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The Probability of Finding a Suitable Related Donor for Bone Marrow
Transplantation in Extended Families
By R.F. Schipper, J. D‘Amaro, and M. Oudshoorn
In bone marrow transplantation, the advantages of family
donors over unrelated donors are threefold. (1) Family donors are better matched because they share complete haplotypes. (2) The time between thestart of the search and the
actual transplantation can be much shorter than for unrelated donors. (3) Related bone marrow transplantation is
cheaper. We developed a procedure for calculating the probability of finding a suitable donor among cousins and bloodrelated aunts and uncles (the extended family). The procePthat any
dure calculates the followingprobabilities ( P ) : (I)
blood-related uncle or aunt is a suitable donor, (2) P that a
suitable donor exists in all blood-related uncles/aunts (from
T
HE COMMON PROCEDURE in the search for a bone
marrow donor for a particular patient is first toexamine
the patient’s parents, brothers, and sisters in search ofan
HLA-identical donor. If no identical individuals are found,
then the search for an unrelated donor is started. The possibility of potential donors in the extended family is ignored.
The chance of finding a suitable donor among those aunts,
uncles, and cousins can be much higher than in an unrelated
donor pool, depending on the relative size of these two
groups and the haplotypes involved. We present a procedure
for calculating the probability of finding suitable donors in
extended families using the frequencies of the patient’s haplotypes in the general population. These haplotypes represent
two of the eight grandparental haplotypes. Because the procedure does not require typing of the grandparents, the remaining six grandparental haplotypes are treated as unknown
(Fig 1).
DEFINITIONS
The nuclear family consists of the parents and siblings of
the patient. The extended family consists of first cousins and
blood-related uncles and aunts of the patient. An identical
family member is one who shares one HLA-haplotype with
the patient and one extended haplotype. An extended haplotype is a specific combination of alleles from different loci
that are in significant linkage disequilibrium in chromosomes
of unrelated individuals.‘
From the Department of ImmunohematologyandBlood
Bunk,
EuropdonorFoundation,LeidenUniversityHospital,Leiden,
The
Netherlands.
Submitted May 22, 1995; accepted August 29, 1995.
Supported in part by the J.A. Cohen Institute for Radiopathology
and Radiation Protection (IRS).
AddressreprintrequeststoR.F.Schipper,MSc,Department
of
Immunohematology and BloodBank, Bldg I E3-Q, Leiden University
Hospital, PO Box 9600, 2300 RC Leiden, The Netherlands.
The publication costs of this article were defrayed
in part by page
chargepayment. This article must thereforebeherebymarked
“advertisement” in accordance with I8 U.S.C. section 1734 solely to
indicate this fact.
0 1996 by The American Society of Hematology.
0006-4971/96/8702-0013$3.00/0
800
[Ill, (3) Pthat any cousin is a suitable donor (as in [l]), (4)
P that a suitable donor exists in all cousins (from [3]), (5) P
that a suitable donor exists in the entire extended family
(from [21 and 141). Additionally, we discus thesuitability of
this procedure in the daily practice of donor procurement.
The procedure is also suitable to search for family donors
who have a single antigen mismatch with the patient. We
also discuss the differences between our method and the
one recently describedby Kaufman (Bone Marrow Transplant 15:279, 1995).
0 1996 by The American Society of Hematology.
MATERIALS AND METHODS
Description of the procedure. We follow the convention of labeling the haplotype that the patient inherited from his father as A
and the haplotype that he inherited from his mother as C. The frequencies (HF) of those haplotypes areused to calculate the probability that an extended family member exists with haplotypes A and
C. The haplotypes B and D, which are not inherited by the patient,
are assumed to be any haplotype that is neither A nor C. Thespecial
case in which any parent of the patient is homozygous is discussed
in the section on homozygosity. The procedure
has two parts, ie.
phase I for uncles and aunts and phase I1 for cousins.
Phase I: uncles and aunts.
