forensim: an open source initiative for method evaluation...

BackgroundThe forensim package

Method evaluation : An example

forensim: an open source initiative for methodevaluation in forensic genetics

Hinda Haned

Laboratory of Biometry and Evolutionary Biology, University of Lyon, France

Wroskhop in Forensic Genetics, Institute of Forensic Medecine,Oslo, November 2009

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Forensic DNA mixtures : A challenging task

Interpretation issues

Is it a mixture ?

How many peopleinvolved ?

Weight of the stain asan evidence ?

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Available methods

I Several methods dedicated to mixtures interpretation areavailable :

LR in case of population substructure Curran et al 1999Number of contributors Egeland et al 2003Unknown related contributors Fung and Hu 2003Genotyping errors Thompson et al 2003

⇒ Lack of evaluation of methods’ efficiency and robustness

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How to evaluate these methods ?

On simulated DNA stains where the circumstances of thehypothetical crime are known by the experimenter.

The experimenter would evaluate method’s efficiency :1 While varying accurate parameters :

type of markers analyzednumber of markers analyzednumber of contributors to the DNA evidence

2 In critical situations :

population subdivision (co-ancestry)partial profilesrelatedness between contributors to the DNA stainallele dropout

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I Laboratory simulated DNA stains :Some scenarios are hard to test in laboratory (ex. populationsubstructure)Cost issues : new experiments are to be conducted for eachtested scenario

I Computer simulated DNA stains :

Complex scenarios can be simulatedNo cost issues

Currently, there is no free software providing simulation toolsspecific to forensic genetics.

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I Laboratory simulated DNA stains :

Some scenarios are hard to test in laboratory (ex. populationsubstructure)Cost issues : new experiments are to be conducted for eachtested scenario

I Computer simulated DNA stains :Complex scenarios can be simulatedNo cost issues

Currently, there is no free software providing simulation toolsspecific to forensic genetics.

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The forensim package

Main features

I forensim is a package for the statistical software

I forensim is freely available

I Relies on object oriented programming

I Sources freely available on

I Compiles and runs on a wide variety of UNIX platforms,Windows and MacOS

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forensim’s structure

Simulation tools

Simulation of datacommonly encounteredin forensic casework

Statistical tools

Main statistical methodsfor forensic DNAevidence interpretation

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Simulation tools

Object oriented programming

Structured code, can easily be modified/ enriched ⇒ allows a widevariety of scenarios

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Statistical tools

Statistical methods usually used to report the weight of a DNAevidence are implemented :

Random man exclusion probability

θ correction for allele dependencies Weir, In Buckelton et al, 2005

Likelihood ratios

General formula for likelihood ratios Curran et al, 1999

Random match probabilities

Accounts for :I relatednessI allele dependencies

Balding & Nichols, 1994

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Simulation tools : Focus on DNA mixtures

Two kinds of information stored :

Usual information

• Alleles present in the stain

• Marker names

• Allele frequencies of the putative population

Simulation-related information

• Number of individuals involved

• Contributors’ genotypes

• Contributors’ populations

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Simulating forensic DNA mixtures

Simulating a 3-person mixture, using the African American allelefrequencies (Butler et al, 2003) :

Step1 : load the package

> library(forensim)

### forensim 1.1.2 is loaded ###

Step2 : generate the data

> data(strusa)> geno <- simugeno(strusa, n = c(100, 0, 0))> mix3 <- simumix(geno, ncontri = c(3, 0, 0))

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Simulating a 3-person mixture, using the African American allelefrequencies (Butler et al, 2003) :

Step1 : load the package

> library(forensim)

### forensim 1.1.2 is loaded ###

Step2 : generate the data

> data(strusa)> geno <- simugeno(strusa, n = c(100, 0, 0))> mix3 <- simumix(geno, ncontri = c(3, 0, 0))

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Mixture representation in forensim

> mix3

# Simumix object: simulated mixture #

@which.loc: vector of 15 locus names@ncontri: [email protected]: 3 x 15 data frame of the contributors [email protected]: list of the alleles found in the mixture@popinfo: populations of the contributors

Display stain profiles at locus FGA

> mix3$mix.all$FGA

[1] "20" "21" "24" "25"

Display contributors profiles at locus FGA

> mix3$mix.prof[, "FGA"]

ind70 ind58 ind1"21/24" "24/25" "21/20"

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> mix3




> mix3$mix.all$FGA

[1] "20" "21" "24" "25"



ind70 ind58 ind1"21/24" "24/25" "21/20"

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> mix3




> mix3$mix.all$FGA

[1] "20" "21" "24" "25"



ind70 ind58 ind1"21/24" "24/25" "21/20"

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Reporting the weight of the evidence

What is the exclusion probability of the DNA evidence ?

