Interpretation of a major/minor
mixture where the minor
contributor is evidential
Peter Gill and Hinda Haned
Introduction
• Yesterday we talked about how to intepret
mixtures using peak height information
• You will remember that when a profile is partial,
ie allele dropout has occurred, we resort to using
the F designation and the 2p rule.
• We accept this is nor ideal, and may be anticonservative
• So we need to introduce new models that can
deal with this.
Example
• Case circumstances
– Murder of woman by stabbing
– The knife was recovered at the crime-scene. It is
identified as the murder weapon and a profile was
obtained from the handle
– We condition the results under Hp on the suspect
and victim
– The suspect’s profile is minor, and there is allele
dropout, so it is incomplete
Crime stain
Load the sample files
Load the reference files
Comparison of reference and crime
stain profiles
Marker Suspect
AMEL
X
D3S1358
15
VWA
16
D16S539
11
D2S1338
19
D8S1179
12
D21S11
26
D18S51
14
D19S433
14
TH01
7
FGA
24
Suspect
Y
16
16
12
23
14
27
15
16
9.3
27
Allele dropout
Victim
X
16
16
11
18
13
29
15
13
6
21
Victim
X
18
16
14
20
17
34.2
19
15
9.3
23
Crime Stain
X
15
16
11
18
12
26
14
13
6
21
Crime Stain
Y
16
16
12
20
13
27
15
14
9.3
23
Crime Stain
Crime Stain
18
14
14
29
19
15
Shared alleles (masking)
How many contributors?
17
34.2
16
Profile Summary tab in LRmix Studio
We can do a ‘traditional’ analysis with
‘mastermix’ excel spreadsheet
• D8 locus (4-allele)
• Mx=0.35
AB,CD
Residual analysis
Heterozygote balance
AC,BD
AD,BC
1
Residual
0.1
0.01
0.001
0
0.2
0.4
0.6
0.8
1
BC,AD
1.00
BD,AC
0.80
CD,AB
0.60
Heterozygote
balance
0.40
Serie1
Serie2
0.20
0.00
AB,CD AC,BD AD,BC BC,AD BD,AC CD,AB
0.0001
Mx (mixture proportion)
Genotype
VWA
16
D16S539
11
D2S1338
19
D8S1179
12
D21S11
26
D18S51
14
Marker Suspect
D19S433
14
AMEL
X7
TH01
D3S1358
15
FGA
24
VWA
16
D16S539
11
D2S1338
19
D8S1179
12
D21S11
26
D18S51
14
D19S433
14
TH01
7
FGA
24
16
16
16
16
16
12
11
14
11
12
14
23
18
20
18
20
14
13
17
12
13
14
17
27
29
34.2
26
27
29
34.2
15
15
19
14
15
19
Suspect
Victim
Victim
Crime
Crime
16
13
15
13Stain Crime
14Stain Crime
15 Stain
16 Stain
Y
X
Y
9.3
6X
9.3
6X
9.3
16
16
18
15
16
18
27
21
23
21
23
16
16
16
16
16
to be 6,9.3,Q
12 Using
11traditional
14 notation,
11 the profile12is assigned 14
23
18 The20
20 threshold = 30
‘7’ allele is18below the LOD
14
13
17
12
13
14
17
1.00034.2
27
29
26
27
29
34.2
15
15
19
14
15
19
16
13
15
13
14
15
16
AA,BC
9.3
6
9.3
6
9.3
BB,AC
0.100 23
27
21
21
23
CC,AB
Three alleles with dropout
Log residual
But the evidence supports
S=7,9.3; V=6,9.3 (Hb>0.6;
Mx=0.3) so we can be sure
that the proposition under
Hp is reasonable.
Under Hd we evaluate all
possibilities for U using 6,9.3,Q
AB,AC
BC,AC
AB,BC
BC,AA
AC,BB
AB,CC
AC,AB
AC,BC
BC,AB
0.010
0.001
0
0.2
0.4
0.6
Mx
0.8
1
VWA
16
16
D16S539
11
12
D2S1338
19
23
Marker Suspect
Suspect
D8S1179
12X
14Y
AMEL
D21S11
26
27
D3S1358
15
16
D18S51
14
15
VWA
16
16
Marker Suspect
Suspect
D16S539
11
12
D19S433
14
16
AMEL
X
Y
D2S1338
23
TH01
719
9.3
D3S1358
15
16
D8S1179
12
14
FGA
24
27
VWA
16
16
D21S11
26
27
D16S539
11
12
D18S51
14
15
D2S1338
19
23
D19S433
14
16
D8S1179
12
14
TH01
7
9.3
D21S11
26
27
FGA
24
27
D18S51
D19S433
TH01
FGA
14
14
7
24
15
16
9.3
27
16
11
18
Victim
13
X
29
16
15
16
Victim
11
13
X18
6
16
13
21
16
29
11
15
18
13
136
29
21
16
16
16
14
11
12
14
20
Victim
Crime18Stain Crime20Stain Crime Stain
Crime Stain
17
12
13
14
17
X
X
Y
34.2
26
27
29
34.2
18
15
16
18
19
14
15
19
16
16
16
Victim
Crime 11
Stain Crime Stain
Crime Stain
Crime Stain
14
12
14
15
13
14
15
16
X20
X18
Y 20
9.3
6
9.3
18
1512
1613
18 14
17
17
23
21
23
16
1626
1627
34.2
29
34.2
14
1114
1215
14 19
19
20
1813
2014
15
15
16
17
126
139.3
14
17
9.3
34.2
2621
2723
29
34.2
23
Locus drop-out
15
13
6
21
19
15
9.3
23
14
13
6
21
15
14
9.3
23
19
15
16
D2 – alleles 19,23 are below threshold
FGA– alleles 24,27 are below threshold
Victim’s alleles are present, suspect’s alleles are present but dropped out under Hp.