This phase calculates the probability
of an identical family member among the blood-related uncles and
aunts of the patient. The calculation consists of three parts.
of the probability ( P ,) that a
Part 1 consists of the calculation
sister or brother of the father is AC, using the fact that the father
inheritedAfromonegrandparent
of thepatientand B fromthe
other grandparent of the patient and that the two other haplotypes
of the father’s parents are unknown. AC individuals can therefore
result from several grandparental mating types, as shown illustrated
in Table 1 (where N is not A and not C). P I is therefore calculated
usingtheequation: P , = .25 X HF, + .5 X HF, X HF,. Part 2
consists of the calculation of the probability ( P , ) that a sister or
brother of the mother is AC: P , = .25 X HF, + .S X HFA X HF,.
Part 3 consists of the combination of P, and P , into a combined P
forallblood-relatedunclesandauntsasfollows:
PI = I - ( I P , ) , , x (1 (equation l ) , where N , and N2 arethenumber
of brotherslsisters of the father and mother, respectively.
Phuse II: cousins. Thesecondphasecalculatestheprobability
of finding a cousin with the same haplotypes as the patient. Table
2 gives the different mating typesof uncles and aunts that can result
of expected AC
in AC cousins of the patient and the percentage
offspring. N again denotes any haplotype but A or C. The chances
of the occurrence of the five haplotypic combinations AN, AA, AC.
that is non-bloodCC.and CN aredifferentfortheuncle/aunt
related to the patient and the uncle/aunt that is blood-related to the
patient. For thenon-blood-relateduncle/aunt,theseprobabilities
equal the product of the haplotype frequencies: PAN= 2 X HFA X
HF,, where HF, = ( I - HF, - HF,.); f A A = HFAZ;PAC = 2 X
HF, x HF,; P,, = HF,’; Pc, = 2 x HFc x HF,. For the bloodrelated uncldaunt on the fathers side, these probabilities are calculated as follows: PAN= .25 + .25 X HF, + .25 X HF, t .5 X HFA
X HF,; PAA= .25 X HFA + .25 X HF,’; P,,. = .25 X HFr + .S
X HF, X HFc; PCc
.25 X HFC’; PC, = .25 X HF,. + .5 X HFv
x HF,. These differ from the non-blood-related side because one
of the grandparents must have A(we will call this thefirst grandparent) and the other B (the second grandparent). We will explain the
Blood, Vol 87,No 2 (January 15). 1996: PP 800-804
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801
FINDING SUITABLE DONORSIN EXTENDED FAMILIES
Table 2. Percentage of Expected AC Offspring for Mating Types of
Uncles and Aunts That Can Yield AC Offspring
AN
AA
AC
cc
CN
25
50
25
~
AN
AA
AC
cc
CN
0
0
0
0
25
50
5025
50
25
50
100
50
50
100
50
50
25
0
0
0
0
Patients extended family
HFN; P A A = .25 X HFA’; P A C = .25 X HFA + .5 X HFA X HFc;
Pc, = .25 x HFc + .25 X HF,’; P C N = .25 + .25 X HF, + .25 X
H F N + .5 X H
F
, X H F N . The haplotypic combinations and their
corresponding percentages in the offspring are set out in Table 4. To
illustrate these calculations, we give an example: if the frequencies of
A, C, and N are . l , . l , and .S, respectively, then, for mating type
A N X A N on the father’s side, the probability of AN is 2 X HFA
x H F N = .l6 for the non-blood-related uncle/aunt and .25 + .5 X
P
a
u
m
/t
. l x .S + .25 x . l + .25 X .S = S15 for the blood-related uncle/
Fig 1. Exampleofanextendedfamily‘spedigree.
A,B andC,D
aunt; but, naturally, the percentage of AC offspring from that mating
denote the haplotypes of tho patient‘s father and mother, respectype = 0, making the contribution to the overall single cousin probatively. A question mark denotes unknown haplotypes. Numbers debility = 0. Mating type AN X CC on the mother’s side, with AN
note the number of children.
