Probabilistic Software for Mixture Interpretation · Why are people moving towards probabilistic...
Transcript of Probabilistic Software for Mixture Interpretation · Why are people moving towards probabilistic...
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Probabilistic Software for Mixture Interpretation
Part I
Simone Gittelson, Ph.D.
WSP CLD Forensic DNA Continuing Education Day Burien, Washington
June 18, 2015
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Disclaimer Points of view in this presentation are mine and do not necessarily represent the official position or policies of the National Institute of Standards and Technology or the U.S. Department of Commerce. Certain commercial products are named in order to specify experimental procedures as completely as possible. In no case does such an identification imply a recommendation or endorsement by the National Institute of Standards and Technology, nor does it imply that any of these products are necessarily the best available for the purpose.
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Contents • introduction • the Likelihood Ratio • why probabilistic genotyping? • the Likelihood Ratio (yes, there’s more)
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Slide courtesy of Dr. John Buckleton 4
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Why are people moving towards probabilistic software for mixture interpretation?
It is a more powerful tool for supporting the inclusion of true
contributors and the exclusion of false contributors.
It uses more information, so it makes better use of the available information.
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Contents • introduction • the Likelihood Ratio • why probabilistic genotyping? • the Likelihood Ratio (yes, there’s more)
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Likelihood Ratio
7 8 9 10 {8,9}
person of interest (POI)
Is the POI a contributor to this
DNA mixture?
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Likelihood Ratio
{8,9}
person of interest (POI) The POI is a contributor.
The POI is not a contributor. 7 8 9 10
1) What is the probability of obtaining these DNA typing results if the POI is a contributor?
2) What is the probability of obtaining these DNA typing results if the POI is not a contributor?
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Likelihood Ratio
{8,9}
person of interest (POI)
7 8 9 10
1) What is the probability of obtaining these DNA typing results if the POI is a contributor?
contributors: POI and someone else
1 × 2𝑝7𝑝10
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Likelihood Ratio
{8,9}
person of interest (POI)
7 8 9 10
2) What is the probability of obtaining these DNA typing results if the POI is not a contributor?
Contributor 1 Contributor 2
7,8 9,10 2𝑝7𝑝8 × 2𝑝9𝑝10
7,9 8,10 2𝑝7𝑝9 × 2𝑝8𝑝10
7,10 8,9 2𝑝7𝑝10 × 2𝑝8𝑝9
8,9 7,10 2𝑝8𝑝9 × 2𝑝7𝑝10
8,10 7,9 2𝑝8𝑝10 × 2𝑝7𝑝9
9,10 7,8 2𝑝9𝑝10 × 2𝑝7𝑝8
�
= 24𝑝7𝑝8𝑝9𝑝10
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Likelihood Ratio
{8,9}
person of interest (POI)
7 8 9 10 24𝑝7𝑝8𝑝9𝑝10 2𝑝7𝑝10
=1
12𝑝8𝑝9 = 8.3333
if 𝑝8 = 0.1 and 𝑝9 = 0.1
It is 8.3333 times more probable to obtain these DNA typing results if the POI is a contributor than if the POI is not a contributor.
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Likelihood Ratio
{8,9}
person of interest (POI)
7 8 9 10
𝐸 12
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Likelihood Ratio
{8,9}
person of interest (POI) 𝐻𝑝: The POI is a contributor.
𝐻𝑑: The POI is not a contributor. 7 8 9 10
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What is the probability of obtaining these DNA typing results if the POI is a contributor?
What is the probability of obtaining these DNA typing results if the POI is not a contributor?
𝑃𝑃 𝐸|𝐻𝑝
𝑃𝑃 𝐸|𝐻𝑑
given The probability of obtaining these DNA typing results given that the POI is a contributor.
𝐿𝐿 = The probability of obtaining these DNA typing results given that the POI is not a contributor.
Likelihood Ratio (LR)
The probability that the POI is a contributor divided by the probability that the
POI is not a contributor.
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Likelihood Ratio (LR)
Pr (𝐸|𝐻𝑝)Pr (𝐸|𝐻𝑑)
0
∞
1
the DNA typing results are just as
probable if the POI is a contributor than
if the POI is not a contributor
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Likelihood Ratio (LR)
Pr (𝐸|𝐻𝑝)Pr (𝐸|𝐻𝑑)
0
∞
1
if 𝑃𝑃 𝐸|𝐻𝑝 > Pr 𝐸|𝐻𝑑
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Likelihood Ratio (LR)
Pr (𝐸|𝐻𝑝)Pr (𝐸|𝐻𝑑)
0
∞
1
if 𝑃𝑃 𝐸|𝐻𝑝 < Pr 𝐸|𝐻𝑑
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Contents • introduction • the Likelihood Ratio • why probabilistic genotyping? • the Likelihood Ratio (yes, there’s more)
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Why Probabilistic Genotyping?
