One Chance in a Million:
Altruism and Bone Marrow Donation
Ted Bergstrom, Rod Garratt,
Damien Sheehan-Connor
Univ of California
Santa Barbara
Background
• Bone marrow transplants dramatically improve
survival prospects of people with leukemia and
other blood diseases.
• For transplants to work, donor must be a genetic
match for recipient.
• Only 30% of patients have matching sibling.
Others must seek match in population at large.
• Institutional solution: National bone marrow
registries.
Probability of a match
• There are about 20 million distinct types
• Probability that two random people match
–
–
–
–
Both US Caucasian : 1/11,000
Both Afr-American: 1/98,000
Both Asian-American: 1/29,000
Afr Am and Caucasian : 1/113,000
• Contrast to kidney and blood donations.
– Hardest type to match can accept from 7% of
population
Distribution of type size is very
nonuniform
• About half the Caucasian population are in
types of frequency smaller than 1/100,000.
• About 20 per cent are in types of frequency
smaller than 1/1,000,000.
• African Americans’ types are even more
diffuse.
Bone Marrow registry
• Bone Marrow Registry contains 4 million people
in US and roughly 10 million worldwide
• Registrants promise to donate to any needy person
if called upon to do so. (not a binding contract)
• Registry collects saliva sample, does a DNA test
for HLA type and records registrant’s contact
information.
Cost to donor
• Traditional method, bone marrow transplant.
– Harvested with large needle stuck into pelvis.
– Anesthesia and overnight stay at hospital.
• Alternative method, drugs administered, then
blood filtered from bloodstream.
• Either method involves some risk and a few
days of not feeling good.
• Beneficiary is almost always a total stranger.
Research Questions
• Is the bone marrow registry large enough?
– A Benefit-Cost Analysis
• What motivates donors?
– A Peculiar Free Rider Problem
– Non-consequentialist altruism?
• How to achieve an optimal registry?
– Are money payments needed?
– International sharing
Some Genetic Background
• Individuals “type” is controlled by 6 alleles,
located in three loci, called HLA-A, HLA-B and
HLA-DR.
• You inherit a string of 3 from Mom and another
string of 3 from Pop.
• Diploid reproduction, each parent has two strings,
randomly picks one to give to you.
• String inherited from a single parent called a
haplotype.
Your most likely match
• Probability that two full siblings match is
about 1/4. They must receive same string
from Mom and also same string from Pop.
Chance of this is 1/2x1/2=1/4.
• Note that chance of a match with a parent is
very small. Same for uncles and aunts and
cousins, etc.
Estimating match probabilities
• Biologists used data from a sample of bone
marrow registrants to estimate the distribution of
HLA types in population for each race.
• They estimated distribution of haplotypes by
maximum likelihood.
• With estimated haplotype distribution and
assumption of random mating w.r.t HLA type, one
can estimate distribution of full distribution of
types by race.
Benefits from an additional donor:
Behind the Veil of Ignorance
• Every person in society faces some small
probability of needing a life-saving transplant.
• Adding a donor increases the probability of a
match for anyone.
• We calculate effect of an extra registrant on
lives saved and value this increment at the
“value of a statistical life” .
• VSL estimated to be about $6.5 million
(Viscusi-Aldy)
Probability of having no match
• Let pix be fraction of the population of race x that
is of HLA type i.
• Probability that a person of type i has no match in
of any race in the registry is:
(1  p
x Rx
i
)
x
• Probability that a randomly selected person of race
z has no match in the registry is
z
x Rx
p
(
1

p
 i i)
i
x
Differences by Race
Race
Number in Fraction
Registry
Available
Effective No.
in Registry
Prob. of no
Match
Caucasian
4,444,335
.65
2,888,818
.08
Afr-Am
485,791
.34
165,169
.38
Asian-Am
432,293
.44
190,209
.21
Hispanic
594,801
.47
279,556
.16
Nat. Am.
70,781
.48.
33,975
.11
Gain from extra registrant of race x
• Calculate the derivative with respect to Rx
of the probability of no match.
• Multiply this by the number of people
seeking matches to find the expected annual
number of additional matches resulting
from one more registrant.
• Multiply number of additional matches by
.21 to get expected number of lives saved.
Annual flow
• A registrant can remain in registry until age 61.
• Median age of registrants is 35.
• We assume that registrants remain in registry
for 25 years, on average.
• We discount benefits appearing in later years.
Present Value of Lives Saved by
Additional Registrant
Race of Additional Registrant
Present value
to this group
Caucasian
Afr- Am
Asian -Am
Hispanic
Nat Am
Caucasian
$1,012
$961
$664
$1,028
$928
Afr-Am
$71
$3,155
$81
$285
$150
Asian-Am
$27
$44
$1,063
$60
$59
Hispanic
$91
$341
$132
$701
$190
Nat Am
$5
$10
$8
$11
$37
Total Value
$1,206
$4,512
$1,947
$2,085
$1,364
Costs
• Cost of tests and maintaining records about
$105 per registrant.
– Usually paid for by registry.
• Physician and hospital costs of transplants
is around $166,000.
Effective Registry
• Need to register more than one person to
make one effective registrant
• Varies by race (Kollman et al.)
– 1.6 Caucasians
– 2.9 Afr. Am.