( P = HFA X HF, = .OS) as non-blood-related and CC ( P = .25 X
HF, + .25 x HF,’ = ,0275) as blood-related combination and a
50% probability of AC offspring, contributes .OS X ,0275 X .5 =
most complex one, PAN(also see the pedigree in Fig 1): .25 because
,001 1 to the overall single cousin probability.
the first grandparent must have A (at least once) and the second
Because the match probabilities of cousins from the same parents
must have B (at least once), resulting in a 25% probability of AB
are dependent, the chance of finding a matched cousin in a particular
offspring; .25 X HFA because the homozygous combination AA
family has to be calculated first. If Pj is the probability of the occur(with a probability of HF,) in the first grandparent combined with
rence of mating type j and 0,is the percentage of AC offspring of
BX (B with any other haplotype) in the second adds a 25%probabilthat mating type, then for mating type j in family i with Ni cousins,
ity of AB offspring; .25 X H F N because the (homozygous NN)
the probability of a matched cousin is as follows: Mi.j= P, X (1 combination B N in the second grandparent combined with A X in
[ l - O,],,) (equation 2).
the first, adds a 25% probability of AB offspring; .25 X H F A X H F N
In the total of J (n = 25) mating types, th9 probability of a matched
because the homozygous combination AA in the first grandparent,
cousin in family is as follows: Mi = ,SI Pj X (1 - [l - OjIN,)
combined with BN in the second grandparent, adds a 25%probability
(equation 3).
of A N offspring; .25 X HFA X HFN because the combination of BA
The overall probability of a matcped cousin in all families is then
in the second grandparent with A N in the first adds a 25%probability
calculated as follows: M = 1 - ,g, (1 - Mi) (equation 4). These
of AN offspring.
probabilities are calculated for the father’s and the mother’s side of
Table 3, with the possible haplotypic combinations of the grandthe family separately because of the difference in mating types (see
parents of the patient at the margins, shows how all the combinations
Tables 3 and 4, respectively) and the probabilities that they occur.
are formed. N denotes any haplotype that is not A or C, and a period
The probability Mr on the father’s side and M, on the mother’s side
denotes 0%. Each cell gives the percentages of AA, AC, CC, AN,
are combined into the overall probability (Pll) of finding an identical
and CN offspring, as follows: upper left, AA; center, AC; upper
cousin using equation 5: PII= 1 - (1 - M,) X (1 - M,) (equation
right, CC; lower left, A N ; and lower right, CN.
5).
Similarly, for the blood-related uncle/aunt on the mother’s side,
Overall probability. The final calculation yields the combined
the probabilities of the five haplotypic combinations that can lead
probability of finding an identical family member in uncles or aunts
F, X
to AC offspring are as follows: P A N = .25 X HFA + .5 X H
I
,
, g “ r @ p J - @
IIQ$*@g$j
m
Table 3. Haplotypic Combinations of the Father’s Grandparents,
With the Corresponding Percentages of AA, CC, AC, AN, and CN
OffsPrina (See Text for Emlanation1
Table 1. The Percentage AC Offspring for the Grandparental
Mating Types on the Father‘s Side
Known
Haplotype
1
A
A
A
Column totals
B
Unknown
Haplotype
B
A
C
N
-
.5
.25
.25
-
.25
.25HFa X HFc
.25HFc +
.25HFa X HFc
First Grandparent
B
0
AA
50
BN
AC
. .
. 25
. .
100
.
50
. 50 50
25
AN
25
25
.
.
25
.
25
25
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802
SCHIPPER, D‘AMARO, AND OUDSHOORN
Table 4. Haplotypic Combinations of the Mother‘s Grandparents
With the Corresponding Percentagesof AA, CC, AC, AN, and CN
Offspring (SeeText for Explanation1
EXTFAM, verllon 4
PIUIIlt &
t.
Patient
A-Al.88.DR3
B=AZ,B44,DR7
Both parents are heterozygous
First Grandparent
cc
CA
25
25
IDN150
501:
’
.
’
100
1 ’.
25
50
.
-
,07198
HF(C1- ,01007
HF (NI= ,91795
“4AUUU
CN
50
HF ( A )
50
Chanceof identical uncle/aunt (father‘s side):
Chance of identical uncle/aunt (mother‘s ride):
0.005752 (N- 2)
0.036378 IN- 2)
Total
chance
of
0.041920
identical uncle/aunt:
”C
Chance of ldentxal cousin (father‘s side):
Chance of rdentlcal cousin (mother’s side):
chance
Total
of identxal cousin:
0.014656 IN= 61
0.083048 (N- 61
0.096487
T
o
w
Total chance of ldentlcal donor:
0.134362 IN- 161
Fig 2. Example of program output.