𝐺𝑃𝑃𝑃 = {13,16} 13
14
15
275
103
325
ST
AT
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Binary LR
𝐺𝑃𝑃𝑃 = {13,16} 13
14
15
275
103
325
ST
AT
numerator of LR: 1 × 2𝑝14𝑝15 20
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Binary LR
𝐺𝑃𝑃𝑃 = {13,16} 13
14
15
275
103
325
ST
AT
denominator of LR (unrestricted): 12𝑝13𝑝14𝑝15 𝑝13 + 𝑝14 + 𝑝15 + 24𝑝13𝑝14𝑝15𝑝𝑄
denominator of LR (restricted): 2𝑝14𝑝15𝑝13 𝑝13 + 2𝑝14 + 2𝑝15 + 2𝑝𝑄 21
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unrestricted:
𝐿𝐿 =1 × 2𝑝14𝑝15
12𝑝13𝑝14𝑝15 𝑝13 + 𝑝14 + 𝑝15 + 24𝑝13𝑝14𝑝15𝑝𝑄
restricted:
𝐿𝐿 =1 × 2𝑝14𝑝15
2𝑝14𝑝15𝑝13 𝑝13 + 2𝑝14 + 2𝑝15 + 2𝑝𝑄
Binary LR
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Binary LR
𝐺𝑃𝑃𝑃 = {13,13} 13
14
15
275
103
325
ST
AT
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unrestricted:
𝐿𝐿 =1 × 2𝑝14𝑝15
12𝑝13𝑝14𝑝15 𝑝13 + 𝑝14 + 𝑝15 + 24𝑝13𝑝14𝑝15𝑝𝑄
restricted:
𝐿𝐿 =1 × 2𝑝14𝑝15
2𝑝14𝑝15𝑝13 𝑝13 + 2𝑝14 + 2𝑝15 + 2𝑝𝑄
Binary LR
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Binary LR
𝐺𝑃𝑃𝑃 = {12,13} 13
14
15
275
103
325
ST
AT
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unrestricted:
𝐿𝐿 =1 × 2𝑝14𝑝15
12𝑝13𝑝14𝑝15 𝑝13 + 𝑝14 + 𝑝15 + 24𝑝13𝑝14𝑝15𝑝𝑄
restricted:
𝐿𝐿 =1 × 2𝑝14𝑝15
2𝑝14𝑝15𝑝13 𝑝13 + 2𝑝14 + 2𝑝15 + 2𝑝𝑄
Binary LR
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Binary LR
13
14
15
275
103
325
ST
AT
𝐺𝑃𝑃𝑃 = {13,16}
𝐺𝑃𝑃𝑃 = {13,13}
𝐺𝑃𝑃𝑃 = {12,13}
Shouldn’t there be a difference in the value of the evidence for each of these POIs depending on how probable allele drop-
out is?
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Binary LR
13
14
15
275
103
325
ST
AT Major Minor 𝒘 𝒎𝒎𝒎𝒎𝒎 𝒑𝒑𝒑𝒑.𝒎𝒎𝒎𝒑𝒑 𝒎𝒎𝒎𝒎𝒎 𝒑𝒑𝒑𝒑.𝒎𝒎𝒎𝒑𝒑
14,15 12,13 𝟏 2𝑝14𝑝15 2𝑝12𝑝13
14,15 13,13 𝟏 2𝑝14𝑝15 𝑝132
14,15 13,14 𝟏 2𝑝14𝑝15 2𝑝13𝑝14
14,15 13,15 𝟏 2𝑝14𝑝15 2𝑝13𝑝15
14,15 13,16 𝟏 2𝑝14𝑝15 2𝑝13𝑝16
14,15 13,17 𝟏 2𝑝14𝑝15 2𝑝13𝑝17
𝒘𝒘𝒎𝒘𝒎𝒎
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Probabilistic Genotyping
13
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275
103
325
ST
AT Major Minor 𝒘 𝒎𝒎𝒎𝒎𝒎 𝒑𝒑𝒑𝒑.𝒎𝒎𝒎𝒑𝒑 𝒎𝒎𝒎𝒎𝒎 𝒑𝒑𝒑𝒑.𝒎𝒎𝒎𝒑𝒑
14,15 12,13 𝟏 2𝑝14𝑝15 2𝑝12𝑝13
14,15 13,13 𝟏 2𝑝14𝑝15 𝑝132
14,15 13,14 𝟏 2𝑝14𝑝15 2𝑝13𝑝14
14,15 13,15 𝟏 2𝑝14𝑝15 2𝑝13𝑝15
14,15 13,16 𝟏 2𝑝14𝑝15 2𝑝13𝑝16
14,15 13,17 𝟏 2𝑝14𝑝15 2𝑝13𝑝17
𝒘𝒘𝒎𝒘𝒎𝒎
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the probability of obtaining these DNA typing
results for a particular genotype set
Concept of weights
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single source:
Concept of weights
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14
15
13 14 15
13 14
13 15
genotype = {14,15}
total: 50 marbles
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single source:
Concept of weights
14 15
14
15
13 14 15
13 14
13 15
genotype = {14,15}
weight = 550
total: 50 marbles
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how large or small a weight is depends on: • possibility of allele drop-out • possibility of allele drop-in • amount of template DNA • possibility of degradation • possibility of oversized stutter peaks
Concept of weights
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Contents • introduction • the Likelihood Ratio • why probabilistic genotyping? • the Likelihood Ratio (yes, there’s more)
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Likelihood Ratio
Pr (𝐸|𝐻𝑝)Pr (𝐸|𝐻𝑑)
𝐸: DNA typing results 𝐺𝐶𝐶: crime stain 𝐺𝐾: known contributors 𝐺𝑉: victim or complainant
𝐺𝑃𝑃𝑃: person of interest
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𝐿𝐿 = Pr (𝐸|𝐻𝑝)Pr (𝐸|𝐻𝑑)
= Pr (𝐺𝐶𝐶,𝐺𝐾|𝐻𝑝)Pr (𝐺𝐶𝐶,𝐺𝐾|𝐻𝑑)
= Pr (𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑝)Pr (𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑑)
×Pr (𝐺𝐾|𝐻𝑝)Pr (𝐺𝐾|𝐻𝑑)
= Pr (𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑝)Pr (𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑑)
×Pr (𝐺𝐾)Pr (𝐺𝐾)
1 36
Likelihood Ratio
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Likelihood Ratio The probability of obtaining these DNA typing results for the crime stain given the genotype of the POI (and victim/complainant) and that the POI is a contributor.
The probability of obtaining these DNA typing results for the crime stain given the genotype of the POI (and victim/complainant) and that the POI is not a contributor.
𝐿𝐿 = Pr 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑝Pr 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑑
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The probability of 𝐺𝐶𝐶 depends on the genotypes considered for the contributors.
