• O-A, O-B, O-AB, A-AB, and B-AB
• Short side of the market
• Pairs (patient- donor) that are easy to match
  offering a kidney in more demand than the one
  they need
• A-O, B-O, AB-O, AB-A, AB-B
• All of these would be different if we werent
  confining our attention to incompatible pairs.
• Increase the number of potential exchanges
  but...how much?

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Why Game Theory helped?

• Rank pairs according to priority matching
  Reflecting time and difficult compatibility
• Any priority matching mechanism makes it a
  dominant strategy for all patient-donor pairs to
• accept all feasible kidneys
• reveal all available donors
• With chains of three pairs we can achieve almost
  perfect efficiency
• Theorem every efficient matching of
  patient-donor pairs in a large market can be
  carried out in exchanges of no more than 4 pairs.
• only 4 blood types and
• AB is very rare

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Creating a Thick (and efficiently organized)
Market Without Money

• New England Program for Kidney Exchangeapproved
  in 2004, started 2005.
• Organizes kidney exchanges among the 14
  transplant centers in New England
• Ohio Paired Kidney Donation Consortium, Alliance
  for Paired Donation (Rees)
• 60 transplant centers and growing
• National (U.S.) kidney exchange?
• Enabling legislation passed the Senate (Feb. 15
  2007) and House (March 7, 2007)
• Still to be signed into law.
• It says that the valuable consideration clause of
  the NOTA "does not apply with respect to human
  organ paired donation."

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Thicker market and more efficient exchange?

• Establish a national exchange
• Make kidney exchange available not just to
  incompatible patient-donor pairs, but also to
  those who are compatible but might nevertheless
  benefit from exchange
• E.g. a compatible middle aged patient-donor pair,
  and an incompatible patient-donor pair with a 25
  year old donor could both benefit from exchange.
  
• This would also relieve the present shortage of
  donors with blood type O in the kidney exchange
  pool, caused by the fact that O donors are only
  rarely incompatible with their intended
  recipient.

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First NEAD chains Rees et al. 2007

• In July 2007, the Alliance for Paired Donation
  started the first of these chains when an
  altruistic donor in Michigan donated his kidney
  to a woman in Phoenix, Arizona.
• As of the end of September this first NEAD chain
  was at 4 transplants (M. in MI gave to B. in AZ
  whose husband R. gave to An. in Toledo, whose mom
  La. gave to Ce. in Columbus whose daughter Li.
  gave to G. in Columbus simultaneously with Ce.'s
  transplant, and now G's sister Av. is the next
  bridge donor) (3 bridge donors donated so far)
• The APD started a second NEAD chain on Dec 7,
  2007 with a NDD T who gave to D in Columbus
  whose daughter M gave to S in Orlando, whose
  daughter E flew to Toledo to give to R from
  Tennessee which didnt work, but she bridged
  instead to MT in Toledo, whose daughter A will be
  the next bridge donor (3 transplants so far, 1
  from a bridge donor)

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First NEAD chains Rees et al. 2007

• In July 2007, the Alliance for Paired Donation
  started the first of these chains

MI
OH
Toledo
M (altruistic donor)
Columbus
An (Patient)
Ans mon
Ce (Patient)
AZ
Ces daughter
B (Patient)
Bs husband
G (Patient)
Gs sister
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Centers (hospitals) are a problem

• Centers with matched pairs do not have an
  incentive to report those pairs
• What if one of those pairs is not matched
  immediately?
• Proposition It is possible to efficiently
  arrange matches so that each center can be
  guaranteed that all pairs that they can exchange
  themselves will be part of the efficient exchange
  selected.
• priority matching with Center-matched pairs
  designated by the center) given top priority.

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Conjecture

• With an appropriately designed Kidney Exchange
  (e.g. in which each hospital does not see the
  patient-donor pairs contributed by the other
  hospitals until a match is suggested) it will
  always/(almost always) be a best reply for each
  hospital to submit all of its pairs to the
  Exchange (after noting which ones could be
  matched internally).

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Kidney exchange summary

• Need a thick market
• So a national exchange will be better than
  regional exchanges
• Enabling legislation passed the Senate and House
  in 2007not yet signed into law
• kidney paired donation shall not be considered
  to involve the transfer of a human organ for
  valuable consideration...
• A national exchange will require overcoming
  incentive problems among transplant centers
  (which we see even in New Englands 14 transplant
  centers)
• Need to overcome congestion to be able to do
  3-way as well as 2-way exchange.
• There are big benefits to opening up kidney
  exchange to compatible patient-donor pairs also.
• Monetary exchange is repugnant