Statistical Methods and Software for Forensic Genetics. Lecture I.1: Basics

Transcription

1 Statistical Methods and Software for Forensic Genetics. Lecture I.1: Basics Thore Egeland (1),(2) (1) Norwegian University of Life Sciences, (2) Oslo University Hospital Workshop. Monterrey, Mexico, Nov 11-13, / 26

2 Short bio Education: Mathematics, statistics, computer science, mostly from University of Oslo. PhD in statistics, University of Oslo, Work: Previously: Research, consulting. From 1996: Professor of statistics, Currently, Norwegian University of Life Sciences. 20% position, Section of Forensics, Oslo University Hospital. Research interests: Statistical, mathematical perspective on (forensic) genetics. Software: Familias (Windows and R). Norwegian: living in Oslo. 2 / 26

3 Contents of workshop Day 1 Basics: Genetics, weight of evidence (LR, Bayes). Day 2 Applications and demonstration of software. Day 3 Theoretical and hands on computer exercises. 3 / 26

4 Contents, this lecture Basic forensic genetics very briefly: Mendelian inheritance Markers: autosomal, X, Y, mtdna, STR-s.. Assumptions: Hardy Weinberg Equilibrium (HWE). Linkage. Linkage disequilibrium (LD). : Standard version. On odds form. On log form. 4 / 26

5 5 / 26

6 Pedigree 6 / 26

7 Genetic markers I 7 / 26

8 Genetic markers II 8 / 26

9 . Genetic markers III. Example: Fusion 6C 9 / 26

10 Mendelian inheritance 10 / 26

11 X linked inheritance 11 / 26

12 Y linked inheritance 12 / 26

13 Mitochondrial (mtdna) inheritance 13 / 26

14 Hypotheses AF 17/18 8/8 CH 17/17 8/8 MO / / H 1 : AF biological father of CH. H 2 : AF and CH unrelated. Notation. Sometimes: H 1 = H P : prosecution hypothesis, H 2 = H D : defence hypothesis. 14 / 26

15 Likelihood ratio. Definition Forensic framework LR = LR H1,H 2 (E) = P(E H 1) P(E H 2 ) is the likelihood ratio for evidence E with respect to the two hypotheses H 1 and H 2. The LR measures how much better (or worse) H 1 explains the evidence E than H / 26

16 Likelihood Ratio. Example AF 17/18 8/8 MO / / LR = P(E H 1) P(E H 2 ) = P(g AF, g CH H 1 ) P(g AF, g CH H 2 ) = P(g CH g AF, H 1 )P(g AF H 1 ) P(g CH ) g AF, H 2 )P(g AF H 2 ) = P(g CH g AF ) P(g CH ) CH 17/17 8/8 LR 1 = 1 2 p 17 p 2 17 = = 2.45 LR 2 = p 8 p8 2 = = 1.81 LR = LR 1 LR 2 = = / 26

17 Likelihood Ratio. Interpretation and assumptions AF 17/18 8/8 CH 17/17 8/8 MO / / Interpretation LR=4.4: The data is 4.4 times more likely if AF is assumed to be the father compared to the unrelated alternative. Assumptions Hardy Weinberg Equilibrium (HWE). Independent markers. No artefacts: (no mutation, no silent alleles, no drop out/in, no error). 17 / 26

18 Realistic number of markers Marker CH AF LR LR(mut) D3S /17 17/ TPOX 8/8 8/ D6S474 16/17 14/ D19S433 12/15 12/ Total / 26

19 W = Posterior probability of paternity Assume prior probabilities P(H P ) = P(H D ) = 0.5 (reasonable?) Prior odds P(H P) P(H D ) = 1. Then P(E H P )P(H P ) W = P(H P E) = P(E H P )P(H P ) + P(E H D )P(H D ) = LR LR + 1 = = = Probability of H P given evidence 19 / 26

20 Bayes theorem on odds form 20 / 26

21 Blackstone ratio 21 / 26

22 Optimal decision rule 22 / 26

23 Adding evidence I 23 / 26

24 Adding evidence II 24 / 26

25 One of many verbal scales 25 / 26

26 T Egeland, D Kling, and P Mostad. Relationship Inference with Familias and R: Statistical Methods in Forensic Genetics. Academic Press, IJ Good. Weight of evidence: A brief survey. Bayesian Statistics, A Tillmar and P Mostad. Choosing supplementary markers in forensic casework. Forensic Science International: Genetics, 13: , / 26