A Short Course of DNA Forensic Statistics
(Organized by CWAG in April 12-16, 2010 at Mexico City. Mexico)
DNA Forensics Statistics
(A 15-lecture Short Course on Statistical Principles of DNA Forensics)
Organized and Delivered by
Ranajit Chakraborty, PhD
Director, Center for Computational Genomic, Institute of Investigative Genetics
Professor, 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: rchakrab@hsc.unt.edu
A. Learning Objectives and Organization of the Course:
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Designed with the learning objectives for preparing the students to understand
basic statistical and population genetic principles that are needed to develop the
statistical protocols for interpretation of DNA Forensic data
Population data as well as casework evidence (DNA) data and their related
statistical interpretations will be discussed
Successful completion of this course should ensure that the students are familiar
with underlying assumptions of DNA Forensic statistical computations and their
interpretations
Reference materials supplied in the course should also equip the students to
understand the scope of general acceptance of such statistical interpretations in
the context of legal use of DNA forensic statistics
Pre-requirement: Students should be familiar with laboratory data of DNA
forensics, and have some knowledge about the DNA forensic scenarios and how
DNA results are used in forensic investigations.
Given in the form of 15 lectures (extending over 5 days), each of 90 minutes
duration (e.g., two lectures in the morning, and one in the early afternoon). The
instructor will be available for additional time to review topics discussed on each
day.
Such review sessions after Parts III and IV may be devoted to use of software to
analyze real cases, and hence participating students can bring their own cases to
apply the principles learned in the course.
For each student, successful completion of the course will be judged based on
student’s: (i) class attendance and participation in the discussions; and (ii)
satisfactory performance in a take-home examination conducted at the end of the
course. Each student should individually complete their own take-home
examination.
The students are allowed to consult lecture notes, reading materials, or do internet
search on their own to complete the examination, but copying from other students
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are strictly forbidden and if so detected, will count against certifying successful
completion of the course.
Power-point slides, list of reference reading materials, and copies of key
publications discussed in the course will be made available to the students for
future references to these materials.
B. Course Syllabus:
B.1. (Part I: Statistical Principles used in DNA Forensic Statistics - Day 1)
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Lecture 1: Elements of Probability Theory (Concepts of: Random Experiment;
Random Variable; Probability Distribution; Examples of Standard Distributions
relevant for Forensics, such as Binomial, Multinomial, Poisson, Normal, Chisquare, etc.; Measures of Central Value and Variability of Random Variables –
Mean and Variance) - all illustrated with real examples relevant for DNA
Forensics
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Lecture 2: Estimation and Hypothesis Testing (Concepts and Differences of
Parameter and Statistic; Features of Good estimators; Precision vs. bias of
estimation; Methods of estimation, such as Method of Moments, Maximum
Likelihood Method; Concept of Simple and composite hypothesis; Testing
Procedures and two types of errors (Type I and Type II), Methods of hypothesis
testing such a likelihood ratio test), concept and use of confidence interval – all
illustrated with DNA Forensics relevant examples
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Lecture 3: Nature of DNA Forensic Data (Discrete Multinomial, Bivariate and
multivariate distributions, concept of pairwise and mutual dependence;
Conditional and Marginal probabilities; Population databases; Data on Relatives –
Modeling of such data based on population genetic models) – real life example of
data will be provided
B.2. (Part II: Population Genetic Principles used in DNA Forensic Statistics- Day 2)
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Lecture 4: Estimation of allele and genotype frequency at the level of one or
more loci (Gene count method, Hardy-Weinberg Equilibrium, Causes and nature
of deviation from HWE, Linkage Disequilibrium and its estimation, Effects of
deviation from HWE and LD on genotype frequencies; Effect of presence of
relatives in population databases)
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Lecture 5: Population Substructure and Genetic Distance (Theory of
population substructure and its impact; Empirical data on Human Genetic
Variation of global populations, and those based on DNA forensic loci; extent of
population substructure in human populations)
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Lecture 6: Evolutionary forces underlying maintenance of genetic variation
of DNA forensic loci (Concepts of genetic drift, mutation, and natural selection;
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Features and rates of mutation for autosomal STR, Y-STR, and mtDNA markers;