Likelihood Ratio
𝐺𝐶𝐶 contributor 1 genotype
contributor 2 genotype
DNA typing results of the crime stain
proposition (𝐻𝑝 or 𝐻𝑑)
profiles of known
contributors
genotype set 𝑺
7 8 9
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Major Minor 𝒘 𝒎𝒎𝒎𝒎𝒎 𝒑𝒑𝒑𝒑.𝒎𝒎𝒎𝒑𝒑 𝒎𝒎𝒎𝒎𝒎 𝒑𝒑𝒑𝒑.𝒎𝒎𝒎𝒑𝒑
14,15 12,13 𝟏 2𝑝14𝑝15 2𝑝12𝑝13
14,15 13,13 𝟏 2𝑝14𝑝15 𝑝132
14,15 13,14 𝟏 2𝑝14𝑝15 2𝑝13𝑝14
14,15 13,15 𝟏 2𝑝14𝑝15 2𝑝13𝑝15
14,15 13,16 𝟏 2𝑝14𝑝15 2𝑝13𝑝16
14,15 13,17 𝟏 2𝑝14𝑝15 2𝑝13𝑝17
Genotype set 𝑆
𝑆1 𝑆2 𝑆3 𝑆4 𝑆5 𝑆6
39
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Likelihood Ratio
𝐿𝐿 = Pr 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑝Pr 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑑
= Pr 𝐺𝐶𝐶|𝑆1 Pr 𝑆1|𝐺𝐾 ,𝐻𝑝 + Pr 𝐺𝐶𝐶|𝑆2 Pr 𝑆2|𝐺𝐾 ,𝐻𝑝 + ⋯+ Pr 𝐺𝐶𝐶|𝑆6 Pr 𝑆6|𝐺𝐾 ,𝐻𝑝Pr 𝐺𝐶𝐶|𝑆1 Pr 𝑆1|𝐺𝐾 ,𝐻𝑑 + Pr 𝐺𝐶𝐶|𝑆2 Pr 𝑆2|𝐺𝐾 ,𝐻𝑑 + ⋯+ Pr 𝐺𝐶𝐶|𝑆6 Pr 𝑆6|𝐺𝐾 ,𝐻𝑑
= ∑6𝑗=1 Pr 𝐺𝐶𝐶|𝑆𝑗 Pr 𝑆𝑗|𝐺𝐾 ,𝐻𝑝∑6𝑗=1 Pr 𝐺𝐶𝐶|𝑆𝑗 Pr 𝑆𝑗|𝐺𝐾 ,𝐻𝑑
40
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Likelihood Ratio
𝐿𝐿 = ∑𝑚𝑗=1 Pr 𝐺𝐶𝐶|𝑆𝑗 Pr 𝑆𝑗|𝐺𝐾 ,𝐻𝑝∑𝑚𝑗=1 Pr 𝐺𝐶𝐶|𝑆𝑗 Pr 𝑆𝑗|𝐺𝐾 ,𝐻𝑑
weights the probability of obtaining these DNA typing
results for genotype set 𝑆𝑗 41
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Likelihood Ratio
match probabilities the probability of genotype set 𝑆𝑗 given that we have observed
genotypes 𝐺𝐾 and that the contributors are as specified in 𝐻𝑝 or 𝐻𝑑
𝐿𝐿 = ∑𝑚𝑗=1 Pr 𝐺𝐶𝐶|𝑆𝑗 Pr 𝑆𝑗|𝐺𝐾 ,𝐻𝑝∑𝑚𝑗=1 Pr 𝐺𝐶𝐶|𝑆𝑗 Pr 𝑆𝑗|𝐺𝐾 ,𝐻𝑑
42
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𝐿𝐿 =∑ 𝑤𝑤𝑤𝑤𝑤𝑤 × 𝑤𝑤𝑔𝑔𝑤𝑔𝑝𝑤 𝑚𝑚𝑤𝑚𝑤 𝑝𝑃𝑔𝑝.𝑔𝑒𝑒𝑒𝑒𝑒𝑝𝑒 𝑠𝑒𝑒𝑠|𝐻𝑝∑ 𝑤𝑤𝑤𝑤𝑤𝑤 × 𝑤𝑤𝑔𝑔𝑤𝑔𝑝𝑤 𝑚𝑚𝑤𝑚𝑤 𝑝𝑃𝑔𝑝.𝑔𝑒𝑒𝑒𝑒𝑒𝑝𝑒 𝑠𝑒𝑒𝑠|𝐻𝑑
Likelihood Ratio
43
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Probabilistic Software for Mixture Interpretation
Part III
Simone Gittelson, Ph.D.
WSP CLD Forensic DNA Continuing Education Day Burien, Washington
June 18, 2015
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Person of interest (POI)
D8 13,16
D21 28,28
D7 8,12
CSF1PO 12,12
D3 16,16
TH01 7,9.3
D13 12,13
D16 12,13
D2 23,25
D19 13,13
vWA 15,19
TPOX 11,11
D18 14,20
D5 11,13
FGA 20,28
crime stain:
2
Boston University Mixture (http://www.bu.edu/dnamixtures/)
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binary semi-continuous continuous
does not model stochastic effects models stochastic effects
observed peaks are discrete variables
observed peaks are continuous variables
Likelihood Ratio
3
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• The observed peaks as a discrete variable:
• The observed peaks as a continuous variable:
present absent
0 50 100 150
Discrete vs. Continuous
0 50 100 150 4
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binary semi-continuous continuous
does not model stochastic effects models stochastic effects
observed peaks are discrete variables
observed peaks are continuous variables
Likelihood Ratio
5
Assumption: 𝜃 = 0
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Locus POI Binary
D8S1179 13,16 0.39
D21S11 28,28 0.71
D7S820 8,12 4.08
CSF1PO 12,12 0.41
D3S1358 16,16 0.44
TH01 7,9.3 2.46
D13S317 12,13 3.49
D16S539 12,13 2.32
D2S1338 23,25 8.57
D19S433 13,13 0.51
vWA 15,19 2.05
TPOX 11,11 1.27
D18S51 14,20 28.09
D5S818 11,13 2.38
FGA 20,28 0.76
𝑳𝑳 = 𝟐.𝟑𝟑 × 𝟏𝟏𝟑
6
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binary semi-continuous continuous
does not model stochastic effects models stochastic effects
observed peaks are discrete variables
