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Probability of Paternity PE Probability of Exclusion RMNE Random Man Not Excluded AFDAA 2012 WINTER MEETING Population Statistics Refresher Course - Lecture 3: Statistics of Kinship Analysis Ranajit Chakraborty, PhD Center for Computational Genomics Institute of Applied Genetics Department of Forensic and Investigative Genetics University of North Texas Health Science Center Fort Worth, Texas 76107, USA Tel. (817) 735-2421; Fax (817) 735-2424 e-mail: [email protected] Lecture given as a part of the AFDAA Population Statistics Refresher Course Held at the AFDAA 2012 Winter Meeting at Auston, TX on February 2, 2012 Statistics of Kinship Analysis Learning Objectives Attendees of this lecture should be able to understand • Objectives of kinship analysis from DNA evidence data • Possible conclusions of kinship analysis • Questions answered from kinship analysis • Concept of exclusion probability and their limitations • Likelihood ratio approach of kinship analysis • Paternity analysis, reverse parentage analysis, and kinship analysis for missing person identification • Advanced issues – mutation, need of linage markers Lecture 3: Statistics for Kinship Analysis from DNA Evidence Topics Covered • What is kinship analysis and its special cases • Possible conclusions from kinship analysis of DNA evidence • Questions answered in kinship analysis • Requirements of data for kinship analysis • Likelihood ratio: Paternity Index, Kinship Index • General formulation of statistics for kinship analysis • Advanced issues (mutation, missing person identification with multiple remains and choice of informative reference samples) Kinship Analysis Kinship Determination Objectives: - Evidence sample’s DNA is compared with that of one or more reference profiles - The objective is to determine the validity of stated biological relatedness among individuals, generally in reference to the placement of a specific target individual in the pedigree of reference individuals’ profiles Kinship Analysis Types of Kinship Analysis - Standard Paternity Analysis - Deficient Paternity Analysis (e.g., Mother-less cases) - Reverse Parentage Analysis - Familial Search (i.e., Pairwise relationship testing) - Missing person identification Three Types of Conclusions Exclusion (Match), or Inclusion Inconclusive What is an Exclusion? In all types of Kinship Analyses Allele sharing among evidence and reference samples disagrees with the Mendelian rules of transmission of alleles with the stated relationship being tested When is the Observation at a Locus Inconclusive? Compromised nature of samples tested failed to definitely exclude or include reference individuals May occur for one or more loci, while other loci typed may lead to unequivocal definite inclusion/ exclusion conclusions Caused often by DNA degradation (resulting in allele drop out), and/or low concentration of DNA (resulting in alleles with low peak height and/or area) for the evidence sample What is an Inclusion? In all types of Kinship Analyses Allele sharing among evidence and reference samples is consistent with Mendelian rules of transmission of alleles with the stated relationship being tested; i.e., the stated biological relationship cannot be rejected (Note: In the context of Kinship analyses, the terminology of “match” is not appropriate) Exclusion Nope Nope Inclusion PATERNITY TESTING MOTHER ALLEGED FATHER CHILD Two alleles for each autosomal genetic marker Language of Paternity Testing Maternal Contribution Obligate Paternal Allele Dual Obligate Paternal Alleles Three Genetic Profiles are Determined Mother A B Child Bm Cp Alleged father C D Typical Paternity Test Two possible outcomes of test: Inclusion The obligate paternal alleles in the child all have corresponding alleles in the Alleged Father Exclusion The obligate paternal alleles in the child DO NOT have corresponding alleles in the Alleged Father Exclusion Nope Nope Results The Tested Man is Excluded as the Biological Father of the Child in Question Inclusion Results The Tested Man Cannot be Excluded as the Biological Father of the Child in Question Several Statistical Values are Calculated to Assess the Strength of the Genetic Evidence Language of Paternity Testing PI Paternity Index CPI Combined Paternity Index W Probability of Paternity PE Probability of Exclusion RMNE Random Man Not Excluded Paternity Index summarizes information provided by genetic testing • Likelihood Ratio • Probability that some event will occur under a set of conditions or assumptions • Divided by the probability that the same event will occur under a set of different mutually exclusive conditions or assumptions Paternity Index • Observe three types – from a man, a woman, and a child • Assume true trio – the man and woman are the true biologic parents of child • Assume false trio – woman is the mother, man is not the father • In the false trio the child’s father is a man of unknown type, selected at random from population (unrelated to mother and tested man) Standard Paternity Index Mother, Child, and Alleged Father • PI is a likelihood ratio = X/Y • Defined as the probability that an event will occur under a particular set of conditions (X). • Divided by the probability that the event will occur under a different set of conditions (Y). Standard Paternity Index • In paternity testing, the event is observing three phenotypes, those of a woman, man and child. • The assumptions made for calculating the numerator (X) is that these three persons are a “true trio”. • For the denominator (Y) the assumptions is that the three persons are a “false trio”. Paternity Biological Relationship Parents M F Child C Paternity Analysis ? Paternity Analysis Hypothetical case DNA Analysis Results in Three Genotypes Mother (AB) Child (BC) Alleged Father (CD) Paternity Analysis AB CD BC An AB mother and a CD father can have four possible offspring: AC, AD, BC, BD Standard Paternity Index PI determination in hypothetical DNA System PI = X / Y Numerator X = is the probability that (1) a woman randomly selected from a population is type AB, and (2) a man randomly selected from a population is type CD, and (3) their child is type BC. Paternity Analysis AB CD BC Standard Paternity Index PI determination in hypothetical DNA System PI = X / Y Denominator Y = is the probability that (1) a woman randomly selected from a population is type AB, (2) a man randomly selected and unrelated to either mother or child is type CD, and (3) the woman’s child, unrelated to the randomly selected man is BC. Paternity Analysis AB CD Tested Man BC CD Untested Random Man Standard Paternity Index When mating is random, the probability that the untested alternative father will transmit a specific allele to his child is equal to the allele frequency in his race. We can no look into how to actually calculate a Paternity Index Hypothetical DNA Example First Hypothesis Numerator Person Type Mother AB Child BC Alleged Father CD In order to explain this evidence Calculate Probability that a) Woman randomly selected from population is type AB b) Man randomly selected from population is type CD, and c) Their child is type BC Paternity Analysis Paternity Index Numerator CD 2pApB AB 2pCpD 0.5 0.5 BC Probability = 2pApB x 2pCpD x 0.5 x 0.5 Hypothetical DNA Example Second Hypothesis Denominator Person Type Mother AB Child BC Alleged Father CD In order to explain this evidence Calculate Probability that a) Woman randomly selected from population is type AB b) An alternative man randomly selected from population is type CD, and c) The woman’s child, fathered by random man, is type BC Paternity Analysis Paternity Index Denominator 2p p 2pApB AB CD C D pC 0.5 BC Probability = 2pApB x 2pCpD x 0.5 x pC Paternity Analysis Paternity Index 2pApB x 2pCpD x 0.5 x 0.5 PI = 2pApB x 2pCpD x 0.5 x pC 0.5 PI = pC Hypothetical DNA Example Probability Statements Person Type Mother AB Child BC Alleged Father CD One might say (Incorrectly) a) Numerator is probability that tested man is the father, and b) Denominator is probability that he is not the father Hypothetical DNA Example Probability Statement Person Type Mother AB Child BC Alleged Father CD A Correct statement is a) Numerator is probability of observed genotypes, given the tested man is the father, and b) Denominator is probability of observed genotypes, given a random man is the father. Paternity M and C share one allele and AF is heterozygous for the other allele Parents AB ? CD M AF Child BC C AF has a 1 in 2 chance of passing C allele Random Man has p chance of passing the C allele PI = 0.5/p There are 15 possible combinations of genotypes for a paternity trio Paternity Biological Relationship Parents M F Child C Paternity Index M and C share one allele and AF is homozygous for the obligatory allele Parents AB ? C M AF Child BC C AF can only pass C allele Random Man has p chance of passing the C allele PI = 1/p Paternity Analysis Paternity Index Numerator 2 C pC 2pApB AB 0.5 1 BC 2 Probability = 2pApB x pC x 0.5 x 1 Paternity Analysis Paternity Index Denominator 2 2pApB AB C pC pC 0.5 BC 2 Probability = 2pApB x pC x 0.5 x pC Paternity Analysis Paternity Index 2 2pApB x pC x 0.5 x 1 PI = 2 2pApB x pC x 0.5 x pC 1 PI = pC Paternity Index M and C share both alleles and AF is heterozygous with one of the obligatory alleles Parents AB ? BC M AF Child AB C M has a 1 in 2 chance of passing A or B allele AF has a 1 in 2 chance of passing B allele RM has (p + q) chance of passing the A or B alleles PI = 0.5/(p+q) Paternity Analysis Paternity Index Numerator 2p p 2pApB AB BC B C 0.5A 0.5B AB Probability = 2pApB x 2pBpC x 0.5(mA) x 0.5(fB) Paternity
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