(from phase I) and in cousins (from phase 11) using equation 6 : P
= 1 - ( l - P,) X (1 - P,,) (equation 6).
Homozygosity. When either parent of the patient is homozygous,
the probability offinding
a matched extended family member
changes accordingly. If the father has haplotypes AA, then Table 1
changes to Table 5. Because both grandparents have haplotype A,
an extra factor of .25 X HF, has to be added to the probability that
a blood-related uncle or aunt on the father’s side is AC, being the
probability of AC offspring from the combination of a possible
haplotype C in the first grandparent and the known haplotype A in
the second grandparent. This extra factor is placed at the right margin
of Table 5. Similarly, the probability that a blood-related uncle or
aunt on the mother’s side is AC increases by a factor .25 X HF,.
The equations for P , and P2 change to the following: P , = .5 X
HFc + .5 X HFA X HFc; P2 = .5 X HFA + .5 X HFA X HFc.
The probability that a first cousin is AC when the father of the
patient is homozygous changes, because the probabilities of the occurrence of the five haplotypic combinations AN, AA, AC, CC, and
CN change to the following: PAN= .5 X HF, + .5 X HFA X HFN;
PA, = .25 + .5 X H F A + .25 X HFA2;P,, = .S X HFc + .S X
HF, X HF,; PC, = .25 X HFcZ;P,, = .5 X HF, X HF,.
P,, and PACincrease, whereas PcNdecreases. P,, can either increase or decrease, depending on the frequencies of the haplotypes
involved. Pc, does not change. In general, the chance of inheriting
A via the blood-line increases, whereas that of inheriting C via the
blood-line decreases. The probability that a first cousin is AC when
the mother of the patient is homozygous changes accordingly, as
follows: P A N = .5 X HFA X HFN;PA, = .25 X HFAZ;PAC = .5 X
HF, + .5 X HFA X HF,;Pc, = .25 + .5 X HFc + .2S X HFc’;
PC., = .5 X HFN + .5 X HF, X HF,.
RESULTS
Figure 2 shows an example of the output of the program
based on a patient with one very frequent haplotype (HLA-
Al, -B& -DR3) and one less frequent haplotype (HLA-A2, B44, -DR7). The first section (Patient data) shows a summary of the input data with the haplotype frequencies. The
second section (Uncledaunts) shows the probability ( P l ) of
finding a suitable donor among the blood-related uncles and
aunts. The third section (Cousins) shows the results of calculating the probability (PI,)of a first cousin with haplotypes
A and C. The last section (Total) shows the overall probability of finding a suitable donor in the extended family. Note
that the combined probabilities in the second, third, and last
section are not the sum of the individual chances, but have
been calculated using equations 1, 5, and 6.
The higher frequency of haplotype A in this example results in a higher probability of finding a suitable donor in
the mother’s side of the family, wheretheless
frequent
haplotype C is inherited via the blood-line, whereas the probability that haplotype A is inherited by chance is quite high.
To illustrate the effectiveness of searching for extended
family donors, we looked at 20 donor searches that had been
performed for Dutch patients by the Europdonor Foundation.
Table 6 summarizes the results of these searches. Fourteen
of these patients had one HLA-A, -B, -DR haplotype, with
a high frequency in the Dutch Caucasoid population; the
remaining 6 had one HLA-A, -B or HLA-B, -DR haplotype
with a high frequency. In all cases, the family lineage with
the least common haplotype was searched first. The second
family lineage was only searched in one case, in which both
haplotypes were rather common. In the remaining cases, an
unrelated donor was searched instead. All donors were found
in the lineage with the least common haplotype.
Table 5. The Percentage of AC Offspring for the Grandparental Mating Types on the Father‘s Side
Known
Haplotype
1
A
A
A
Column totals
The father is homozygous.