observed peaks are continuous variables
Likelihood Ratio
7
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Semi-continuous LR allele drop-out
heterozygote: 𝑃𝑃 𝑑𝑃𝑔𝑝 − 𝑔𝑜𝑤 = 𝐷𝐻 𝑃𝑃 𝑔𝑔𝑤 𝑑𝑃𝑔𝑝 − 𝑔𝑜𝑤 = 1 − 𝐷𝐻 = 𝐷𝐻
homozygote: 𝑃𝑃 𝑑𝑃𝑔𝑝 − 𝑔𝑜𝑤 = 𝐷2𝐻 𝑃𝑃 𝑔𝑔𝑤 𝑑𝑃𝑔𝑝 − 𝑔𝑜𝑤 = 1 − 𝐷2𝐻 = 𝐷2𝐻
8
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Semi-continuous LR Examples: {8,9}
8 9
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑝 = 𝐷𝐻 𝐷𝐻 × 1 = 𝐷𝐻2
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑑 = 𝐷𝐻 𝐷𝐻 × 2𝑝8𝑝9 = 𝐷𝐻2 × 2𝑝8𝑝9
𝐿𝐿 =𝐷𝐻
2
𝐷𝐻2 × 2𝑝8𝑝9
=1
2𝑝8𝑝9
9
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Semi-continuous LR Examples: {8,9}
8 9
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑝 = 𝐷𝐻 𝐷𝐻 × 1 = 𝐷𝐻 𝐷𝐻
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾,𝐻𝑑 = 𝐷2𝐻 × 𝑝82 + 𝐷𝐻 𝐷𝐻 × 2𝑝8𝑝𝑄
Contributor
8,8 𝐷2𝐻 × 𝑝82
8,Q 𝐷𝐻 𝐷𝐻 × 2𝑝8𝑝𝑄
where 𝑝𝑄 = 1 − 𝑝8
10
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Semi-continuous LR Examples: {8,9}
8 9
𝐿𝐿 =𝐷𝐻 𝐷𝐻
𝐷2𝐻 × 𝑝82 +𝐷𝐻 𝐷𝐻 × 2𝑝8𝑝𝑄
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑝 = 𝐷𝐻 𝐷𝐻 × 1 = 𝐷𝐻 𝐷𝐻
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾,𝐻𝑑 = 𝐷2𝐻 × 𝑝82 + 𝐷𝐻 𝐷𝐻 × 2𝑝8𝑝𝑄
11
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person of interest (POI)
{13,16} 13
14
15
275
103
325
AT 14 13 15
D8S1179
drop-out is possible!
Semi-continuous LR
12
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Semi-continuous LR person of interest (POI)
{13,16} 14 13 15
D8S1179
1) What is the probability of obtaining these DNA typing results if the POI is a contributor?
Pr 𝐺𝐶𝐶 𝐺𝐾 ,𝐻𝑝 = 𝐷𝐻𝐷𝐻 × 1 × 𝐷𝐻2 × 2𝑝14𝑝15
= 𝐷𝐻𝐷𝐻3 × 2𝑝14𝑝15 13
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Semi-continuous LR person of interest (POI)
{13,16} 14 13 15
D8S1179
2) What is the probability of obtaining these DNA typing results if the POI is not a contributor?
Major Minor Weight Genotype Match Prob. 13,13 14,15 𝐷2𝐻 𝐷𝐻
2 × 𝑝132 × 2𝑝14𝑝15
14,14 13,15 𝐷2𝐻 𝐷𝐻2 × 𝑝142 × 2𝑝13𝑝15
15,15 13,14 𝐷2𝐻 𝐷𝐻2 × 𝑝152 × 2𝑝13𝑝14
14,15 13,13 𝐷2𝐻 𝐷𝐻2 × 2𝑝14𝑝15 × 𝑝132
13,15 14,14 𝐷2𝐻 𝐷𝐻2 × 2𝑝13𝑝15 × 𝑝142
13,14 15,15 𝐷2𝐻 𝐷𝐻2 × 2𝑝13𝑝14 × 𝑝152
13,14 13,15 𝐷2𝐻 𝐷𝐻2 × 2𝑝13𝑝14 × 2𝑝13𝑝15
13,14 14,15 𝐷2𝐻 𝐷𝐻2 × 2𝑝13𝑝14 × 2𝑝14𝑝15
13,15 14,15 𝐷2𝐻 𝐷𝐻2 × 2𝑝13𝑝15 × 2𝑝14𝑝15
13,15 13,14 𝐷2𝐻 𝐷𝐻2 × 2𝑝13𝑝15 × 2𝑝13𝑝14
14,15 13,14 𝐷2𝐻 𝐷𝐻2 × 2𝑝14𝑝15 × 2𝑝13𝑝14
14,15 13,15 𝐷2𝐻 𝐷𝐻2 × 2𝑝14𝑝15 × 2𝑝13𝑝15 14
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Semi-continuous LR
14 13 15
D8S1179
where 𝑝𝑄 = 1 − 𝑝13 − 𝑝14 − 𝑝15
(continued) Major Minor Weight Genotype Match Prob. 13,14 15,Q 𝐷𝐻
3𝐷𝐻 × 2𝑝13𝑝14 × 2𝑝15 𝑝𝑄
13,15 14,Q 𝐷𝐻3𝐷𝐻 × 2𝑝13𝑝15 × 2𝑝14𝑝𝑄
14,15 13,Q 𝐷𝐻3𝐷𝐻 × 2𝑝14𝑝15 × 2𝑝13𝑝𝑄
15,Q 13,14 𝐷𝐻3𝐷𝐻 × 2𝑝15𝑝𝑄 × 2𝑝13𝑝14
14,Q 13,15 𝐷𝐻3𝐷𝐻 × 2𝑝14𝑝𝑄 × 2𝑝13𝑝15
13,Q 14,15 𝐷𝐻3𝐷𝐻 × 2𝑝13𝑝𝑄 × 2𝑝14𝑝15
15
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Semi-continuous LR
14 13 15
D8S1179
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾,𝐻𝑑 = 𝐷2𝐻 𝐷𝐻2 × 4𝑝13𝑝14𝑝15 𝑝13 + 𝑝14 + 𝑝15
+𝐷2𝐻 𝐷𝐻2 × 8𝑝13𝑝14𝑝15 𝑝13 + 𝑝14 + 𝑝15
+ 𝐷𝐻3𝐷𝐻 × 24𝑝13𝑝14𝑝15𝑝𝑄
Homs
Hets with stacking
Hets with drop-out 16
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Semi-continuous LR
14 13 15
D8S1179
𝐿𝐿 =𝐷𝐻𝐷𝐻
3 × 2𝑝14𝑝15 𝐷2𝐻 𝐷𝐻
2 × 4𝑝13𝑝14𝑝15 𝑝13 + 𝑝14 + 𝑝15+ 𝐷2𝐻 𝐷𝐻
2 × 8𝑝13𝑝14𝑝15 𝑝13 + 𝑝14 + 𝑝15+ 𝐷𝐻
3𝐷𝐻 × 24𝑝13𝑝14𝑝15𝑝𝑄
17
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Major Minor Weight Genotype Match Prob.
