Computing likelihood ratios using peak heights
Methods for comparing a first DNA profile with a second DNA profile are provided. The likelihood ratio for one hypothesis relative to another, as to the sources of the DNA, is conditioned on quantity of DNA in the test sample providing the first DNA profile and/or another sample providing the second DNA profile.
1. A computer implemented method of comparing a test sample result set with another sample result set, the method including:
obtaining a test sample and analysing the test sample to provide a test sample result;
providing information for the test sample result set on the one or more identities detected for a variable characteristic of DNA;
providing information for the another sample result set on the one or more identities detected for a variable characteristic of DNA, the another sample result having been obtained from another test sample by analysis;
establishing a likelihood ratio for one hypothesis relative to an alternative hypothesis, wherein the likelihood ratio is defined as:
LR
=
Pr
(
C
❘
S
,
H
p
)
∑
i
Pr
(
C
❘
U
i
,
S
,
H
d
)
Pr
(
U
i
❘
S
,
H
d
)
where: C is the test result set from a test sample, S is the another sample result set, H p is one hypothesis, H d is an alternative hypothesis, U i is one of the supposed sources stated in H d ;
wherein the likelihood ratio is conditioned on quantity of DNA in the test sample and/or another sample result set;
wherein the likelihood ratio is displayed to the user by the computer; and
wherein the method provides evidence as to the likelihood ratio of one hypothesis to another hypothesis, the one hypothesis being that advanced by the prosecution in the legal proceedings and the another hypothesis being that advanced by the defence in the legal proceedings.
2. The computer implemented method according to claim 1 in which the likelihood ratio includes a definition of the likelihood of observing the set of peak heights in C given a supposed source.
3. The computer implemented method according to claim 2 in which the likelihood ratio is defined as:
LR
=
f
(
C
❘
S
,
H
p
)
∑
i
f
(
C
❘
U
i
,
S
,
H
d
)
Pr
(
U
i
❘
S
,
H
d
)
where the f terms are factors that are likelihoods.
4. The computer implemented method according to claim 3 in which the factors f(C|S,H p ) and/or f(C|U i ,S,H d ) are definitions of the likelihood of observing the set of peak heights in C given a supposed source.
5. The computer implemented method according to claim 1 in which the comparison includes the consideration of the term: f(C|G), where G denotes the supposed source genotype.
6. The computer implemented method according to claim 5 in which the likelihood is computed by conditioning on DNA quantity, in the form:
f
(
C
❘
G
)
=
∑
j
f
(
C
❘
G
,
χ
j
)
Pr
(
χ
j
❘
I
(
h
)
)
(
1
)
where Pr(χ j |I(h)) is a probability distribution of DNA quantity, χ j , given peak height information, I(h).
7. The computer implemented method according to claim 5 in which the term f(C|G) is an estimation.
8. The computer implemented method according to claim 5 in which the term f(C|G) is derived from experimental data.
9. The computer implemented method according to claim 8 in which the term f(C|G) includes one or more probability distribution functions.
10. The computer implemented method according to claim 9 in which the probability distribution for Pr(χ j |I(h)) relates to a list of discrete probabilities for DNA quantities χ 1 to χ j , where
∑
j
Pr
(
χ
j
❘
I
(
h
)
)
=
1.
11. The computer implemented method according to claim 10 in which the probability distribution is obtained by considering an observed distribution from the analysis of control samples of DNA.
12. The computer implemented method according to claim 9 in which the probability distribution function is provided by estimating a two dimensional pdf for a pair of heights h 1 and h 2 , in the space defined by mean heights, m, and heterozygote imbalance, r.
13. The computer implemented method according to claim 12 , wherein each pair of heights is transformed by
(
h
1
,
h
2
)
↦
(
m
=
h
1
+
h
2
2
,
r
=
h
1
h
2
)
.
14. The computer implemented method according to claim 13 , wherein given a pdf f M,R , a pdf in the space of pairs of heights is obtained with the formula:
f
H
1
,
H
2
(
h
1
,
h
2
)
=
1
h
2
2
(
h
1
+
h
2
2
)
×
f
M
,
R
(
m
,
r
)
.