4
A
A
Unknown
Haplotype
A
C
A
-
.5
.5
25
C
.5
N
.25HFn X.25HFc
HFc
+ .25HFn X
A
N
25
HFc
0
.25 X HFc
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FINDING SUITABLEDONORS
803
IN EXTENDEDFAMILIES
Table 6. Resub of Searching for Donors in the Extended Families
of 20 Dutch Caucasoid Patients
Average for
No. of
Extended Family
No. of
Members Tested
Found
Patients Found per Patient
No. of Patients
One
Whom
Antigen
an
Identical
Donor
Was
Donor
Was
No. of Patients
for Whom a
HLA
Mismatched
A. Patients with one frequent HLA-A, -B, -DR haplotype
14
3
6
B. Patients with one frequent HLA-A, -B, or -B, -DR haplotype
0
3
6
9.3
For the 14 patients with a frequent HLA-A, -B, -DR haplotype, an average of 6.4 family members was typed per patient. For 3 of these patients, an identical donor was found;
for 6 of these patients, a donor with one HLA mismatch was
found. For the 6 patients with a frequent HLA-A, -B or
-B, -DR haplotype, more family members had to be typed
(an average of 9.3 per patient). Although no identical donors
were found for them, a donor with one HLA mismatch was
found for 3 of them.
DISCUSSION
HLA-matched related donors are preferable to unrelated
donors because unrelated donors are merely matched at the
phenotypic level. Moreover, their phenotypes are usually
determined by serology, showing only part of the genetic
polymorphism.’ However, a related donor shares haplotypes
with the patient. A haplotype that is shared via the blood
line is completely identical for the HLA region, whereas
extended haplotypes are very likely to be completely identical.’ Also, family donors may be better matched for other
factors that are not routinely tested for, such as antigens
from minor histocompatibility loci. Additionally, the motivation of family members to act as donors is usually high, so
the availability of matched family donors probably exceeds
that of unrelated donors.
It is quite a common procedure to start searching for unrelated donors whenno identical family member has been
found in the nuclear family. The procedure described here
can be a motivating factor for the patient’s physician to
consider recruiting donors in the patient’s extended family.
In general, the larger the size of the extended family, the
more useful the search for identical related donors will be,
although the probability of finding one depends largely on
the frequencies of the haplotypes involved.
Our procedure is also usable for calculating the probability
that an extended family member exists that is mismatched
with the patient at one of the HLA loci. This can be performed by replacing the frequency of one of the haplotypes
by the frequency of the corresponding haplotype with one
B8
locus less, leaving out the locus for which a mismatch
is
allowed. For example, if one of the patient’s haplotypes is
HLA-A66, -B8, -DR3, then the calculation of the probability
B60misof finding an extended family member with a possible
B35
match for HLA-A on that haplotype can be made by using
the frequency of the HLA-B8, -DR3 haplotype in the general
population. The survival of a patient who received marrow
from a family donor who has only one antigen mismatch
with the patient may be equal to that of patients who received
marrow from an HLA-identical sibling3or from a phenotypically matched unrelated donor?
The increased probability of finding identical related donors as compared with identical unrelated donors is most
striking when one of the patient’s haplotypes has a very low
frequency in the population and the other haplotype has a
high frequency. Table 7 shows the probability of finding an
identical family member when one haplotype frequency is
less then 1 in 10,OOO, whereas the other haplotype is one of
the five most frequent haplotypes in the Dutch Caucasoid
population’ and for a hypothetical situation of exactly three
children per household ( 16 extended family members). Note
that the contribution to the overall probability of the family
lineage that inherited the common haplotype is negligible.
The probabilities in Table 7 are established entirely through
the family lineage that inherited the uncommon haplotype.
The side of the family that contributes most to the overall
probability is the side one should start examining. Any family members that are either too old or too young to act as
bone marrow donors should be left out of the calculations
by simply reducing the number of their category in the procedure.
It is imperative that haplotype frequency estimates are
derived in the same population, ie, ethnic group, that the
patient’s family belongs to. For haplotype frequencies to be
usedin this manner, the genes in the different HLA loci
in that population naturally should be in Hardy-Weinberg
equilibrium.
