Statistical DNA Forensics Theory, Methods and Computation

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1 Statistical DNA Forensics Theory, Methods and Computation Wing Kam Fung and Yue-Qing Hu Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong

3 Statistical DNA Forensics

4 STATISTICS IN PRACTICE Advisory Editor Stephen Senn University of Glasgow, UK Founding Editor Vic Barnett Nottingham Trent University, UK Statistics in Practice is an important international series of texts which provide detailed coverage of statistical concepts, methods and worked case studies in specific fields of investigation and study. With sound motivation and many worked practical examples, the books show in downto-earth terms how to select and use an appropriate range of statistical techniques in a particular practical field within each title s special topic area. The books provide statistical support for professionals and research workers across a range of employment fields and research environments. Subject areas covered include medicine and pharmaceutics; industry, finance and commerce; public services; the earth and environmental sciences, and so on. The books also provide support to students studying statistical courses applied to the above areas. The demand for graduates to be equipped for the work environment has led to such courses becoming increasingly prevalent at universities and colleges. It is our aim to present judiciously chosen and well-written workbooks to meet everyday practical needs. Feedback of views from readers will be most valuable to monitor the success of this aim. A complete list of titles in this series appears at the end of the volume.

5 Statistical DNA Forensics Theory, Methods and Computation Wing Kam Fung and Yue-Qing Hu Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong

6 Copyright # 2008 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (þ44) (for orders and customer service enquiries): cs-books@wiley.co.uk Visit our Home Page on or All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or ed to permreq@wiley.co.uk, or faxed to (þ44) This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA , USA Wiley-VCH Verlag GmbH, Boschstr. 12, D Weinheim, Germany John Wiley & Sons Australia Ltd, 42 McDougall Street, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore John Wiley & Sons Canada Ltd, 6045 Freemont Blvd, Mississauga, ONT, L5R 4J3 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN: Typeset in 10/12pt Times by Thomson Digital, India Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.

7 To Yuet Siu, Ka Chung and Ka Wing and the Memory of My Parents Yau Yung and Yiu Fung To Tian Shuang and Jia Wen

9 Contents Preface List of figures List of tables xi xiii xvii 1 Introduction Statistics, forensic science and the law The use of statistics in forensic DNA Genetic basis of DNA profiling and typing technology Genetic basis Typing technology About the book Probability and statistics Probability Dependent events and conditional probability Law of total probability Bayes Theorem Binomial probability distribution Multinomial distribution Poisson distribution Normal distribution Likelihood ratio Statistical inference Test of hypothesis Estimation and testing Problems Population genetics Hardy Weinberg equilibrium Test for Hardy Weinberg equilibrium Observed and expected heterozygosities Chi-square test Fisher s exact test Computer software... 30

10 viii CONTENTS 3.3 Other statistics for analysis of a population database Linkage equilibrium Power of discrimination DNA profiling Subpopulation models Relatives Problems Parentage testing Standard trio Paternity index An example Posterior odds and probability of paternity Paternity computer software Steps in running the software The software to deal with an incest case A relative of the alleged father is the true father Alleged father unavailable but his relative is Motherless case Paternity index Computer software and example Motherless case: relatives involved A relative of the alleged father is the true father Alleged father unavailable but his relative is Computer software and example Determination of both parents Probability of excluding a random man from paternity Power of exclusion A random man case A relative case An elder brother case: mother available Other issues Reverse parentage Mutation Problems Testing for kinship Kinship testing of any two persons: HWE Computer software Kinship testing of two persons: subdivided populations Joint genotype probability Relatives involved Examples with software Three persons situation: HWE Computer software and example Three persons situation: subdivided populations Standard trio... 96

11 CONTENTS ix A relative of the alleged father is the true father Alleged father unavailable but his relative is Example General method and computer software Complex kinship determinations: method and software EasyPA_In_1_Minute software and the method EasyPAnt_In_1_Minute EasyIN_In_1_Minute EasyMISS_In_1_Minute Other considerations: probability of paternity and mutation Problems Interpreting mixtures An illustrative example Some common cases and a case example One victim, one suspect and one unknown One suspect and two unknowns Two suspects and two unknowns Case example Exclusion probability A general approach Population in Hardy Weinberg equilibrium Population with multiple ethnic groups Subdivided population Single ethnic group: simple cases Single ethnic group: general situations Multiple ethnic groups Computer software and example NRC II Recommendation Single ethnic group Multiple ethnic groups Proofs The proof of Equation (6.6) The proof of Equation (6.8) The proof of Equation (6.9) The proofs of Equations (6.11) and (6.12) The proofs of Equations (6.14) and (6.15) Problems Interpreting mixtures in the presence of relatives One pair of relatives: HWE Motivating example A probability formula Tested suspect with an unknown relative Unknown suspect with a tested relative Two related persons were unknown contributors An application