13,13 14,15 𝐷2𝐻 𝐷𝐻2 × 2𝑝132 𝑝14𝑝15
14,14 13,15 𝐷2𝐻 𝐷𝐻2 × 2𝑝13𝑝142 𝑝15
15,15 13,14 𝐷2𝐻 𝐷𝐻2 × 2𝑝13𝑝14𝑝152
14,15 13,13 𝐷2𝐻 𝐷𝐻2 × 2𝑝132 𝑝14𝑝15
13,15 14,14 𝐷2𝐻 𝐷𝐻2 × 2𝑝13𝑝142 𝑝15
13,14 15,15 𝐷2𝐻 𝐷𝐻2 × 2𝑝13𝑝14𝑝152
13,14 13,15 𝐷2𝐻 𝐷𝐻2 × 4𝑝132 𝑝14𝑝15
13,14 14,15 𝐷2𝐻 𝐷𝐻2 × 4𝑝13𝑝142 𝑝15
13,15 14,15 𝐷2𝐻 𝐷𝐻2 × 4𝑝13𝑝14𝑝152
13,15 13,14 𝐷2𝐻 𝐷𝐻2 × 4𝑝132 𝑝14𝑝15
14,15 13,14 𝐷2𝐻 𝐷𝐻2 × 4𝑝13𝑝142 𝑝15
14,15 13,15 𝐷2𝐻 𝐷𝐻2 × 4𝑝13𝑝14𝑝152
13,14 15,Q 𝐷𝐻3𝐷𝐻 × 4𝑝13𝑝14𝑝15𝑝𝑄
13,15 14,Q 𝐷𝐻3𝐷𝐻 × 4𝑝13𝑝14𝑝15𝑝𝑄
14,15 13,Q 𝐷𝐻3𝐷𝐻 × 4𝑝13𝑝14𝑝15𝑝𝑄
15,Q 13,14 𝐷𝐻3𝐷𝐻 × 4𝑝13𝑝14𝑝15𝑝𝑄
14,Q 13,15 𝐷𝐻3𝐷𝐻 × 4𝑝13𝑝14𝑝15𝑝𝑄
13,Q 14,15 𝐷 3𝐷 × 4𝑝13𝑝14𝑝15𝑝𝑄
Major Minor Weight Genotype Match Prob.
13,13 14,15 0.075 × 2𝑝132 𝑝14𝑝15
14,14 13,15 0.075 × 2𝑝13𝑝142 𝑝15
15,15 13,14 0.075 × 2𝑝13𝑝14𝑝152
14,15 13,13 0.075 × 2𝑝132 𝑝14𝑝15
13,15 14,14 0.075 × 2𝑝13𝑝142 𝑝15
13,14 15,15 0.075 × 2𝑝13𝑝14𝑝152
13,14 13,15 0.075 × 4𝑝132 𝑝14𝑝15
13,14 14,15 0.075 × 4𝑝13𝑝142 𝑝15
13,15 14,15 0.075 × 4𝑝13𝑝14𝑝152
13,15 13,14 0.075 × 4𝑝132 𝑝14𝑝15
14,15 13,14 0.075 × 4𝑝13𝑝142 𝑝15
14,15 13,15 0.075 × 4𝑝13𝑝14𝑝152
13,14 15,Q 0.016 × 4𝑝13𝑝14𝑝15𝑝𝑄
13,15 14,Q 0.016 × 4𝑝13𝑝14𝑝15𝑝𝑄
14,15 13,Q 0.016 × 4𝑝13𝑝14𝑝15𝑝𝑄
15,Q 13,14 0.016 × 4𝑝13𝑝14𝑝15𝑝𝑄
14,Q 13,15 0.016 × 4𝑝13𝑝14𝑝15𝑝𝑄
13,Q 14,15 0.016 × 4𝑝13𝑝14𝑝15𝑝𝑄
𝐷𝐻 = 0.716 𝐷2𝐻 = 0.073
Semi-Continuous
𝑳𝑳 = 𝟏.𝟑𝟑𝟑 × 𝟏𝟏𝟑 18
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Locus Binary Semi-Continuous
D8S1179 0.39 0.16 D21S11 0.71 1.44 D7S820 4.08 4.75 CSF1PO 0.41 0.50 D3S1358 0.44 0.91 TH01 2.46 3.22 D13S317 3.49 3.91 D16S539 2.32 2.88 D2S1338 8.57 10.43 D19S433 0.51 0.79 vWA 2.05 1.43 TPOX 1.27 1.90 D18S51 28.09 28.09 D5S818 2.38 2.52 FGA 0.76 0.50
𝐷𝐻 = 0.716 𝐷2𝐻 = 0.073
Binary
𝑳𝑳 = 𝟐.𝟑𝟑 × 𝟏𝟏𝟑
Semi-Continuous
𝑳𝑳 = 𝟏.𝟑𝟑𝟑 × 𝟏𝟏𝟑
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binary semi-continuous continuous
does not model stochastic effects models stochastic effects
observed peaks are discrete variables
observed peaks are continuous variables
Likelihood Ratio
20
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From Semi-continuous to Continuous
𝐿𝐿 =∑ 𝑤𝑤𝑤𝑤𝑤𝑤 × 𝑤𝑤𝑔𝑔𝑤𝑔𝑝𝑤 𝑚𝑚𝑤𝑚𝑤 𝑝𝑃𝑔𝑝.𝑔𝑒𝑒𝑒𝑒𝑒𝑝𝑒 𝑠𝑒𝑒𝑠|𝐻𝑝∑ 𝑤𝑤𝑤𝑤𝑤𝑤 × 𝑤𝑤𝑔𝑔𝑤𝑔𝑝𝑤 𝑚𝑚𝑤𝑚𝑤 𝑝𝑃𝑔𝑝.𝑔𝑒𝑒𝑒𝑒𝑒𝑝𝑒 𝑠𝑒𝑒𝑠|𝐻𝑑
13 14
15
275
103
325
AT 14 13 15
D8S1179
21
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Locus Binary Semi-Continuous Continuous
