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How TrueAllele® Works (Part 1)

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1 How TrueAllele® Works (Part 1)
Cybergenetics Webinar October, 2014 Mark W Perlin, PhD, MD, PhD Cybergenetics, Pittsburgh, PA Cybergenetics © Cybergenetics ©

2 Biological evidence Q S

3 Forensic question Did suspect S contribute his DNA
to biological evidence Q?

4 DNA laboratory extract, amplify, separate, detect

5 TrueAllele® Casework: Infer
ViewStation User Client Database Server Interpret/Match Expansion Visual User Interface VUIer™ Software Parallel Processing Computers 8 to 80 questions simultaneously

6 Bayesian probability model
Background noise PCR variation Mixture weight PCR stutter Relative amplification Genotype (separated) Differential degradation Rev Bayes, 1765 No calibration needed; learn from the data

7 No analytical threshold needed; model the data
Perlin, M.W. and Sinelnikov, A. An information gap in DNA evidence interpretation. PLoS ONE, 4(12):e8327, 2009. Background noise No analytical threshold needed; model the data

8 PCR variation No stochastic threshold needed; model the data
Perlin, M.W., Legler, M.M., Spencer, C.E., Smith, J.L., Allan, W.P., Belrose, J.L., and Duceman, B.W. Validating TrueAllele® DNA mixture interpretation. Journal of Forensic Sciences, 56(6): , 2011. PCR variation No stochastic threshold needed; model the data

9 Mixture weight Mother Son Father
Perlin, M.W. and Szabady, B. Linear mixture analysis: a mathematical approach to resolving mixed DNA samples. Journal of Forensic Sciences, 46(6), , 2001. Mixture weight Mother Son Father

10 Hierarchical variables
kth contributor dk,1 dk,2 … experiment data dk,N locus weights Wk,1 Wk,2 … Wk,N template weight Wk prior probability W0

11 M.W. Perlin, "Expert systems for automated STR analysis", Scientific Working Group on DNA Analysis Methods (SWGDAM), Quantico, VA, 14-Jan-2003. PCR stutter

12 Relative amplification
M.W. Perlin, "Expert systems for automated STR analysis", Scientific Working Group on DNA Analysis Methods (SWGDAM), Quantico, VA, 14-Jan-2003. Relative amplification

13 Perlin, M.W. and Szabady, B. Linear mixture analysis: a mathematical approach to resolving mixed DNA samples. Journal of Forensic Sciences, 46(6), , 2001. Genotype pattern

14 process transformation
Hierarchical pattern DNA quantity degradation mixture weight relative amplification PCR stutter data pattern capillary injection process transformation pattern variation

15 Markov chain Monte Carlo
Local choices, global solution Every cycle, visit all 100 variables Next state? Current state Pr(Next state) Transition probability = Pr(Current state)

16 Joint probability distribution
all the variables together in a high-dimensional space locus 1 2 3 contributor genotype genotype(contributor, locus) mixture-weight(contributor, locus) PCR-stutter(locus) variance-parameters(locus) hierarchical variables ...

17 Marginalize to separate
reduce to one variable, sum over all the other variables locus 1 2 3 contributor genotype objectively inferred genotype at locus 8 for contributor 2

18 TrueAllele® Casework: Match
ViewStation User Client Database Server Interpret/Match Expansion Visual User Interface VUIer™ Software Parallel Processing Computers 2 hours for each question

19 The likelihood ratio 1940's, Bletchley Park, UK: Alan Turing measures
how data changes belief LR is a ratio of probabilities, information is log(LR), unit is the "ban" WWII Bombe computer cracks Enigma code exclusion inconclusive inclusion ban

20 Suspect S contributed his DNA to biological evidence Q
Hypothesis Suspect S contributed his DNA to biological evidence Q Known: the suspect’s genotype is the allele pair: s = [a,b]

21 Original Turing & Good formulation (1950)
Odds form Original Turing & Good formulation (1950) Bayes factor, or likelihood ratio (LR)

22 Hypotheses correspond to HP and HD
Perlin, M.W. Explaining the likelihood ratio in DNA mixture interpretation, in Proceedings of Promega's Twenty First ISHI. San Antonio, TX, 2010. Likelihood form Hypotheses correspond to HP and HD

23 TrueAllele can separate genotypes
Genotype expansion TrueAllele can separate genotypes likelihood prior

24 Reduce summation to just suspect's term
Apply hypothesis Reduce summation to just suspect's term likelihood

25 Bayes theorem Reorganize terms

26 Genotype form Posterior over prior posterior prior

27 Ratio of genotype probabilities
Visualize the LR Ratio of genotype probabilities 15x 61% Prob(evidence) Prob(coincidence) 4%

28 Genotype match over coincidence
Match form Genotype match over coincidence Q posterior S posterior prior

29 Match statement Ratio of match probabilities
A match between the shotgun shell and the son is 6 trillion times more probable than coincidence • accurate mathematics • understandable language • no conditionals to transpose • compares separated genotypes

30 Sum of genotype match over coincidence
Evidence to evidence Sum of genotype match over coincidence Q posterior S posterior prior standard form of LR in probability theory

31 Single contributor LR Separated genotypes for each contributor
• TrueAllele does the heavy lifting • separates out the genotypes • single-source simplicity Easy to understand, report and explain Straightforward direct and cross examination Relevant: focus is on one person Compares genotype with genotype

32 The unseparated LR HP: X=x, Y=y, Z=z HD: X=?, Y=?, Z=z
• "data" is not quantitative data (thresholds) • lacks Bayesian foundation (wrong math) • subjective genotype values (just guessing) • uses defendant genotype (not objective) • implicates multiple people (not relevant) • doesn't separate genotypes (incomplete) • ignores most of the data (inaccurate) • considers few possibilities (not thorough) • many hypothesis formulations (subjective) • difficult to state or explain (unworkable)

33 Part 2 continues with Drop out, degraded DNA, kinship, DNA databases
M.W. Perlin, "TrueAllele® interpretation of DNA mixture evidence", Keynote talk, 9th International Conference on Forensic Inference and Statistics, Leiden University, The Netherlands, 20-Aug-2014. M.W. Perlin, "TrueAllele® Casework", Almost Everything You Wanted to Know About Probabilistic Software (But Were Afraid to Ask), Promega's Twenty Fifth International Symposium on Human Identification, Phoenix, AZ, 29-Sep-2014.

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