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Strategies and calculations in DNA kinship cases

Outline. Kinship methodLikelihood ratiosPaternity, Avuncular"Mutationold way, suggested new wayDNAVIEW demonstration. Kinship method. Genetic evidenceLikelihood ratioKinship programref: Brenner, CH Symbolic Kinship Program", Genetics 145:535-542, 1997 Feb. Likelihood ratio. Kinship I (Bas

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Strategies and calculations in DNA kinship cases

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    1. Strategies and calculations in DNA kinship cases Charles Brenner consulting in forensic mathematics because I thought of it

    2. Outline Kinship method Likelihood ratios Paternity, “Avuncular” Mutation old way, suggested new way DNA•VIEW demonstration

    3. Kinship method Genetic evidence Likelihood ratio Kinship program ref: Brenner, CH “Symbolic Kinship Program”, Genetics 145:535-542, 1997 Feb

    4. Likelihood ratio Kinship I (Basic) Paternity avuncular Vs. “exclusion”

    5. What a likelihood ratio is Compares two explanations for data The heart of “forensic mathematics” http://dna-view.com cbrenner@uclink.berkeley.edu

    6. Likelihood ratio for being French Data: Subject speaks 100 French words in 1 hour Explanation #1: subject is French 20% event Explanation #2: subject is not French 1% event LR=20; Data is 20 times more characteristic of French person

    7. Paternity: why likelihood ratio?

    8. Likelihood ratio for paternity (PI) PI = X/Y, where X=P(genetic types | man=father) Y=P(genetic types | man not father) Interpretations: Odds favoring paternity over non-paternity assuming all other evidence is equally divided Evidence is PI times more characteristic of paternity

    9. What the “exclusion” method is Considers only one hypothesis which it assumes may be disproven by some data sets -- an artificial assumption at best (what about mutations? Laboratory error?) and completely useless in many situations siblingship uncle

    10. Paternity: how likelihood ratio?

    11. Data: Mother=PS, Child=PQ, Man=RQ explanation #1: man is father (2ps)(2qs)/4 event explanation #2: not father; his Q is coincidence (2ps)(2qs)(q/2) event LR=1/(2q) If q=1/20, data 10 times more characteristic of “father” explanation Likelihood ratio for Paternity (PI)

    12. Avuncular index (Is the man an uncle?)

    13. Other kinship cases Kinship program missing person null alleles

    14. Missing person kinship case

    15. Null allele loss of primer site

    16. PI when possible mutation Concept Old method Str data New method

    17. Mutation analysis: concept Data: Mother=PS, Child=PQ, Man=RT Likelihood ratio analysis -- compute probability of data assuming Explanation #1: Paternity; plus mutation need “model” of mutation Explanation #2: Nonpaternity; real father ? Q #2 usually better explanation. LR<<1.

    18. Paternity case: one “exclusion” PI=20000 (combined, 4 loci) PI=1/500 (PS, PQ, RT locus) overall PI = 40. Conclusion: probably paternity & mutation

    19. Paternity case: two “exclusions” PI=2000 (combined, 3 loci) PI=1/500 (PS, PQ, RT locus) PI=1/200 (PS, PQ, YZ locus) overall PI = 1/50. Conclusion: probably non-paternity

    20. Mutation (old method) Data: Mother=PS, Child=PQ, Man=RT Explanation #1: Paternity; T or R ? N man transmits T (or R -- doesn’t matter) ? chance T mutates ?? chance it ends up as Q Explanation #2: Nonpaternity; real father ? Q sperm is Q

    21. Old mutation formula LR= ? ?=rate of mutations/meosis, e.g. 1/1000. Correct on average Much too low for small changes Much too high for big changes

    22. Old mutation formula is simple, but badly inaccurate suggests the “2 exclusion” rule rule probably more accurate than the formula rule adequate for RFLP’s rule not adequate for STR’s need a new formula

    23. Mutation model (old formula)

    24. Mutation model (more realistic)

    25. Reasonable mutation model, STR’s

    26. Mutation LR (new, for STR’s) Data: Mother=PS, Child=PN, Man=RŃ Explanation #1: Paternity; RŃ ? N 50% chance transmit Ń ? = chance Ń mutates m = chance Ń ends up as N, assuming mutation m =0.5 if N, Ń are 1 step apart m=0.05 if 2 steps, etc Explanation #2: Real father ? N LR= ?/(4q) (assuming single step) q=allele frequency of the paternal allele N

    27. STR mutation rates

    28. Mutation reference http://dna-view.com/mudisc.htm

    29. Kinship II (advanced) More than two scenarios Three Many Strategies Whom to test Example Whether effective result is likely

    30. More than two scenarios Three Many disasters

    31. Three scenarios -- Father? Uncle? Unrelated?

    32. Father/Uncle/Unrelated analysis

    33. Likelihood ratios are “transitive” means that if explanation “father” is s times better than “uncle” and “uncle” is t times better than “unrelated” then “father” explains data st times better than “unrelated.”

    34. Summary Likelihood ratios are the way to quantify evidence Mutation calculation must be changed for STR’s Kinship: All kinship problems have an explicit solution Multiple scenarios: Triple ratio for three scenarios Lattice approach for the most complicated situations

    35. Thanks Prof Antonio Alonso & GEP-ISFH Audience for sitting patiently

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