1. Solving Crimes using MCMC to Analyze Previously Unusable DNA Evidence
Mark W Perlin, PhD, MD, PhD
Cybergenetics, Pittsburgh, PA
Joint Statistical Meetings
August, 2014
Boston, MA
Cybergenetics ©
Cybergenetics ©

2. One person, one genotype8 12
locus

3. DNA reference data One or two allele peaks at a locus victim
peak height
peak size
Cybergenetics ©

4. Two people, two genotypes8 12
locus 10 13

5. DNA mixture data Quantitative peak height pattern at 13 genetic loci
One locus
D7S820
Evidence from
victim's fingernails
victim
other
Cybergenetics ©

6. Hierarchical Bayesian model
Mixture weight
Genotype
• small DNA amounts
• degraded contributions
• K = 1, 2, 3, 4, 5, 6, ...
unknown contributors
• joint likelihood function

7. Markov chain Monte Carlo
Sample from joint posterior probability distribution
victim
93% 7%
other

8. Separate mixture data into two contributor components
Mixture weight
Separate mixture data into two contributor components 7%
93%
other
victim

9. Genotype inference Thorough: consider every possible genotype solution
Objective: does not know the comparison genotype
Victim's allele pair
Explain the peak pattern
Another person's allele pair
Better explanation
has a higher likelihood

10. Evidence genotype
Objective genotype determined solely from the DNA data.
Never sees a comparison reference.
99.9%

11. How much more does the suspect match the evidence
DNA match information
How much more does the suspect match the evidence
than a random person?
Likelihood ratio
99.9%
Prob(evidence match)
Prob(coincidental match)
LR =
= 58
1.7%

12. DNA match statistic Product of 13 independent genetic loci
A match between the victim's fingernails
and the suspect
is 189 billion times more probable
than coincidence.
Statistic Method
CPI = 13 thousand inclusion (human)
LR = 189 billion TrueAllele (computer)
Cybergenetics ©

13. TrueAllele Casework on Virginia DNA Mixture Evidence:
Computer and Manual Interpretation in 72 Reported Criminal Cases.
Perlin MW, Dormer K, Hornyak J, Schiermeier-Wood L, Greenspoon S
PLoS ONE (2014) 9(3): e92837
Sensitive
The extent to which interpretation identifies the correct person
True DNA mixture inclusions
101 reported genotype matches
82 with DNA statistic over a million

14. TrueAllele sensitivity
log(LR) match distribution
11.05 (5.42)
113 billion
TrueAllele

15. Specific
The extent to which interpretation does not misidentify the wrong person
True exclusions, without false inclusions
101 matching genotypes x 10,000 random references
x 3 ethnic populations,
for over 1,000,000 nonmatching comparisons

16. TrueAllele specificity
log(LR) mismatch distribution
– 19.47

17. Reproducible The extent to which interpretation gives
the same answer to the same question
MCMC computing has sampling variation
duplicate computer runs
on 101 matching genotypes
measure log(LR) variation

18. TrueAllele reproducibility
Concordance in two independent computer runs
standard deviation
(within-group)
0.305

19. Manual inclusion method
Over threshold, peaks become binary allele events
Allele pairs
7, 7
7, 10
7, 12
7, 14
10, 10
10, 12
10, 14
12, 12
12, 14
14, 14
All-or-none allele peaks,
disregard quantitative data
Analytical
threshold

20. Simplify data, easy procedure,
CPI information
6.83 (2.22)
6.68 million
CPI
Combined probability of inclusion
Simplify data, easy procedure,
apply simple formula
PI = (p1 + p pk)2

21. Modified inclusion method
Higher threshold for human review
Apply two thresholds,
doubly disregard the data
Stochastic
threshold
in 2010
Analytical
threshold
in 2000

22. Modified CPI information
6.83 (2.22)
6.68 million
CPI
2.15 (1.68)
140
mCPI

23. Method comparison 6.83 (2.22) 6.68 million CPI 2.15 (1.68) mCPI 140
11.05 (5.42)
113 billion
TrueAllele

24. Method accuracy Kolmogorov Smirnov test K-S p-value 0.106 0.215
e-22
e-25

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