• Inflates costs differently across races
• Also number of transplants resulting from
registrant differs across race
Benefit Cost Comparison:
Present values of new registrant
Caucasian Afr- Am
Asian- Am
Hispanic
Nat Am
Benefit
$1,206
$4,512
$1,947
$2,078
$1,364
Cost
$297
$800
$446
$455
$359
B/C Ratio
4.1
5.6
4.4
4.6
3.8
Optimal Registry Sizes
• Larger registry is called for on efficiency grounds
• As registry gets larger new registrants add less
• Calculating optimal registry is complicated by
cross matches
• In optimal registry the marginal benefit to persons
of all races from adding an additional registrant of
any race is equal to the marginal cost.
Actual and Optimal Registry;
Number in Millions
Race
Actual
Number
Optimal
Number
Ratio
Caucasian
4.44
(2.7%) 12.11
(7.1%)
2.72
Afr-Am
0.49
(2.4%) 4.73
(23.8%)
9.75
Asian-Am
0.43
(6.5%) 1.76
(26.5%)
4.07
Hispanic
0.59
(2.9%) 2.93
(14.3%)
4.93
No Match Probabilities
Race
Prob of no match
Actual Registry
Prob of no match
Optimal Registry
Caucasian
.08
.03
Afr-Am
.38
.12
Asian-Am
.21
.09
Hispanic
.11
.06
Racial equity?
• Not a Rawlsian minmax outcome.
• “Social optimum” reflects difference is in
number of people of each race seeking
transplants and differences in diversity of
HLA types within races.
Incentives and Voluntary Donations
• The standard equilibrium model of
voluntary contributions to public goods
does not apply:
– In standard model, people add to public goods
for their own benefit. Nobody gets gain from
own registration here.
– In standard model, individuals’ contributions
are perfect substitutes. Not true here.
A peculiar free rider problem
• It may be that you are the only match in
the registry for a needy patient, and hence
would save a life.
• It may be that there is another willing donor
of your type in registry.
• It may be that nobody of your type will
need a transplant.
What would Homo economicus Do?
• Our selfish old friend h.e. would contribute
nothing.
– So we are in unfamiliar territory for economists.
• Lets try making him nicer, but highly rational.
• Consequentialist altruist. Cares about the patient’s
outcome, not about social acclaim, or credit.
• If someone else wants to save the patient, he would
gladly defer.
Meditations of a Consequentialist
Altruist
Calculates the conditional probability h that if
asked to donate, he is pivotal (i.e., the only one of
his type in the registry.)
• Let C be the cost of donating.
• B the value of making a pivotal donation.
• Assume B>C and value of donating if not pivotal
is 0.
C.A’s calculations
• Will join the registry if and only if he
would donate if asked to.
• Where h is the conditional probability of
being pivotal, he will join registry if and
only if
hB>C
or equivalently
B/C>1/h
Probabilities of being asked and of
being pivotal if asked
Current Registry
Optimal Registry
Race
P(Asked|Reg)
Lifetime
P(Pivotal|Asked) P(Asked|Reg)
h
Lifetime
P(Pivotal|Asked)
h
Caucasian
.013
.08
.004
.03
Afr-Am
.005
.78
.001
.19
Asian-Am
.006
.30
.002
.11
Hispanic
.008
.22
.003
.08
How generous are donors?
• For Caucasians:
– current registry requires most generous 2.7% of
population to have B/C>12
– optimal registry requires most generous 7% to have
B/C>33.
• For African-Americans:
– current registry requires most generous 2.4% of
population to have B/C>5
– optimal registry requires most generous 24% to have
B/C>5.
Non-Consequentialist Motives
• Desire for acclaim.
– Problem with sign-up and refuse to donate.
– Probability that a registrant is ever asked is about 1%.
• Sense of obligation.
– Maybe people don’t feel that their contribution is less if
there was an alternative donor in wings.
Refocused Efforts
• The US bone marrow registry recruitment
strategy in recent years is to focus on recruiting
minority donors (numbers of new Caucasian
recruits falling since 1996, others rising)
• “Registry has developed to the stage where
racial diversity (quality) is a higher priority
than recruitment volume (quantity).”
Do we need to pay donors?
• You can join the registry by ordering a tissue-typing kit
online .
• But new registrants have to pay a fee of $52.
– Fees are likely to be waived for minorities and members of armed
services.
• An obvious first step: Government support to pay fees.
• A second step: Greater recruitment efforts.
• Survey of 360 UCSB students:
– 54% have heard of registry,
– 20% have considered joining,
– 6% have joined.
Other national registries
•
•
•
•
•
•
•
•
•
Percentage of eligible population registered
Israel 10%
Germany 7%
U.S. 2.7%
U.K 2%
Canada, Scandinavia, Italy1%
France, Netherlands, Switzerland 0.5%
Taiwan, Hong Kong 1.5%, Japan 0.5%,
Africa, Russia, Mexico, China , India ~0.
Observations
• Optimum for whites could be achieved if U.S.
and other European countries could approximate
German enrollment rates,
– German registrants are not paid.
• Poor countries where bone marrow transplants
are rare have negligible registries.
• Expanded registries in Asia, would improve
Asian-Americans’ chances.
• It is hard to see how to get African American
registries close to optimal without paying
donors.
Summary
• Benefit-cost analysis.
– Current registry has too few people of all races, but
U.S. charges new registrants $52.
– Especially short of African Americans
• Unusual form of free-rider problem raises
interesting questions about altruistic motives.
• German experience suggests that with no
charges and greater recruitment, optimal
registry for whites might be possible.
• For Asian -Americans, expansion of Asian
registries would be helpful.
• For African-Americans, payments to donors
may be needed.
Had enough?
OK,
I’m done.