D8S1179 0.39 0.16 0.09 D21S11 0.71 1.44 38.9 D7S820 4.08 4.75 15.7 CSF1PO 0.41 0.50 7.39 D3S1358 0.44 0.91 15.4 TH01 2.46 3.22 5.88 D13S317 3.49 3.91 8.87 D16S539 2.32 2.88 10.2 D2S1338 8.57 10.43 11.2 D19S433 0.51 0.79 13.9 vWA 2.05 1.43 3.19 TPOX 1.27 1.90 16.7 D18S51 28.09 28.09 169 D5S818 2.38 2.52 9.07 FGA 0.76 0.50 1
Continuous
𝑳𝑳 = 𝟑.𝟑𝟑 × 𝟏𝟏𝟏𝟑
Semi-Continuous
𝑳𝑳 = 𝟏.𝟑𝟑𝟑 × 𝟏𝟏𝟑
Binary
𝑳𝑳 = 𝟐.𝟑𝟑 × 𝟏𝟏𝟑
22
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Locus Binary Semi-Continuous Continuous
D8S1179 0.39 0.16 0.09 D21S11 0.71 1.44 38.9 D7S820 4.08 4.75 15.7 CSF1PO 0.41 0.50 7.39 D3S1358 0.44 0.91 15.4 TH01 2.46 3.22 5.88 D13S317 3.49 3.91 8.87 D16S539 2.32 2.88 10.2 D2S1338 8.57 10.43 11.2 D19S433 0.51 0.79 13.9 vWA 2.05 1.43 3.19 TPOX 1.27 1.90 16.7 D18S51 28.09 28.09 169 D5S818 2.38 2.52 9.07 FGA 0.76 0.50 1
28
142
30 32.2
289 293
{28,28}
23
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Locus Binary Semi-Continuous Continuous
D8S1179 0.39 0.16 0.09 D21S11 0.71 1.44 38.9 D7S820 4.08 4.75 15.7 CSF1PO 0.41 0.50 7.39 D3S1358 0.44 0.91 15.4 TH01 2.46 3.22 5.88 D13S317 3.49 3.91 8.87 D16S539 2.32 2.88 10.2 D2S1338 8.57 10.43 11.2 D19S433 0.51 0.79 13.9 vWA 2.05 1.43 3.19 TPOX 1.27 1.90 16.7 D18S51 28.09 28.09 169 D5S818 2.38 2.52 9.07 FGA 0.76 0.50 1
{16,16} 16
14 18
229 130
215
24
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Locus Binary Semi-Continuous Continuous
D8S1179 0.39 0.16 0.09 D21S11 0.71 1.44 38.9 D7S820 4.08 4.75 15.7 CSF1PO 0.41 0.50 7.39 D3S1358 0.44 0.91 15.4 TH01 2.46 3.22 5.88 D13S317 3.49 3.91 8.87 D16S539 2.32 2.88 10.2 D2S1338 8.57 10.43 11.2 D19S433 0.51 0.79 13.9 vWA 2.05 1.43 3.19 TPOX 1.27 1.90 16.7 D18S51 28.09 28.09 169 D5S818 2.38 2.52 9.07 FGA 0.76 0.50 1
{11,11}
8 11
666
163
25
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Continuous LR
𝐿𝐿 =∑ 𝑤𝑤𝑤𝑤𝑤𝑤 × 𝑤𝑤𝑔𝑔𝑤𝑔𝑝𝑤 𝑚𝑚𝑤𝑚𝑤 𝑝𝑃𝑔𝑝.𝑔𝑒𝑒𝑒𝑒𝑒𝑝𝑒 𝑠𝑒𝑒𝑠|𝐻𝑝∑ 𝑤𝑤𝑤𝑤𝑤𝑤 × 𝑤𝑤𝑔𝑔𝑤𝑔𝑝𝑤 𝑚𝑚𝑤𝑚𝑤 𝑝𝑃𝑔𝑝.𝑔𝑒𝑒𝑒𝑒𝑒𝑝𝑒 𝑠𝑒𝑒𝑠|𝐻𝑑
We can obtain the weights through simulations that attempt to reproduce the observed peak heights by
varying the genotype set and model parameters.
26
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Continuous LR
𝐿𝐿 =∑ 𝑤𝑤𝑤𝑤𝑤𝑤 × 𝑤𝑤𝑔𝑔𝑤𝑔𝑝𝑤 𝑚𝑚𝑤𝑚𝑤 𝑝𝑃𝑔𝑝.𝑔𝑒𝑒𝑒𝑒𝑒𝑝𝑒 𝑠𝑒𝑒𝑠|𝐻𝑝∑ 𝑤𝑤𝑤𝑤𝑤𝑤 × 𝑤𝑤𝑔𝑔𝑤𝑔𝑝𝑤 𝑚𝑚𝑤𝑚𝑤 𝑝𝑃𝑔𝑝.𝑔𝑒𝑒𝑒𝑒𝑒𝑝𝑒 𝑠𝑒𝑒𝑠|𝐻𝑑
observed peak heights
simulated peak heights
27
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Continuous LR
𝐿𝐿 =∑ 𝑤𝑤𝑤𝑤𝑤𝑤 × 𝑤𝑤𝑔𝑔𝑤𝑔𝑝𝑤 𝑚𝑚𝑤𝑚𝑤 𝑝𝑃𝑔𝑝.𝑔𝑒𝑒𝑒𝑒𝑒𝑝𝑒 𝑠𝑒𝑒𝑠|𝐻𝑝∑ 𝑤𝑤𝑤𝑤𝑤𝑤 × 𝑤𝑤𝑔𝑔𝑤𝑔𝑝𝑤 𝑚𝑚𝑤𝑚𝑤 𝑝𝑃𝑔𝑝.𝑔𝑒𝑒𝑒𝑒𝑒𝑝𝑒 𝑠𝑒𝑒𝑠|𝐻𝑑
The better the genotype set and the parameters explain the observed peak heights, the greater the weight for that genotype set.
