Finding Stem Cell Donors For Mixed-Race PatientsTed 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.

Match Probability by Race

Race Effective No. in Registry

Prob. of no Match

Caucasian 2,888,818 .08

Afr-Am 165,169 .38

Asian-Am 190,209 .21

Hispanic 279,556 .16

Nat. Am. 33,975 .11

Some Genetic Background

• Individual’s type is controlled by 6 alleles, located in three loci, called HLA-A, HLA-B and HLA-DR.

• You inherit a string of 3 alleles from Mom and another string of 3 from Pop.

• Each parent has two of these strings and randomly picks one to give to you.

• String inherited from a single parent called a haplotype.

A1

B1

A2

B2

C1

C2

The crucial six-pack (phenotype):

Six alleles (all on the same chromosome) determine your immunity type. You have two of each color, one fromMom, one from Pop. Two persons are a match if they carry the same six-packs.

A1 B1

A2 B2

C1

C2

Could come from these haplotypes:

Parent 1

Parent 2

A2 B1

A1 B2

C1

C2

Or from these:

Parent 1

Parent 2

A2 B2

A1 B1

C1

C2

Or these:

Parent 1

Parent 2

Or any of eight such possibilities.

A Clever Trick

• Biologists used data from 300,000 bone marrow registrants to estimate the distribution of phenotypes (six-packs) in population.

• Since there are 20 million possible types, sample is way too small.

• They can not observe the strings between alleles (haplotypes). They only see six-packs.

• But they can estimate distribution of haplotypes in each racial group by maximum likelihood, assuming random mating within races.

A1

B1

A2

B2

C1

C2

Biologists see the distribution of these for each population group:

A1 B1 C1

They use maximum likelihood to estimate distribution the distribution of haplotypes most likely to yield the observed distribution of 6-packs.

A haplotype

Phenotypes from Haplotypes

• Assumed that mating is random within population groups, we can reconstitute an

estimated distribution of HLA types.

• This reconstituted distribution has many more types than the observed sample.

Calculation Method

• For each possible 6-pack (phenotype) – Find the 8 haplotype pairs that yield that 6-pack.– Probability of each pair is product of its haplotype

probabilities.– Add these 8 products.

• This sum is the probability of the 6-pack.

A1 B1 C1

A2 B2 C2

A1 B1 C2

A2 B2 C1

A1 B1 C1

A2 B2 C2

A1 B2 C1

A2 B1 C2

A1 B1 C1

A2 B2 C2

A2 B1 C1

A1 B2 C2

A1 B1 C1

A2 B2 C2

A2 B2 C1

A1 B1 C2

Phenotypes Distribution for Mixed Races

• Parents come from separate populations with different HLA type distributions.

• Child inherits one haplotype from each parent.

• His 6-pack is assembled by draws of two haplotypes, one from each distribution.

• Our method extends easily to this case.

Marrow Donors Rare For Mixed-Race Patients

Nick is looking for a bone marrow transplant. When his doctor found out that he was a quarter Japanese and three-quarters Caucasian, he said there is a zero percent chance of finding a donor.

“ (Persons..) whose ethnic background is a mix

of Asian and Caucasian are potential donors for Nick….one does not need to be 75% Caucasian and 25% Asian — any potential mix could work. While the most likely match would be from a person who is 75% Caucasian and 25% Japanese, it is absolutely possible that other combinations of Caucasian-Asian background in different proportions could work.”

Falling probability?

"The truth is, when people of different backgrounds marry and produce offspring, it creates more types that are harder to match," said Michelle Setterholm, NMDP’s director of scientific services. "The probability just gets lower when you have people of mixed ancestral DNA."

Is mixing ancestral DNA

Like mixing paint?

Not for HLA type

• You do not inherit an equal amount of HLA type from each of your four grandparents.

• You inherit your type from only two randomly chosen grandparents, one from your father’s side, one from your mother’s.

If 3 of your grandparents are Caucasian and 1 is Japanese

• With probability ½, your two HLA haplotypes come from Caucasians.

• With probability ½, one comes from a Caucasian and one from a Japanese.

Consequences

• If you are ¼ Japanese and ¾ Caucasian, your prospects of finding a match are better,

not worse than if you are half and half.• If you have no match in Caucasian registry,

your best prospect for a match is someone who is half and half, not ¼ and ¾.

A Cablanasian’s Prospects

Who can match the Tiger?• Tiger Woods is ¼ Caucasian, ¼ Black, and

½ Thai.• Does he need another Cablanasian ?

– Probability ½, Tiger has two Thai haplotypes.– Prob ¼, one Thai, one Caucasian haplotype– Prob ¼, one Thai, one Black haplotype.

• A Cablanasian is no more likely to match Tiger than a Thai, or either of two types of half -Thais.

Homework assignment:

What about Tiger’s children?

Hint: Another look at Elin

And Tiger’s Mom

Research Plan

• The only population groups for which we currently have estimates of the distribution of HLA types are the self-declared racial classifications of donors in the U.S.

• Our method will extend these estimates to mixed racial groups.

• Europe does not ask race, but does record regional origin. Work is being done to estimate distribution by geographic origin.

Seeking a Match when the registry fails

Pinpointing Likely Donors

• If a patient has no match in the registry– Doctors know what’s in his six-pack.

• Where should her friends look hardest to recruit new registrants?

A1

B1

A2

B2

C1

C2

What the doctors see

The immediate question• Among which population group(s) is a matchmost likely to be found.

• If we know the haplotype distributions in several population groups, we can find the probability of a match for our patient in any mixture of these groups.

How do we do this?• There are eight possible pairs of haploids that

could produce the observed 6-pack.• Let H be this set of 8 haplotype pairs (h,h*) and

let Pih be the frequency of haplotype h in race i.

• Then the probability that the observed 6-pack is found in a person with one parent of race i and one of race j will be

Sij=Σ (h,h*)εH Pih Pj

h *

Who to Target?

• If it is equally easy to get persons of any mixed combination, then the most effort should be spent per capita on recruiting persons of the racial mix i and j, that maximizes Sij.

• But the probability that a patient finds a match in a particular racial mix also depends on the size of the group. This probability is Sij Nij where Nij is the number of persons of mixed race i and j.

Nick’s case

. • About 10% of Caucasians have no match. Suppose

that fraction p of persons who are half Asian, half Caucasian find no match.

• Apply Bayes’ Law: Given that he found no match, probability that he has an unmatched Caucasian type is 1/(1+10p)>1/11.

• .

• Doctors found no match for him Maybe because he is of mixed race,but maybe he inherited his 6-pack is entirely from Caucasians.

But we can do better

• Since Nick’s type is known, we can find directly which mixed types are most likely to produce a match for him.

• With better detail about subpopulation type distributions, search could be sharply focused on persons of mixed heritage not only by nationality, but by regional origin of each parent.

Who to Target?

• If it is equally easy to get persons of any mixed combination, then the most effort should be spent per capita on recruiting persons of the racial mix i and j, that maximizes Sij.

• But the probability that a patient finds a match in a particular racial mix also depends on the size of the group. This probability is Sij Nij where Nij is the number of persons of mixed race i and j.

Had enough?

OK, I’m done.