The method recently described by Kaufman‘ is different
from ours in several aspects. His model predicts only the
probability of finding a matched extended family member
who inherited one matching haplotype (A or C) from the
common grandparent. In the appendix of his report, Kaufman6 makes two assumptions that exclude from his model
the probability that the other haplotype of a grandparent is
A or C, leading to extra matched extended family members.
This assumption is reasonable, but even ifHFc is low
(Cl%), the contribution to the overall probability can be
more than negligible, especially when many extended family
members are available. Also, Kaufman’s model does not
take into account the possibility that either parent of the
Table 7. Minimal Probability of Finding an Identical Family Member
for the Five Most Frequent Haplotypes in the Dutch Caucesoid
Population Based on Three Children per Household
Haolotvpe
A1
A3
A2
A2
A3
07
B7
DR3
DR2
DR2
DR13
DR1
Haplotype
Freauencv
Probability of
an Identical
Family
Member
0.0720
0.0470
0.0238
0.0237
0.0214
11.3%
7.5%
3.9%
3.9%
3.5%
From www.bloodjournal.org by guest on June 18, 2017. For personal use only.
804
patient may be homozygous, which considerably changes the
probability of finding an identical extended family member.
Finally, it would have been quite useful if the model described by Kaufman had been built into a computer program,
making the calculations much easier than performing them
by hand.
The procedure we describe is very efficient. After identifying the haplotypes in the nuclear family and examining
the structure of the extended family, calculation is performed
in a matter of minutes. We plan to extend the procedure to
include nephews and nieces of the patient. We developed a
Personal Computer program, EXTFAM, that calculates the
probability that at least one identical family member exists
in the extended family of a patient. The program is available
on request to the corresponding author.
In conclusion, we describe a method for calculating the
probability of finding a haplotype-matched related donor
among the blood-related uncles, aunts, and first cousins of
a patient and provide a computer program that calculates
such probabilities for any combination of haplotype frequencies and family compositions. The use of family donors
avoids lengthy matching procedures and provides patients
with donors who are not only identical for determinants in
the matched loci but also for others in the unexamined loci.
SCHIPPER, D'AMARO, AND OUDSHOORN
ing family donor search results. We also thank E. Oudshoorn-van
Pallandt for fruitful discussions.
REFERENCES
1. Awdeh ZL, Eynon E, Stein R, Alper CA, Alosco SM,
Yunis
EJ: Unrelated individualsmatchedforMHCextendedhaplotypes
andHLA-identicalsiblingsshowcomparableresponses
in mixed
lymphocyte culture. Lancet 853, 1985
2. TiercyJM,Morel
C, FreidelAC,Zwahlen
F, Gebuhrer L.
Bttuel H, Jeannet M, Mach B: Selection
of unrelated donors for bone
marrow transplantation is improved by
HLA class I1 genotyping with
oligonucleotidehybridization.Proc
Natl AcadSci USA 88:7121.
1991
3. Hansen JA, Anasetti C, Petersdorf EW, Choo
SY, Mickelson
EM, Martin PJ: The status of clinical marrow transplantation and
current issues in donor matching, in Tsuji K, Aizawa M, Sasazuki
T (eds): HLA 1991-Proceedings of the Eleventh InternationalHistocompatibility Workshop and Conference. Oxford,UK. Oxford Science Publications, 1992, p 13
4. Anasetti C, Beatty PG, Storb R, Martin PJ, Mori M, Sanders
JE, ThomasED, Hansen JA: Effectof HLA incompatibility on graftversus-host disease, relapse, and survival after marrow transplantation for patients with leukemia or lymphoma. Hum Immunol 29:79.
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ACKNOWLEDGMENT
621:78,1991
6. Kaufman R: HLApredictionmodelforextendedfamily
The authors thank Drs M. Giphart and J.J van Rood for critically
reviewing the manuscript and the Europdonor foundation for provid- matches. Bone Marrow Transplant IS:279, 1995
From www.bloodjournal.org by guest on June 18, 2017. For personal use only.
1996 87: 800-804
The probability of finding a suitable related donor for bone marrow
transplantation in extended families [see comments]
RF Schipper, J D'Amaro and M Oudshoorn
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