Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure...
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![Page 1: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/1.jpg)
Attaching statistical weight to Attaching statistical weight to DNA test resultsDNA test results
1. Single source samples
2. Relatives
3. Substructure
4. Error rates
5. Mixtures/allelic drop out
6. Database searches
![Page 2: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/2.jpg)
Single Source SamplesSingle Source Samples
• If the defendant is not the source of the evidence DNA then the observed match is a coincidence.
• Therefore a relevant weight for the evidence is the probability of a randomly chosen person having a matching DNA profile to the evidence
![Page 3: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/3.jpg)
Single Source: population geneticsSingle Source: population genetics
• For each locus the frequency of each genotype if computed from the Hardy-Weinberg law
• Homozygotes: AiAi• Let freq(Ai) be pi then the HW genotype
frequency is pi2
• Heterozygotes: AiAj• 2pipj
![Page 4: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/4.jpg)
RelativesRelatives
• Relatives are more likely to share alleles in common that they have inherited from their common ancestor.
• Full Sibs: AiAi:(1+2pi+pi2)/4AiAj:(1+pi+pj+2pipj)/4
• Example: p14(D3) = 0.14HW frequency= 0.02Pr(matching sibling) = 0.32
![Page 5: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/5.jpg)
Population SubstructurePopulation Substructure
Source populationps
p1 p2 p3 p4pm
Source population is very large
Each subpopulation has N individuals, and are isolated from each other
Allele frequencies in each subpopulation become different over timet
N
2
111
Populations separatedt generations
![Page 6: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/6.jpg)
Effects of substructureEffects of substructure
• In the pooled subpopulations genotype frequencies depart from the Hardy-Weinberg expectations
• Freq(AiAi) = pi2 +pi(1-pi)
• Freq(AiAj) = (1-)2pi(1-pj)
• The NRCII recommendation is to correct homozygote frequencies using the first formula
![Page 7: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/7.jpg)
Conditional ProbabilitiesConditional Probabilities
• If we assume defendant and perpetrator are likely to be form the same subpopulation different calculations are relevant
211
)1()1(2)|Pr(
211
)1(3)1(2)|Pr(
jijiji
iiiiii
ppAAevidenceAA
ppAAevidenceAA
![Page 8: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/8.jpg)
Error RatesError Rates
• Use likelihood ratios, n- false negative, p false positive
• Prosecution hypothesis: perpetrator and suspect the same person, no false negative-{1(1-n)}
• Defense hypothesis: suspect matches evidence coincidentally and no false negative, or suspect does not match evidence and a false positive- {RMP(1-n) + (1-RMP)p}.
• Suppose, RMP=10-15, n=10-3, p=10-4, then the LR= 0.999/[10-150.999+(1-10-15)10-4] 1/p
![Page 9: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/9.jpg)
Mixtures/Drop outMixtures/Drop out
• Combined probability of inclusion, add up all possible contributing genotype
• Evidence: a, b, c
• Possible genotypes: aa, ab, ac, bb, bc, cc
• This method does not require that you make any assumption about the number of contributors, or major/minor donors – but can not take into account drop out easily
![Page 10: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/10.jpg)
Mixtures/Likelihood ratiosMixtures/Likelihood ratios
• This requires that the number of contributors be specified
• These methods can take into account allelic drop out – removing these loci is not a sufficient solution
• Calculations can get very complicated
• Popstats has software to do this although it does not account for drop out.
![Page 11: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/11.jpg)
State Match State Match ReportReport
Matches at both high and moderate stringency
Analyst eliminates this match after an evaluation that can’t be written into the computer program or the lab’s SOP.
![Page 12: Attaching statistical weight to DNA test results 1.Single source samples 2.Relatives 3.Substructure 4.Error rates 5.Mixtures/allelic drop out 6.Database.](https://reader035.fdocuments.in/reader035/viewer/2022070305/55146753550346284e8b5bc7/html5/thumbnails/12.jpg)
Methods for computing statisticsMethods for computing statistics
• NRC I – use one set of loci for the search and a second set to confirm
• NRC II – multiply the RMP by the size of the database
• Bayesian – gives weight to the exclusions, number is close to the RMP
• RMP only – based on illogic that retest of known resets case to probable cause