12 x CONTENTS 7.2 Two pairs of relatives: HWE Two unknowns related respectively to two typed persons One unknown is related to a typed person and two other unknowns are related Two pairs of related unknowns Examples Extension Related people from the same subdivided population Introductory example A simple case with one victim, one suspect and one relative General formulas An example analyzed by the software Proofs Preliminary The proof of Equation (7.5) The proof of Equation (7.7) The proof of Equation (7.9) The proof of Equation (7.11) The proof of Equation (7.13) The proofs of Equations (7.18) and (7.20) Problems Other issues Lineage markers Haplotypic genetic markers for mixture Bayesian network Peak information Mass disaster Database search Solutions to problems 201 Appendix A: The standard normal distribution 225 Appendix B: Upper 1% and 5% points of v 2 distributions 227 Bibliography 229 Index 237

13 Preface In the early 1990 s, one of the authors attended a forensic conference in Arizona, USA and became familiar with DNA profiling. In the meeting, there were heated debates among forensic scientists, statisticians and legal professionals on the pros and cons of the then new forensic DNA technology. These debates began to settle down after the US National Research Council released its second report on the evaluation of forensic DNA evidence in Currently, the technique is widely employed and accepted in the courtroom due to its high discriminating power and reliability. It is a very powerful tool, not only in the investigation of serious criminal offences including rapes and homicides, but also in voluminous offences such as thefts and burglaries. Statistics and probability play an important role in the interpretation of forensic DNA. Unlike other areas of forensic science, probability is often needed in assessing the weight of DNA evidence; probabilities in the magnitude of one in millions or one in billions are commonly heard in court cases. A major aim of this book is to introduce the fundamental statistical and probability theory and methods for the evaluation of DNA evidence. The book covers three main applications of DNA profiling, namely identity testing, determination of parentage and kinship, and interpretation of mixed DNA stains. Moreover, we place emphasis on the computational aspects of statistical DNA forensics. Computer programs are available at for possible use. Readers can use the software to check the numerical findings of the examples given in the book. This can help readers understand and appreciate the theory and methods behind statistical forensic DNA analysis. We are most grateful to the following people for their continuous support and assistance: Dart Man Wong and Pui Tsui for introducing the fundamental concepts and sharing their knowledge and experience in DNA forensics; Sze Chung Leung and his forensic laboratory colleagues for encouragement and support; Yuk Ka Chung, Hong Lee and Yan Tsun Choy for computing assistance; John Buckleton for introducing the mixed stain problem; and specifically to Ada Lai for excellent secretarial support and typing the manuscript. We thank the staff at John Wiley for their editorial assistance. Last but not least, we wish to express our gratitude to our families, Yuet Siu, Ka Chung, Ka Wing, and Tian Shuang, Jia Wen, for their patience and immense support. W.K. Fung and Y.Q. Hu Hong Kong

15 List of figures 1.1 An STR profile of a DNA sample from a crime scene, obtained by ABI machines and software Tree diagram for three throws of a die Normal density curves; (a) X Nð70; 6 2 Þ and (b) X Nð80; 10 2 Þ Evaluate the probability for a normal distribution. Left-hand figure: P(64 < X <78.1), where X N(70, 6 2 ); right-hand figure: P( 1 < Z < 1.35), where Z = (X m)/s with m = 70, s = 6, and Z N(0, 1). The two probabilities are the same A chi-square distribution with v ¼ 5 degrees of freedom. The value 11:07 corresponds to the upper 5% point of the distribution Captured screen for running the EasyDNA_PopuData software for the Hong Kong Chinese population database DNA profiles of the crime stain, suspects 1 and 2 and the victim at three STR loci THO1, TPOX and CSF1PO obtained using ABI proprietary machines and software Captured screen for running the EasyDNA_Trio software for a standard trio problem with genotype data given in Table Captured screen for the output file of a standard trio problem with genotype data given in Table Captured screen for paternity testing for a trio problem where H d : a brother of the alleged father Z is the true father of the child C Captured screen for running the EasyDNA_Motherless software for a motherless case with genotype data of the child C and alleged father AF given in Table Captured screen for paternity testing for a motherless case where H p : a brother of Z is the true father of the child C versus H d : the true father is a random unrelated man Captured screen for running the EasyDNA_BothParents software for determination of both parents with genotype data given in Table

Statistical DNA Forensics Theory, Methods and Computation

Statistical DNA Forensics Theory, Methods and Computation Wing Kam Fung and Yue-Qing Hu Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong Statistical DNA Forensics