evidence of null and multiple alleles; possible limitations of mutation rate
estimates and their differences across different types of loci; drift effect on these
loci as seen in population variability in large cosmopolitan versus small isolated
populations)
B.3. (Part III: DNA Forensic Statistics Protocols – Standard Cases - Day 3)
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Lecture 7: DNA Forensic Issues and Their Statistical Assessments (A brief
review of History of DNA Forensics and changes in DNA markers used in
Forensics; Currently employed sets of markers – autosomal STRs, mtDNA, and
Y-STR haplotypes; Three generic types of forensic issues: Transfer evidence,
Mixture Analysis, and Kinship Analysis and the associated questions for these
issues; Three types of approaches to address these issues – Frequency-based,
Likelihood based, and Bayesian logic. Associated assumptions and data
requirement underlying these approaches
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Lecture 8: Current Paradigm of Solving Transfer Evidence (Issues for DNA
from a single source; Discussion on NRC-I and NRC-II rules and their
inadequacies and adequacies; Changes of approaches based on questions;
Random match probability and conditional random match probability; Likelihood
and ratio of likelihoods and their interpretations – concept of prosecutor fallacy;
Database search and its impact on RMP calculation)
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Lecture 9: Statistics for DNA Mixture Analysis (Methods of deconvolution of
DNA mixture and their attendant assumptions; Concept of exclusion probability;
likelihood calculations based on mixture hypothesis; Effects of population
substructure and relationships between contributors in a mixture
B.4. (Part IV: DNA Forensic Statistics Protocols – Complex Cases - Day 4)
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Lecture 10: Statistics for Kinship Analysis (Logic of parentage testing;
exclusion probability and Paternity Index; Generalization of this to reverse
parentage; pedigree-based likelihoods; applications for missing person
identification; impact of population substructure and mutations)
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Lecture 11: Database search issues and familial search (Pairwise comparison
of profiles and their I-T-O expectations; Multilocus allele and genotype sharing;
empirical data on observations and expectations, effects of population subdivision
and presence of relatives; concept of familial search and limitations of its use in
large databases; cautionary guards for using familial search results; impact of
mutations)
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Lecture 12: Lineage markers and Relevant Statistics (mtDNA and Y-STR
markers; Some features of mtDNA and Y-STR population databases; Genetic
differences between populations based on mtDNA and Y-STR variation; FST for
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mtDNA and Y-STR haplotypes; Counting method for using mtDNA and Y-STR
in forensic cases; Conservativeness using confidence interval versus substructure
effect; effects of mutation on matches based on lineage markers)
B.5. (Part V: DNA Forensic Statistics – More Recent Approaches and Limitations –
Day 5)
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Lecture 13: SNPs and their utility in DNA Forensics (Brief outline of SNPs in
the human genome – effect of mutation and genetic drift on SNPs; Different
platforms of SNP typing; Concept of Haploblock organization of SNPs and their
portability across populations; Number of SNPs needed for efficient use of SNPs
for DNA Forensics; Possible approaches for increasing efficiency of utility of
SNPs for DNA Forensics)
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Lecture 14: Statistics for Low Copy Number (LCN) DNA Evidence (brief
biological background of LCN; Current practices of interpreting LCN data and
concerns in such approaches; Concerns of interpreting LCN data in DNA
mixtures; Possible approaches of refinement)
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Lecture 15: Lecture 15: Joint Match Probabilities for mtDNA,
Y-Chromosome and Autosomal Markers (Mendelian genetics of Y- and
mtDNA-inheritance; Meaning of Y-STR/SNP and/or mtDNA match vs. that
based on autosomal loci; Match probability computations for these types of
systems (i.e., Y-linked and mtDNA vs autosome); How to define population and
how to define parameters of substructure adjustments; Can or should the evidence
from autosome, Y-, and mtDNA-markers be combined?; Can they be multiplied
for getting a combined value? – Some recent results; Current recommendations)
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General Comments and Take Home Examination: (Experiences from
presenting court evidence and testimony; Addressing issues of “right” vs.
“wrong” questions; Addressing issues of multiple questions require multiple
answers which are not indicative of lack of general acceptance; Examples of use
of analogy in answering technical questions; e.g., daily use of the concept of
sampling and estimation from small sample sizes; use of non-technical
interpretation of complicated statistics; e.g., Np rule of cold-hit statistic does not
alter the RMP statistic for rarity of a DNA profile)
Take Home Examination and Expectation from that
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