Under Hd we assume that U= includes any allele as unknown contributor, using Q
designation
We are now ready to analyse complex
cases
• By remembering some simple guidelines we
can analyse very complex cases
• First step: develop hypotheses:
– Consider the casework circumstances
– Examine the epg
– How many contributors?
– Use info re. peak height (first day) to help your
assessment
– Its OK to evaluate several scenarios
Propositions
• The set of hypotheses (based on
casework circumstances):
–Hp: Suspect + victim 1
–Hd: unknown 1 +victim 1
Case assessment
• It seems reasonable to propose a two person
mixture
• We can carry out an assessment from day 1 to
estimate Mx, in order to confirm presence of
major/minor mixture.
• The minor contributor appears partial as there
are several alleles missing.
• There is also ‘masking’
Probability of drop-in
• The important thing to consider is that drop-in is an
‘independent’ event. It is not supposed to explain
away multiple ‘unknown’ alleles which are best
accommodated by including an ‘unknown’
contributor (ISFG guidelines)
• Consequently, invoking dropout to explain more than
two contaminant alleles is not recommended.
• To calculate Pr(C), simply divide number of
observations in negative controls by the total
number of negative controls analysed
Analysis
• We use LRmix Studio to estimate the PrD using
a qualitative estimator (described by Hinda
previously)
• Our assessment forms the basis of the model
Analysis screen
Ignore PrD for time being
Untick the box
Don’t forget to set number of unknown contributors
Set drop-in and theta
• This screen is just used to set the propositions in the first instance
• We have to do a sensitivity analysis next (it uses the information from this screen)
Do sensitivity analysis to work out the
lower bound PrD
Both tabs
must be activated
consecutively
A table can be printed
from the report tab
Now plug the lowest PrD value into the model on the analysis tab
Analysis screen
Don’t forget to set all
These parameters to
be the same
Note low LR
Results (from exported table)
• Note that D2,
TH01, FGA are not
‘neutral’ because
LR<1. Overall
LR=465.
How robust is the answer?
Please formulate your answer on the strength of the evidence
Strength of evidence
• LR=465(logs-33,-22,-10). Maximum = log -7.
(does this seem robust?)
Do we want to test more scenarios?
How to implement a major/minor
calculation with LRmix Studio
• Difference between LRmix and LRmix studio
• Whereas LRmix employs an average across all
contributors, LRmix Studio (analysis tab)
allows different PrDs to be set per contributor
• Usually we only consider this if there is a clear
major profile from a known contributor
• Example follows
Re-evaluate the evidence
• Examine epg
• Is it reasonable that the victim’s profile can be
attributed as a clear major profile?
• Remember we condition on the victim under
both defence and prosecution hypotheses so
we can just check to be sure that all alleles are
present
Profile summary tab
New sensitivity analysis
Switch off victim
Conditioned as
major profile
New analysis (conditioning on major
profile)
Note victim
Set to zero
Note greater LR
Non contributor performance test
Statement (using LRmix split drop
model)
• I have evaluated the proposition that Mr X is a contributor to the crime
stain Y compared to the alternative proposition that Mr X is not a
contributor to crime stain Y using the conditions defined in the LRmix
model. These conditions are as follows:
• a) Mr X and the victim are both contributors to the sample
• b) An unknown person and the victim are both contributors to the sample
• The evidence is 10,000 times more likely if the first proposition (a) is true,
compared to the alternative described by (b).
• Optional: This figure can be qualified with a test of robustness. To do this
we replace Mr X with a random unrelated individual and we repeat the
measurement of the likelihood ratio. We do this a total of 10,000 times,
with a different random individual each time.
• When this was carried out the greatest likelihood ratio observed was of
the order of 0.01
Exploratory data analysis
• Can we think a bit more about the profile
• What can we do to evaluate the evidence
further.
• Its clear that the loci with low LRs occur when
dropout of Suspect alleles are observed
• We cant assume neutrality
Exploratory data analysis
• For example, examination of the epgs show that
the FGA locus has alleles 24, 27 that are below
LOD=50 (falls within our definition of dropout).
• Expert opinion suggests it is not unreasonable to
suppose that these alleles are present and have
not strictly dropped out (also illustrates some
difficulties with strict rule-sets). They may be
exculpatory.
• Let’s see what happens if we plug these alleles
into the crime stain evidence?
FGA locus
Alleles 24 and 27 are clearly
visible but have dropped out
under our definition (<50rfu)
Illustration of effect of 2 new FGA
alleles using split-drop model
LR=6m (previous LR=10,000)
•
•
This illustrates that the FGA locus has a large effect on the overall LR It illustrates
the importance of using the model to explore the data
It would be a good idea to repeat the biochemical analysis (possibly using
enhancement) so that the alleles may be properly included in the report
Performance test
Summary
• We have shown:
– Interpretation of complex DNA profiles can be carried
out with a consideration of drop-out, drop-in and the
number of contributors
• The analysis shows which loci favour the defence
hypothesis as well as the prosecution hypothesis
• Sensitivity analysis demonstrates how sensitive
the data are to changes in probability of dropout
• We also suggest how evaluation can be improved
by further casework analysis
• Analysis allows us to understand what is going on