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Analyzing mixture evidence when there are many possible explanations using SNP-s

Analyzing mixture evidence when there are many possible explanations using SNP-s. Thore Egeland National University Hospital, Norway, Petter F. Mostad Chalmers University, Sweden. Contents. General background. Why SNP-s ( diallelic markers)?

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Analyzing mixture evidence when there are many possible explanations using SNP-s

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  1. Analyzing mixture evidence when there are many possible explanationsusing SNP-s Thore Egeland National University Hospital, Norway, Petter F. Mostad Chalmers University, Sweden Thore.Egeland@basalmed.uio.no

  2. Contents • General background. • Why SNP-s (diallelic markers)? • How many markers are needed to:- exclude innocent, - determine no of contributors to a stain, - obtain sufficiently strong evidence (LR-s)? • A model for linked SNP-s: -Many linked or fewer independent?

  3. Criminal cases involving DNA, Norway

  4. Problems with traditional methods • "The interpretation of these mixtures can be a challenging task for the DNA scientist". Ladd et al (2001) • "Powerful methods based on likelihood ratios havebeen developed by Evett et al.(1) and Weir et al.(2) tointerpret mixtures. However, these models presupposeunambiguous identification of alleles prior to analysis andtake no account of their relative peak areas." Gill et al. • See however Evett, Gill and Lambert (1998) and Wang et al (2002).

  5. SNP Single Nucleotide Polymorphism • single base pair positions in DNA at which different sequence alternatives (alleles) exist in normal individuals in a population

  6. Why SNP-s? • Problems of interpretation reduced. • May work better than STR-s for degraded biological material. • Many available, may compensate for less variability.

  7. Notation Stain Contributor 1 Contributor 1 Locus 1 p1=P(0) 0 1 Locus 2 p2=P(0) 0 Data z=(2,0) z=(0,1) z=(2,2)

  8. Likelihoods Probabilities of zi being 0,1, or 2 assuming independence within and between individuals : p0,i=pi2x, p1,i=(1-pi)2x, p2,i=1-pi2x- (1-pi)2x Likelihood for 1 marker p0,i1-zip1,izip2,i-zi(1-zi) Likelihood for N independent markers

  9. Three main questions • How many markers are needed to 1. exclude innocent, 2. determine no of contributors to a stain, 3. obtain sufficiently strong evidence (LR-s)?

  10. x=1 x=2 x=5 p=0.3

  11. H1: victim and suspect contributed H2: two unknown contributed Data simulated assuming H1. LR=P(data| H1)/LR=P(data| H2) LR=1,000,000 p=0.25

  12. Model for dependent SNP-s No recombination Once upon a time: (1,1) Mutation (0,0) (0,1) P(0,.) = p1, P(,0)=p2, P(1,0)=0 P(0,0) =p2 Px(0,0)=p22x (x-contributors) independence (p1p2)2x

  13. The assumption of independence: Estimating the number of contributors The error could be of arbitrary magnitude

  14. The assumption of independence:Computing the likelihood ratio (LR). H1: victim and suspect contributed H2: two unknown contributed Assume victim, suspect and stain all (1,1). Then LR=1/(1-p1)4 LRInd= 1/( (1-p1) (1-p2))4 Again:The error could be of arbitrary magnitude

  15. Independence Correct LR=1,000,000 95% pointwise conf interval

  16. References • Ladd et al. (2001). Croatian Med J,42(3), 244-46, 2001. • Evett and Weir (1998). “Interpreting DNA evidence”. Sinauer, MA, USA. • Evett, Gill and Lambert (1998). J For Sci, 43 (1):62-69 • Gill et al. www.promega.com/geneticidproc/ussymp9proc/content/03.pdf • Weir et al (1997). J Forensic Sci.,42, 213-222. • Weir (1995). DNA statistics in the Simpson matter. nat gen, 11, 366-368 • Stockmarr (2000). In “Stat Science in the courtroom”, ed Gastwirth, Springer. • Wang et al (2002). First advanced CE STR Working Group meeting.

  17. Conclusions • Difficult to use dependent SNP-s (collected for other purposes in vast numbers). • SNP-s could always be a useful supplement and often replace STR-s. • Problems with many contributors and frequency around 0.5.

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