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Statistical Weights of DNA Profiles
Forensic Bioinformatics (www.bioforensics.com)
Dan E. Krane, Wright State University, Dayton, OH
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DNA statistics
• Coincidental 10 locus DNA profile matches are very rare
• Several factors can make statistics less impressive– Mixtures– Incomplete information– Relatives– Database searches
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DNA profile
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Comparing electropherograms
Evidence sample Suspect #1’s reference
EXCLUDEEXCLUDE
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Comparing electropherograms
Evidence sample Suspect #2’s reference
CANNOT EXCLUDECANNOT EXCLUDE
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What weight should be given to DNA evidence?
Statistics do not lie.
But, you have to pay close attention to the questions they are addressing.
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What weight should be given to DNA evidence?
Statistics do not lie.
But, you have to pay close attention to the questions they are addressing.
What is the chance that a randomly chosen, unrelated individual from a given population would have the same DNA profile observed in a sample?
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Single source statistics:
Random Match Probability (RMP) or “Random Man Not Excluded”
(RMNE)
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Single source samples
Formulae for RMNE:
At a locus:Heterozygotes:Homozygotes:
Multiply across all loci
p2
Statistical estimates: the product rule
2pq 2pq 2pq 2pq
2pq 2pq 2pq 2pq
2pq 2pq
2pq 2pq
2pqp2 p2
p2
x x x x
x x x x
x x x x
x
x
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0.1454 x 0.1097 x 2
Statistical estimate: Single source sample
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3.2% 6.0% 4.6% 1.2%
9.8% 9.5% 6.3% 2.2% 1.0%
2.9% 5.1% 29.9% 4.0%
1.1% 6.6%
X X X X
XXXXX
X X X X
X
Statistical estimate: Single source sample
1 in 608,961,665,956,361,000,000
1 in 608 quintillion(“less than one in one billion”)
= 0.0320.1454 0.1097 2x x
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What weight should be given to DNA evidence?
Statistics do not lie.
But, you have to pay close attention to the questions they are addressing.
What is the chance that a randomly chosen, unrelated individual from a given population would have the same DNA profile observed in a sample?
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Mixture statistics:
Combined Probability of Inclusion (CPI) or Likelihood
Ratios (LR)
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Mixed DNA samples
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Put two people’s names into a mixture.
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How many names can you take out?
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How many names can you take out?
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How many contributors to a mixture if analysts can discard a locus?
How many contributors to a mixture?
Maximum # of alleles observed in a 3-person mixture # of occurrences Percent of cases
2 0 0.00
3 78 0.00
4 4,967,034 3.39
5 93,037,010 63.49
6 48,532,037 33.12
There are 146,536,159 possible different 3-person mixtures of the 959 individuals in the FB I database (Paoletti et al., November 2005 JFS).
3,398
7,274,823
112,469,398
26,788,540
0.00
4.96
76.75
18.28
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How many contributors to a mixture?
Maximum # of alleles observed in a 4-person mixture # of occurrences Percent of cases
4 13,480 0.02
5 8,596,320 15.03
6 35,068,040 61.30
7 12,637,101 22.09
8 896,435 1.57
There are 57,211,376 possible different 4-way mixtures of the 194 individuals in the FB I Caucasian database (Paoletti et al., November 2005 JFS). (35,022,142,001 4-person mixtures with 959 individuals.)
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CPI Stats
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CPI Stats
• Probability that a random, unrelated person could be included as a possible contributor to a mixed profile
• For a mixed profile with the alleles 14, 16, 17, 18; contributors could have any of 10 genotypes:
14, 14 14, 16 14, 17 14, 18 16, 16 16, 17 16, 18
17, 17 17, 18 18, 18
Probability works out as:
CPI = (p[14] + p[16] + p[17] + p[18])2
(0.102 + 0.202 + 0.263 + 0.222)2 = 0.621
Combined Probability of Inclusion
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62.1%
91.5% 23.5% 19.2% 40.7%
47.6% 99.0% 54.4% 61.2% 8.4%
91.6% 63.7% 8.8%
82.9% 31.1%
X X X X
XXXXX
X X X X
X
62.1%
CPI Stats
1 in 1.3 million
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What weight should be given to DNA evidence?
Statistics do not lie.
But, you have to pay close attention to the questions they are addressing.
What is the chance that a randomly chosen, unrelated individual from a given population would have the same DNA profile observed in a sample?
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Mixtures with drop out
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The testing lab’s conclusions
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Ignoring loci with “missing” alleles
• Labs often claim that this is a “conservative” statistic
• Ignores potentially exculpatory information
• “It fails to acknowledge that choosing the omitted loci is suspect-centric and therefore prejudicial against the suspect.”– Gill, et al. “DNA commission of the
International Society of Forensic Genetics: Recommendations on the interpretation of mixtures.” FSI. 2006.