28
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Major Minor Binary Weight Semi-continuous Weight Continuous Weight
28,28 30,32.2 0.056 0.075 0
30,30 28,32.2 0.056 0.075 0
32.2,32.2 28,30 0.056 0.075 0
30,32.2 28,28 0.056 0.075 0.992
28,32.2 30,30 0.056 0.075 0
28,30 32.2,32.2 0.056 0.075 0
28,30 28,32.2 0.056 0.075 0
28,30 30,32.2 0.056 0.075 0
28,32.2 30,32.2 0.056 0.075 0
28,32.2 28,30 0.056 0.075 0
30,32.2 28,30 0.056 0.075 0.003
30,32.2 28,32.2 0.056 0.075 0.004
28,30 32.2,Q 0.056 0.016 0
28,32.2 30,Q 0.056 0.016 0
30,32.2 28,Q 0.056 0.016 0.001
32.2,Q 28,30 0.056 0.016 0
30,Q 28,32.2 0.056 0.016 0
28,Q 30,32.2 0.056 0.016 0
28
142
30 32.2
289 293
{28,28}
29
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Continuous LR
28
142
30 32.2
289 293
person of interest (POI)
{28,28}
Major Minor Weight Genotype Match Prob. 30,32.2 28,28 0.992 × 2𝑝30𝑝32.2
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑝 = 0.992 × 2𝑝30𝑝32.2
30
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Continuous LR
28
142
30 32.2
289 293
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑑 = 0.992 × 2𝑝30𝑝32.2𝑝282 + 0.004 × 4𝑝28𝑝30𝑝32.22
+0.003 × 4𝑝28𝑝302 𝑝32.2 + 0.001 × 4𝑝28𝑝30𝑝32.2𝑝𝑄
Major Minor Weight Genotype Match Prob. 30,32.2 28,28 0.992 × 2𝑝30𝑝32.2 × 𝑝282 30,32.2 28,32.2 0.004 × 2𝑝30𝑝32.2 × 2𝑝28𝑝32.2 30,32.2 28,30 0.003 × 2𝑝30𝑝32.2 × 2𝑝28𝑝30 30,32.2 28,Q 0.001 × 2𝑝30𝑝32.2 × 2𝑝28 𝑝𝑄
where 𝑝𝑄 = 1 − 𝑝28 − 𝑝30 − 𝑝32.2
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Continuous LR
28
142
30 32.2
289 293
person of interest (POI)
{28,28}
LR =0.992 × 2𝑝30𝑝32.2
0.992 × 2𝑝30𝑝32.2𝑝282 + 0.004 × 4𝑝28𝑝30𝑝32.22
+0.003 × 4𝑝28𝑝302 𝑝32.2 + 0.001 × 4𝑝28𝑝30𝑝32.2𝑝𝑄
= 38.9 32
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Major Minor Binary Weight Semi-Continuous Weight Continuous Weight
14,14 16,18 0.056 0.075 0
16,16 14,18 0.056 0.075 0
18,18 14,16 0.056 0.075 0
16,18 14,14 0.056 0.075 0
14,18 16,16 0.056 0.075 0.991
14,16 18,18 0.056 0.075 0
14,16 14,18 0.056 0.075 0
14,16 16,18 0.056 0.075 0
14,18 16,18 0.056 0.075 0.003
14,18 14,16 0.056 0.075 0.003
16,18 14,16 0.056 0.075 0
16,18 14,18 0.056 0.075 0
14,16 18,Q 0.056 0.016 0
14,18 16,Q 0.056 0.016 0.002
16,18 14,Q 0.056 0.016 0
18,Q 14,16 0.056 0.016 0
16,Q 14,18 0.056 0.016 0
14,Q 16,18 0.056 0.016 0
{16,16}
16 14 18
229 130
215
33
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Continuous LR
person of interest (POI)
{16,16}
Major Minor Weight Genotype Match Prob. 14,18 16,16 0.991 × 2𝑝14𝑝18
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑝 = 0.991 × 2𝑝14𝑝18
34
16 14 18
229 130
215
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Continuous LR
16 14 18
229 130
215 Major Minor Weight Genotype Match Prob. 14,18 16,16 0.991 × 2𝑝14𝑝18 × 𝑝162 14,18 14,16 0.003 × 2𝑝14𝑝18 × 2𝑝14𝑝16 14,18 16,18 0.003 × 2𝑝14𝑝18 × 2𝑝16𝑝18 14,18 16,Q 0.002 × 2𝑝14𝑝18 × 2𝑝16 𝑝𝑄
where 𝑝𝑄 = 1 − 𝑝14 − 𝑝16 − 𝑝18
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑑 = 0.991 × 2𝑝14𝑝18𝑝162 + 0.003 × 4𝑝142 𝑝16𝑝18 +0.003 × 4𝑝14𝑝16𝑝182 + 0.002 × 4𝑝14𝑝16𝑝18𝑝𝑄
35
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Continuous LR
person of interest (POI)
{16,16}
𝐿𝐿 =0.991 × 2𝑝14𝑝18
16 14 18
229 130
215
0.991 × 2𝑝14𝑝18𝑝162 + 0.003 × 4𝑝142 𝑝16𝑝18 +0.003 × 4𝑝14𝑝16𝑝182 + 0.002 × 4𝑝14𝑝16𝑝18𝑝𝑄
= 15.4
36
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Major Minor Binary Weight Semi-Continuous Weight Continuous Weight
8,8 11,11 0.053 0.160 0.997
11,11 8,8 0.053 0.160 0
8,11 8,11 0.053 0.160 0
8,8 8,11 0.053 0.160 0.003
8,11 8,8 0.053 0.160 0
8,11 11,11 0.053 0.160 0
11,11 8,11 0.053 0.160 0
8,11 8,Q 0.053 0.053 0
8,Q 8,11 0.053 0.053 0
8,11 11,Q 0.053 0.053 0
11,Q 8,11 0.053 0.053 0
8,8 11,Q 0.053 0.053 0
11,Q 8,8 0.053 0.053 0
11,11 8,Q 0.053 0.053 0
8,Q 11,11 0.053 0.053 0
8,11 Q,Q 0.053 0.001 𝑔𝑃 0.008 0
Q,Q 8,11 0.053 0.001 𝑔𝑃 0.008 0
8,Q 11,Q 0.053 0.008 0
11,Q 8,Q 0.053 0.008 0
{11,11}
8 11
666
163
37
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Continuous LR
person of interest (POI)
{11,11}
Major Minor Weight Genotype Match Prob. 8,8 11,11 0.997 × 𝑝82
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾 ,𝐻𝑝 = 0.997 × 𝑝82
8 11
666
163
38
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Continuous LR Major Minor Weight Genotype Match Prob. 8,8 11,11 0.997 × 𝑝82 × 𝑝112 8,8 8,11 0.003 × 𝑝82 × 2𝑝8𝑝11
where 𝑝𝑄 = 1 − 𝑝8 − 𝑝11
𝑃𝑃 𝐺𝐶𝐶|𝐺𝐾,𝐻𝑑 = 0.997 × 𝑝82𝑝112 + 0.003 × 2𝑝83𝑝11
39
8 11
666
163
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Continuous LR
person of interest (POI)
{11,11}
𝐿𝐿 =0.997 × 𝑝82
0.997 × 𝑝82𝑝112 + 0.003 × 2𝑝83𝑝11
8 11
666
163