15. The computer implemented method according to claim 14 in which the factor
1
h
2
2
(
h
1
+
h
2
2
)
is the Jacobian of the transformation.
16. The computer implemented method according to claim 14 in which the factor
f M,R (m,r)
is estimated from experimental data.
17. A computer implemented method of comparing a test sample result set with another sample result set, the method including:
providing information for the test sample result set on the one or more identities detected for a variable characteristic of DNA;
providing information for the another sample result set on the one or more identities detected for a variable characteristic of DNA;
establishing a likelihood ratio for one hypothesis relative to an alternative hypothesis, wherein the likelihood ratio is defined as:
LR
=
Pr
(
C
❘
S
,
H
p
)
∑
i
Pr
(
C
❘
U
i
,
S
,
H
d
)
Pr
(
U
i
❘
S
,
H
d
)
where: C is the test result set from a test sample, S is the another sample result set, H p is one hypothesis, H d is an alternative hypothesis, U i is one of the supposed sources stated in H d ; and
wherein the likelihood ratio is conditioned on quantity of DNA in the test sample and/or another sample result set.
18. The computer implemented method according to claim 17 in which the likelihood ratio includes a definition of the likelihood of observing the set of peak heights in C given a supposed source.
19. The computer implemented method according to claim 17 in which the likelihood ratio is defined as:
LR
=
f
(
C
❘
S
,
H
p
)
∑
i
f
(
C
❘
U
i
,
S
,
H
d
)
Pr
(
U
i
❘
S
,
H
d
)
where the f terms are factors that are likelihoods.
20. The computer implemented method according to claim 19 in which the factors f(C|S,H p ) and/or f(C|U i ,S,H d ) are definitions of the likelihood of observing the set of peak heights in C given a supposed source.
21. The computer implemented method according to claim 17 in which the comparison includes the consideration of the term: f(C|G), where G denotes the supposed source genotype.
22. The computer implemented method according to claim 21 in which the likelihood is computed by conditioning on DNA quantity, in the form:
f
(
C
❘
G
)
=
∑
j
f
(
C
❘
G
,
χ
j
)
Pr
(
χ
j
❘
I
(
h
)
)
(
2
)
where Pr(χ j |I(h)) is a probability distribution of DNA quantity, χ j , given peak height information, I(h).
23. The computer implemented method according to claim 21 in which the term f(C|G) is an estimation.
24. The computer implemented method according to claim 21 in which the term f(C|G) is derived from experimental data.
25. The computer implemented method according to claim 24 in which the term f(C|G) includes one or more probability distribution functions.
26. The computer implemented method according to claim 25 in which the probability distribution for Pr(χ j |I(h)) relates to a list of discrete probabilities for DNA quantities χ 1 to χ j , where
∑
j
Pr
(
χ
j
❘
I
(
h
)
)
=
1.
27. A method according to claim 25 in which the probability distribution is obtained by considering an observed distribution from the analysis of control samples of DNA.
28. The computer implemented method according to claim 25 in which the probability distribution function is provided by estimating a two dimensional pdf for a pair of heights h 1 and h 2 , in the space defined by mean heights, m, and heterozygote imbalance, r.
29. The computer implemented method according to claim 28 , wherein each pair of heights is transformed by
(
h
1
,
h
2
)
↦
(
m
=
h
1
+
h
2
2
,
r
=
h
1
h
2
)
.
30. The computer implemented method according to claim 29 , wherein given a pdf f M,R , a pdf in the space of pairs of heights is obtained with the formula:
f
H
1
,
H
2
(
h
1
,
h
2
)
=
1
h
2
2
(
h
1
+
h
2
2
)
×
f
M
,
R
(
m
,
r
)
.
31. The computer implemented method according to claim 30 in which the factor
1
h
2
2
(
h
1
+
h
2
2
)
is the Jacobian of the transformation.
32. The computer implemented method according to claim 30 in which the factor
f M,R (m,r)
is estimated from experimental data.