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The statistical weight of mixed samples with allelic drop out

The statistical weight of mixed samples with allelic drop out. First serious attempt by Gill et al. 2006, Forensic Science International 160 :90 An important general paper about mixtures: Curran et al. 1999, J. Forensic Science 44 :987. Mixed sample with drop out. Standard Mixture Analysis.

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The statistical weight of mixed samples with allelic drop out

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  1. The statistical weight of mixed samples with allelic drop out First serious attempt by Gill et al. 2006, Forensic Science International160:90 An important general paper about mixtures: Curran et al. 1999, J. Forensic Science44:987

  2. Mixed sample with drop out

  3. Standard Mixture Analysis • Assume there are 2 people and 3 alleles: A1, A2, A3 • There must be a total of 4 alleles allowing for the following possible combinations: (A1,A1,A2,A3) and (A1,A2,A2,A3) and (A1,A2,A3,A3). • Let the frequency of the 3 alleles bep1p2p3

  4. Details of (A1,A1,A2,A3) • Possible pairs of sampled genotypes are:[A1/A1 and A2/A3] or [A2/A3 and A1/A1][A1/A2 and A1/A3] or [A1/A3 and A1/A2] • These pairs are chosen with frequencies2[p122 p2 p3]2[2 p1 p22 p1 p3] • The sum of these is 12p12 p2 p3 • Repeating this for the other two orderings and adding them all up gives 12p1p2 p3(p1+p2+p3)

  5. General formula • let c=number of distinct alleles • x= number of people in the mixture • ui= number of copies of allele i • the frequency of any particular combination

  6. Mixtures with drop out • Let Q be the dropped out allele • The frequency of Q is 1-sum(distinct alleles) • Suppose evidence is A1,A2,Q • Possible orderings are (A1,A1,A2,Q) and (A1,A2,A2,Q) but not (A1,A2,Q,Q) since we have assumed only one allele dropped out • frequency is 12p1p2 pQ(p1+p2)

  7. Two people mixtures

  8. Likelihood Ratios • Compare the probability of two hypotheses, the prosecution and the defense • Each hypothesis must compute the probability of the observed genetic evidence • Let L = Prob[evidence|prosecution] / Prob[evidence|defense]

  9. Example • Three person mixture • Evidence: 9 • Suspect: 11, 14 • Two alleles dropped out • Let D be the probability that one allele will drop out. • In this sample the State assumes at least two alleles dropped out, and four alleles did not: • This probability is: (1-D)4D2

  10. Example: state hypothesis • (1-D)4D2 {prob[two people with only the 9 allele]} • (1-D)4D2p94

  11. Example: defense hypothesis • There are several possibilities • No drop out: (1-D)6p96 • One allele dropped out, five did not: (1-D)5Dprob[three people with only the 9 allele and one allele dropped out] = (1-D)5D 6p95pQ • Two alleles dropped out, four did not: (1-D)4D2prob[three people with only the 9 allele and two alleles dropped out] =(1-D)4D215p94pQ2

  12. Example Results • 13 loci with a total of 5 alleles dropped out and a minimum of three people in the mixture, 1 known, 2 unknown • The lab CPI for Caucasians was 1 in 42 million

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