Strategies and calculations in DNA kinship cases

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Strategies and calculations in DNA kinship cases

• Charles Brenner
• consulting in forensic mathematics
• because I thought of it

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Outline

• Kinship method
• Likelihood ratios
• Paternity, Avuncular
• Mutation
• old way, suggested new way
• DNAVIEW demonstration

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Kinship method

• Genetic evidence
• Likelihood ratio
• Kinship program
• ref Brenner, CH Symbolic Kinship Program,
  Genetics 145535-542, 1997 Feb

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Likelihood ratio

• Kinship I (Basic)
• Paternity
• avuncular
• Vs. exclusion

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What a likelihood ratio is

• Compares two explanations for data
• The heart of forensic mathematics
• http//dna-view.com
• cbrenner_at_uclink.berkeley.edu

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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
• LR20 Data is 20 times more characteristic of
  French person

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Paternity why likelihood ratio?
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Likelihood ratio for paternity (PI)

• PI X/Y, where
• XP(genetic types manfather)
• YP(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

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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

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Paternity how likelihood ratio?
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Likelihood ratio for Paternity (PI)

• Data MotherPS, ChildPQ, ManRQ
• explanation 1 man is father
• (2ps)(2qs)/4 event
• explanation 2 not father his Q is coincidence
• (2ps)(2qs)(q/2) event
• LR1/(2q)
• If q1/20, data 10 times more characteristic of
  father explanation

PS
RQ
PQ
PS
RQ
PQ
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Avuncular index (Is the man an uncle?)
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Other kinship cases

• Kinship program
• missing person
• null alleles

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Missing person kinship case
Explanation 1
Explanation 2
PS
PQ
PS
Mom
Body
PQ
PQ
PQ
Bro
Missing child
Body
Bro pq, Body pq Mom ps Dad
Bro pq, Child Mom pq Dad
LR(1q)/8pq -- e.g. about 14 if pq0.1
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Null allele

• loss of primer site

Explanation 1
Explanation 2
PS
PS
Q
Q-
P
P-

• LR o / (2op)(oq), where onull allele
  frequency
• e.g LR1/7 if pq0.25 and o0.01

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PI when possible mutation

• Concept
• Old method
• Str data
• New method

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Mutation analysis concept

• Data MotherPS, ChildPQ, ManRT
• 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

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Paternity case one exclusion

• PI20000 (combined, 4 loci)
• PI1/500 (PS, PQ, RT locus)
• overall PI 40.
• Conclusion probably paternity mutation

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Paternity case two exclusions

• PI2000 (combined, 3 loci)
• PI1/500 (PS, PQ, RT locus)
• PI1/200 (PS, PQ, YZ locus)
• overall PI 1/50.
• Conclusion probably non-paternity

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Mutation (old method)

• Data MotherPS, ChildPQ, ManRT
• Explanation 1 Paternity T or R ? N
• man transmits T (or R -- doesnt matter)
• ? chance T mutates
• ?? chance it ends up as Q
• Explanation 2 Nonpaternity real father ? Q
• sperm is Q

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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

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Old mutation formula is

• simple, but badly inaccurate
• suggests the 2 exclusion rule
• rule probably more accurate than the formula
• rule adequate for RFLPs
• rule not adequate for STRs
• need a new formula

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Mutation model (old formula)
Population fragment size distribution used
as mutation product size distribution
Allele of
Paternal allele
alleged father
of child
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Mutation model (more realistic)
mutation product size distribution
Population fragment size distribution
Allele of
Paternal allele
alleged father
of child
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Reasonable mutation model, STRs
Suggested model m ? /2 if s ? 1 m ? /20
if s ? 2 etc. where ? total (paternal)
mutation rate. c.f. Brinkmann et al
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Mutation LR (new, for STRs)

• Data MotherPS, ChildPN, ManRÑ
• Explanation 1 Paternity RÑ ? N
• 50 chance transmit Ñ
• ? chance Ñ mutates
• m chance Ñ ends up as N, assuming mutation
• m 0.5 if N, Ñ are 1 step apart
• m0.05 if 2 steps, etc
• Explanation 2 Real father ? N
• LR ?/(4q) (assuming single step)
• qallele frequency of the paternal allele N

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STR mutation rates
D12S1090 43/5272 paternal THO1 1/316
maternal
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Mutation reference

• http//dna-view.com/mudisc.htm

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Kinship II (advanced)

• More than two scenarios
• Three
• Many
• Strategies
• Whom to test
• Example
• Whether effective result is likely

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More than two scenarios

• Three
• Many
• disasters

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Three scenarios --

• Father?
• Uncle?
• Unrelated?

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Father/Uncle/Unrelated analysis
Example LR for tested man being father, vs
uncle, is 53
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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.

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Summary

• Likelihood ratios are the way to quantify
  evidence
• Mutation calculation must be changed for STRs
• Kinship
• All kinship problems have an explicit solution
• Multiple scenarios
• Triple ratio for three scenarios
• Lattice approach for the most complicated
  situations

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Thanks

• Prof Antonio Alonso GEP-ISFH
• Audience for sitting patiently