How TrueAllele® Works (Part 3)
Kinship, Paternity and Missing Persons
Cybergenetics Webinar
December, 2014
Mark W Perlin, PhD, MD, PhD
Cybergenetics, Pittsburgh, PA
Cybergenetics © 2003-2014
Kinship
Task. Infer genotypes and match them
Tool. Bayes theorem
Data. Genotypes of family members
Bayes theorem
posterior µ likelihood ´ prior
Pr ( X = x data) µ Pr ( data | X = x) ´ Pr ( X = x)
Pedigree
father
F
mother
M
person
X
child1
C1
spouse
S
child2 child3
C2
C3
Prior probability
How a variable is affected
father
F
aa
mother
M
ab
person
X
Pr ( X = x F, M )
Prior probability
father
F
aa
mother
M
bc
person
X
Pr ( X = x F = aa, M = bc)
Punnett square
b
c
a
ab
ac
a
ab
ac
X = ab
1/2
ac
1/2
Likelihood
How a variable affects others
Pr ( C | X = x,S)
person
X
spouse
S
bb
child
C
ab
Likelihood
Pr ( C = ab | X = x,S= bb)
ìaa,1
ì
L = ìaa,1 2
ìaa,0
ì
person
spouse
X
S
aa
bb
aa child
aa
C
ab
Posterior probability
Pr ( X = x C,S, F, M ) µ Pr ( C | X = x,S) ´ Pr ( X = x F, M )
father
F
aa
mother
M
bc
person
spouse
X
S
bb
child
C
ab
Posterior probability
Pr ( X = x C,S, F, M ) µ Pr ( C | X = x,S) ´ Pr ( X = x F, M )
father
F
aa
mother
M
bc
person
spouse
X
ìab,1 2
Pr ( X = x C,S, F, M ) = ì
child
ac,1
2
ì
C
ab
S
bb
Pr ( C = ab | X = x,S= bb) ´ Pr ( X = x F = aa, M = bc)
Genotype comparison
alleged
person
A
ab
father
F
aa
mother
M
bc
person
spouse
X
ìab,1 2
ì
child
ac,1
2
ì
C
ab
S
bb
Bayes theorem, second round
Hypothesis: The missing and reference
persons are the same individual
O( H C,S, F, M )
LR =
O( H )
Pr ( X = ab C,S, F, M )
=
Pr ( X = ab)
Posterior to prior genotype probability ratio (Essen-Moller, 1938).
Match strength
Pr ( X = ab C,S, F, M )
LR =
Pr ( X = ab)
12
=
2 pa pb
1
=
4 pa pb
Paternity
biological
father
spouse
S
X
child
C
Paternity genotype
D7S820
Genotype comparison
alleged
father
biological
father
A
X
spouse
S
child
C
Paternity index
10,10
LR = 3.28
log(LR) = 0.52
LR = 258,000
log(LR) = 5.41
Paternity
Maternity question
biological
mother
X
child
C
alleged
mothers
A1
A4
A2
A5
A3
A6
Biological mother genotype
biological
mother
X
child
C
Identifying the mother
A1
A2
A3
A4
A5
A6
Missing person
1
person
X
child1
C1
1+2
child2 child3
C2
C3
1+2+3
Children + Spouse
1
person
X
child1
C1
spouse
S
child2 child3
C2
C3
1+2
1+2+3
Parents + Children
father
F
mother
M
person
X
child1
C1
1
1+2
child2 child3
C2
C3
1+2+3
Parents + Children + Spouse
father
F
mother
M
person
X
child1
C1
spouse
S
child2 child3
C2
C3
1
1+2
1+2+3
DNA mixture
Mixture + Kinship
father
F
person
X
Mixture + Kinship genotypes
CSF1PO
Separated minor contributor
Kinship inferred son
Random person
Contributor genotype match
LR = 39,700
log(LR) = 4.60
mixture
å
xÎG
kinship
Pr ( X = x dM ) Pr (Y = x dK )
Pr ( X = x)
population
-18.00
-20.58
-20.66
-20.76
-22.00
-24.00
-24.00
-24.97
-26.00
-28.00
How TrueAllele Works
Part 1, 16-Oct-2014
Genotype modeling and the likelihood ratio
Part 2, 20-Nov-2014
Degraded DNA and allele dropout
Part 3, 18-Dec-2014
Kinship, paternity and missing persons
Part 4, 15-Jan-2015
Genotype database and DNA investigation
http://www.cybgen.com/information/webinar/page.shtml
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