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:

• Probability that a randomly selected person of race z has no match in the registry is

x

Rxi

xp )1(

x

Rxi

i

zi

xpp )1(

Differences by Race

Race Number in Registry

Fraction 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

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

Race of Additional Registrant

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 matchActual 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) h

P(Asked|Reg) 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.

• For optimal registry registrants need to be 3 times as generous and there need to be 2 to 5 times as many of them.

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.