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Likelihood approaches for mixtures where allelic drop out may have occurred
• Determining the rate of allelic drop-out is problematic
• Determining the rate of allelic drop-in is problematic
• Considering more than two possible contributors is computationally intensive
• Considering mixtures of different racial groups can be computationally intensive
• Contributions from different kinds of close relatives require special considerations
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How many names can you take out if you can use blanks?
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How many names can you take out if you can use blanks?
The more blanks the harder it is to eliminate anyone’s name as possibly being in the mix.
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What weight should be given to DNA evidence?
Statistics do not lie.
But, you have to pay close attention to the questions they are addressing.
What is the chance that a randomly chosen, unrelated individual from a given population would have the same DNA profile observed in a sample?
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The alternative suspect pool
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Which allele frequency database should be used?
• Random match probabilities are typically generated for each of three major racial groups
• Literally hundreds of alternative allele frequency databases are available
• The racial background of a suspect is not relevant.
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What is the relevant population?
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A process of elimination
• Consider that a suspect matches an evidence sample
• If he is not the source of the DNA then it must be someone else’s. Whose might it be?
• Could the actual source be: Caucasian, Afro-Caribbean, or Indo-Pakistan?
• If it cannot be and there is no one else in the alternative suspect pool then the suspect must be the source.
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A suspect pool
D matches.
It means something if we find that A, B and C are all unlikely to also match.
A
B C
D
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Database searches
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What weight should be given to DNA evidence?
Statistics do not lie.
But, you have to pay close attention to the questions they are addressing.
What is the chance that a randomly chosen, unrelated individual from a given population would have the same DNA profile observed in a sample?
![Page 42: Statistical Weights of DNA Profiles Forensic Bioinformatics () Dan E. Krane, Wright State University, Dayton, OH](https://reader035.vdocuments.us/reader035/viewer/2022062618/5514673b550346494e8b5bd1/html5/thumbnails/42.jpg)
Consider cold hits
UK’s National DNA Database (NDNAD)
Maintained by the Home Office
Contains 6,929,946 arrested individuals as of 31 March, 2012
Assisted in 409,715 investigations (2,595 murders)
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In which case is the DNA evidence most damning?
• Probable Cause Case
– Suspect is first identified by non-DNA evidence
– DNA evidence is used to corroborate traditional police investigation
• Cold Hit Case
– Suspect is first identified by search of DNA database
– Traditional police work is no longer focus
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In which case is the DNA evidence most damning?
• Probable Cause Case
– Suspect is first identified by non-DNA evidence
– DNA evidence is used to corroborate traditional police investigation
– RMNE = 1 in 10 million
• Cold Hit Case
– Suspect is first identified by search of DNA database
– Traditional police work is no longer focus
– RMNE = 1 in 10 million
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In which case is the DNA evidence most damning?
• Probable Cause Case
– Suspect is first identified by non-DNA evidence
– DNA evidence is used to corroborate traditional police investigation
– RMNE = 1 in 10 million
• Cold Hit Case
– Suspect is first identified by search of DNA database
– Traditional police work is no longer focus
– RMNE = 1 in 10 million
– DMP = 0.693 in 1
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What weight should be given to DNA evidence?
Statistics do not lie.
But, you have to pay close attention to the questions they are addressing.
What is the chance that a randomly chosen, unrelated individual from a given population would have the same DNA profile observed in a sample?
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Familial searches
• Database search yields a close but imperfect DNA match
• Can suggest a relative is the true perpetrator
• UK performs them relatively rarely – a total of 29 were carried out in 2011-12
• Reluctance to perform them in US since 1992 NRC report
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Is the true DNA match a relative or a random individual?
• Given a closely matching profile, who is more likely to match, a relative or a randomly chosen, unrelated individual?
• Use a likelihood ratio
( ))|(
|
randomEP
relativeEPLR =
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Is the true DNA match a relative or a random individual?
• This question is ultimately governed by two considerations:
– What is the size of the alternative suspect pool?
– What is an acceptable rate of false positives?
( ))|(
|
randomEP
relativeEPLR =
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What weight should be given to DNA evidence?
Statistics do not lie.
But, you have to pay close attention to the questions they are addressing.
What is the chance that a randomly chosen, unrelated individual from a given population would have the same DNA profile observed in a sample?
![Page 52: Statistical Weights of DNA Profiles Forensic Bioinformatics () Dan E. Krane, Wright State University, Dayton, OH](https://reader035.vdocuments.us/reader035/viewer/2022062618/5514673b550346494e8b5bd1/html5/thumbnails/52.jpg)
Additional (free) resources
Forensic Bioinformatics (www.bioforensics.com)
GenoStat®(http://www.bioforensics.com/genostat/index.html)
Eight 50-minute YouTube videos(http://www.bioforensics.com/video/index.html)