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

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

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

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

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

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

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

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

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

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.

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.

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