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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 anti-conservative
• 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 Suspect Victim Victim Crime Stain Crime Stain Crime Stain Crime Stain
AMEL X Y X X X Y
D3S1358 15 16 16 18 15 16 18
VWA 16 16 16 16 16 16
D16S539 11 12 11 14 11 12 14
D2S1338 19 23 18 20 18 20
D8S1179 12 14 13 17 12 13 14 17
D21S11 26 27 29 34.2 26 27 29 34.2
D18S51 14 15 15 19 14 15 19
D19S433 14 16 13 15 13 14 15 16
TH01 7 9.3 6 9.3 6 9.3
FGA 24 27 21 23 21 23
Allele dropout Shared alleles (masking)
How many contributors?
Profile Summary tab in LRmix Studio
We can do a ‘traditional’ analysis with ‘mastermix’ excel spreadsheet
• D8 locus (4-allele)
• Mx=0.35
0.0001
0.001
0.01
0.1
1
0 0.2 0.4 0.6 0.8 1
Resid
ua
l
Mx (mixture proportion)
Residual analysis AB,CD
AC,BD
AD,BC
BC,AD
BD,AC
CD,AB
0.00
0.20
0.40
0.60
0.80
1.00
AB,CD AC,BD AD,BC BC,AD BD,AC CD,AB
Heterozygote balance
Genotype
Heterozygote balance
Serie1
Serie2
Three alleles with dropout
Marker Suspect Suspect Victim Victim Crime Stain Crime Stain Crime Stain Crime Stain
AMEL X Y X X X Y
D3S1358 15 16 16 18 15 16 18
VWA 16 16 16 16 16 16
D16S539 11 12 11 14 11 12 14
D2S1338 19 23 18 20 18 20
D8S1179 12 14 13 17 12 13 14 17
D21S11 26 27 29 34.2 26 27 29 34.2
D18S51 14 15 15 19 14 15 19
D19S433 14 16 13 15 13 14 15 16
TH01 7 9.3 6 9.3 6 9.3
FGA 24 27 21 23 21 23
Marker Suspect Suspect Victim Victim Crime Stain Crime Stain Crime Stain Crime Stain
AMEL X Y X X X Y
D3S1358 15 16 16 18 15 16 18
VWA 16 16 16 16 16 16
D16S539 11 12 11 14 11 12 14
D2S1338 19 23 18 20 18 20
D8S1179 12 14 13 17 12 13 14 17
D21S11 26 27 29 34.2 26 27 29 34.2
D18S51 14 15 15 19 14 15 19
D19S433 14 16 13 15 13 14 15 16
TH01 7 9.3 6 9.3 6 9.3
FGA 24 27 21 23 21 23
Using traditional notation, the profile is assigned to be 6,9.3,Q
The ‘7’ allele is below the LOD threshold = 30
0.001
0.010
0.100
1.000
0 0.2 0.4 0.6 0.8 1
Lo
g r
esid
ual
Mx
AA,BC
BB,AC
CC,AB
AB,AC
BC,AC
AB,BC
BC,AA
AC,BB
AB,CC
AC,AB
AC,BC
BC,AB
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
Locus drop-out Marker Suspect Suspect Victim Victim Crime Stain Crime Stain Crime Stain Crime Stain
AMEL X Y X X X Y
D3S1358 15 16 16 18 15 16 18
VWA 16 16 16 16 16 16
D16S539 11 12 11 14 11 12 14
D2S1338 19 23 18 20 18 20
D8S1179 12 14 13 17 12 13 14 17
D21S11 26 27 29 34.2 26 27 29 34.2
D18S51 14 15 15 19 14 15 19
D19S433 14 16 13 15 13 14 15 16
TH01 7 9.3 6 9.3 6 9.3
FGA 24 27 21 23 21 23
Marker Suspect Suspect Victim Victim Crime Stain Crime Stain Crime Stain Crime Stain
AMEL X Y X X X Y
D3S1358 15 16 16 18 15 16 18
VWA 16 16 16 16 16 16
D16S539 11 12 11 14 11 12 14
D2S1338 19 23 18 20 18 20
D8S1179 12 14 13 17 12 13 14 17
D21S11 26 27 29 34.2 26 27 29 34.2
D18S51 14 15 15 19 14 15 19
D19S433 14 16 13 15 13 14 15 16
TH01 7 9.3 6 9.3 6 9.3
FGA 24 27 21 23 21 23
Marker Suspect Suspect Victim Victim Crime Stain Crime Stain Crime Stain Crime Stain
AMEL X Y X X X Y
D3S1358 15 16 16 18 15 16 18
VWA 16 16 16 16 16 16
D16S539 11 12 11 14 11 12 14
D2S1338 19 23 18 20 18 20
D8S1179 12 14 13 17 12 13 14 17
D21S11 26 27 29 34.2 26 27 29 34.2
D18S51 14 15 15 19 14 15 19
D19S433 14 16 13 15 13 14 15 16
TH01 7 9.3 6 9.3 6 9.3
FGA 24 27 21 23 21 23
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 Untick the box Ignore PrD for time being
Don’t forget to set number of unknown contributors
• 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)
Set drop-in and theta
Do sensitivity analysis to work out the lower bound PrD
Now plug the lowest PrD value into the model on the analysis tab
Both tabs must be activated
consecutively
A table can be printed from the report tab
Analysis screen
Note low LR
Don’t forget to set all These parameters to be the same
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
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