1. No category

Statistical interpretation of
DNA mixtures
Thore Egeland
Copenhagen April 20-23 2015
Mixtures
1
Repetition: TH01
Pr( E | Hp )
1
=
LR2 =
Pr( E | Hd ) 2 p6 p7
1
= 11.34
2*0.21*0.21
Mixtures
2
Likelihood ratio: Interpretation (LR)
=
LR LR
=
10.87 *11.34
= 123
1 LR2
«I have considered two hypotheses. The data is 123 times
more likely assuming the victim and the suspect to be the
contributors compared to the victim and an unknown,
unrelated person»
Mixtures
3
Drop-in and drop-out
• Drop-in and drop-out are stochastic phenomena that appears in low
template DNA
• Drop-out: an allele fails to amplify (below detection level)
• Drop-in: False allele
– Not reproducible
• Drop-in is not the same as contamination
– Drop-in events occur independently for markers as
opposed to contamination
Mixtures
4
Drop-out
• Evidence
1
• Suspect
1
2
Match? Then allele 2 must have
dropped out of the evidence
Mixtures
Gill ISFG 2013 workshop
5
Drop-out model
• Hp: Suspect
• Hd: Unknown
1
1
2
Suspect
Evidence
• Probability that an allele drops out = d
• Assumption, simplification:
–Alleles drop out independently
Mixtures
6
Example 1: LR with dropout
• Hp: Suspect
• Hd: Unknown
1
1
2
Suspect
Evidence
• For Hp to be true
–allele 2 in the suspect’s profile has dropped out
–allele 1 in the suspect’s profile has not dropped out
Mixtures
7
• Hp: Suspect
• Hd: Unknown
1
1
2
Suspect
Evidence
• For Hd to be true
– the unknown must have a genotype that
contains the allele 1, i.e.,
–either 1/1 and no dropout or
1/Q with Q dropping out
Mixtures
8
• Hp: Suspect
• Hd: Unknown
LR
1
1
2
Suspect
Evidence
Pr( E | H p )
(1 − d ) d
=
Pr( E | H d ) p12 (1 − d 2 ) + 2 p1 pQ (1 − d ) d
d
= 2
p1 (1 + d ) + 2 p1 (1 − p1 )d
pQ = 1 − p1
Mixtures
9
Numbers
Suspect
1
2
Evidence
1
• What is the effect of dropout probability and allele
frequency on LR?
• p1=0.23, pQ=0.77, d=0.05
LR
0.05(1 − 0.05)
=
0.68
2
2
0.23 (1 − 0.05 ) + 2 × 0.23 × 0.77 × 0.05(1 − 0.05)
Mixtures
10
Mixtures
11
Drop-in
• Evidence
1
2
• Suspect
1
Match?
Then allele 2 must have
dropped in to the evidence
Mixtures
Gill ISFG 2013 workshop
12
Example 2
• Evidence
• Suspect
1
2
1
c = drop in parameter =0.05
p1 = 0.21
cp2
Pr( E | suspect )
c
LR =
≈
= =
0.12
Pr( E | unknown) 2 p1 p2 2 p1
Mixtures
13
Mixtures
14
Example 3 Case C, Haned, Slooten, Gill,
suppl. 2012:
Drop-out and drop-in
• Suspect
7
9
• Evidence
9
10
Hp: Suspect
Hd: Unknown
Mixtures
15
Exact and approximate LR
• Formula included only to explain that LR is not exact with
both drop-out and drop-in
d
LR =
c
2 p9 (1 − d )
d (− p7 − p9 + d (−4 + p7 + 3 p9 )) 2
+
c
2
4(d − 1) p9
+O (c 3 )
d
≈
c for small c and d
2 p9 (1 − d )
= 0.0198
=
=
=
c 0.05,
p9 0.14)
(d 0.1,
Mixtures
16
Mixtures
17