= 16.7
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Locus Binary Semi-Continuous Continuous
D8S1179 0.39 0.16 0.09 D21S11 0.71 1.44 38.9 D7S820 4.08 4.75 15.7 CSF1PO 0.41 0.50 7.39 D3S1358 0.44 0.91 15.4 TH01 2.46 3.22 5.88 D13S317 3.49 3.91 8.87 D16S539 2.32 2.88 10.2 D2S1338 8.57 10.43 11.2 D19S433 0.51 0.79 13.9 vWA 2.05 1.43 3.19 TPOX 1.27 1.90 16.7 D18S51 28.09 28.09 169 D5S818 2.38 2.52 9.07 FGA 0.76 0.50 1 41
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Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014.
42
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1:1 mixture
Figure 1 from: Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014. 43
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2:1 mixture
Figure 1 from: Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014. 44
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3:1 mixture
Figure 1 from: Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014. 45
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4:1 mixture
Figure 1 from: Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014. 46
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5:1 mixture
Figure 1 from: Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014. 47
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Comparison
Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014.
1:1 2:1 3:1 4:1 5:1
Continuous:
Semi-continuous:
mRMP:
CPI:
1 to 107 1 to 106 1 to 104
48
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CPI 1:1 major:minor
7 8 9 10 7 8 9
ST ST
useable not useable
49
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Comparison
Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014.
1:1 2:1 3:1 4:1 5:1
Continuous:
Semi-continuous:
mRMP:
104 to 1010 106 to 1014 106 to 1015 102 to 1021 10 to 1022
CPI:
1 to 107 1 to 106 1 to 104
50
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1:1 major:minor mRMP
Contributor 1 Contributor 2
7,8 9,10
7,9 8,10
7,10 8,9
8,9 7,10
8,10 7,9
9,10 7,8
7 8 9 10 7 8 9
ST ST
Major Minor
8,9 7,any
51
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Comparison
Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014.
1:1 2:1 3:1 4:1 5:1
Continuous:
Semi-continuous: 109 to 1014 105 to 1014 103 to 1014 102 to 1014
mRMP:
104 to 1010 106 to 1014 106 to 1015 102 to 1021 10 to 1022
CPI:
1 to 107 1 to 106 1 to 104
52
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Semi-continuous
Contributor 1 Contributor 2
7,8 9,10
7,9 8,10
7,10 8,9
8,9 7,10
8,10 7,9
9,10 7,8
7 8 9
ST
Major Minor
7,any 8,9
8,any 7,9
9,any 7,8
8,9 7,any
7,9 8,any
7,8 9,any
7 8 9 10
ST
1:1 major:minor
53
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Comparison
Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014.
1:1 2:1 3:1 4:1 5:1
Continuous:
107 to 1014
1012 to 1024
1014 to 1024 1012 to 1024 103 to 1022
Semi-continuous: 109 to 1014 105 to 1014 103 to 1014 102 to 1014
mRMP:
104 to 1010 106 to 1014 106 to 1015 102 to 1021 10 to 1022
CPI:
1 to 107 1 to 106 1 to 104
54
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Continuous
Contributor 1 Contributor 2
7,8 9,10
7,9 8,10
7,10 8,9
8,9 7,10
8,10 7,9
9,10 7,8
7 8 9
ST
Major Minor
8,9 7,*
*any gentoype the model considers possible given the observed peak heights
7 8 9 10
ST
1:1 major:minor
55
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Comparison
Bille T.W., Weitz S.M., Coble M.D., Buckleton J., Bright J-A. Comparison of the performance of different models for the interpretation of low level mixed DNA profiles. Electrophoresis 35: 3125-3133, 2014.
1:1 2:1 3:1 4:1 5:1
Continuous:
107 to 1014
1012 to 1024
1014 to 1024 1012 to 1024 103 to 1022
Semi-continuous: 109 to 1014 105 to 1014 103 to 1014 102 to 1014
mRMP:
104 to 1010 106 to 1014 106 to 1015 102 to 1021 10 to 1022
CPI:
1 to 107 1 to 106 1 to 104
56
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Questions?
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Additional References • Taylor D., Bright J-A., Buckleton J. The interpretation of
single source and mixed DNA profiles. Forensic Science International Genetics 2013; 7: 516-528.
• Bright J-A., Evett I.W., Taylor D., Curran J.M., Buckleton J. A
series of recommended tests when validating probabilistic DNA profile interpretation software. Forensic Science International Genetics 2015; 14: 125-131.
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Acknowledgements • John Buckleton
• Robin Cotton, Catherine Grgicak, Margaret Terrill, Charlotte Word, Sarah
Cortes for the Boston University Mixtures (http://www.bu.edu/dnamixtures/)