>PE(mix3, freq = strusa, refpop = "Afri", theta = 0, byloc =FALSE)

PE0.999989

Help page

I mix : the DNA mixture

I freq : the allele frequencies to use

I refpop : the reference population, used only if freq contains allele frequencies formultiple populations

I theta : θ correction for allele dependencies

I byloc : logical indicating whether the PE is computed by/overall loci

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What is the exclusion probability of the DNA evidence ?

>PE(mix3, freq = strusa, refpop = "Afri", theta = 0, byloc =FALSE)

PE0.999989

Help page





I byloc : logical indicating whether the PE is computed by/overall loci

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By locus exclusion probability

> PE(mix3, freq = strusa, refpop = "Afri", byloc = TRUE)

PE_lCSF1PO 0.6315FGA 0.6320TH01 0.4140TPOX 0.2629VWA 0.1739D3S1358 0.2893D5S818 0.2018D7S820 0.2259D8S1179 0.6082D13S317 0.1739D16S539 0.4404D18S51 0.5828D21S11 0.5426D2S1338 0.6339D19S433 0.8437

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Determining the number of contributors to a DNA mixture

I In many situations, scarce data is available about the origin ofthe satin

No available suspectUnknown contributorsScarce non genetic evidence

An estimate of the number of contributors can help theinvestigators !

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Determining the number of contributors to a DNA mixture

I A common laboratory practice : the number of contributorsset to the minimum required to explain the profiles.

An alternative approach :

I A maximum-likelihood estimator of the number ofcontributors to a forensic DNA mixture

Egeland et al. Estimating the number of contributors to a DNA profile. Int J Legal

Med 2003 ;117(5) : 271-5.

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The maximum likelihood apporach

Let A be a specific locus with alleles A1, ...,Ak withfrequencies p1, ..., pk in a given population.

Crime scene profiles : A1 and A2 .

What is the likelihood of these profiles, if there were twocontributors supplying these alleles ?

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The maximum likelihood apporach

7 genotype pairs are possible :

(A1A1,A2A2) (A2A2,A1A1) (A1A1,A1A2)(A2A2,A1A2) (A1A2,A1A1) (A1A2,A1A2)(A1A2,A2A2)

Assuming the independence of alleles between and withinindividuals :

Pr(A1A1) = p21 and Pr(A1A2) = 2p1p2

Pr(A1A1,A1A2) = Pr(A1A1)× Pr(A1A2)

Adding the genotype probabilities for all 7 genotype pairs

LA(x = 2) = 4p31p2 + 6p2

1p22 + 4p1p

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The likelihood function

I Generalization :Multiallelic lociAllele dependencies due to population subdivision

I Need for automatizationInspired from the general formula for likelihood ratios fromCurran et al. (1999)

LA(x) =r∑

r1=0

r∑r2=0

...

r−r1−r2−...−rc−2∑rc−1

(2x)!c∏

i=1

ui !

×

c∏i=1

ui−1∏j=0

[(1− θ)pi + jθ]

2x−1∏j=0

[(1− θ) + jθ]

Haned et al Estimating the number of contributors to forensic DNA mixtures : Does maximum likelihood perform

better than maximum allele count ? J. Forensic. Sci., accepted (2010) 24 / 33



Maximum likelihood estimation

The maximum likelihood estimation of x , when a single marker Ais considered, verifies :

maxj=1,2,3,...

LA(x = j)

When multiple loci are considered simultaneously :

maxj=1,2,3...

∏A

LA(x = j)

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Method evaluation

Does maximum likelihood perform better then maximumallele count ?

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Implementation

Maximum allele count

>mincontri(mix3)

[1] 3

Maximum likelihood

>likestim(mix = mix3, freq = strusa, refpop = "Afri"’, theta = 0)

max maxval3 2.6e-26

Help page





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Implementation

Maximum allele count

>mincontri(mix3)

[1] 3

Maximum likelihood

>likestim(mix = mix3, freq = strusa, refpop = "Afri"’, theta = 0)

max maxval3 2.6e-26

Help page





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Method evaluation procedure

I 1000 DNA stains comprising x contributors, x=1,...,5.

> Mix2<-replicate(1000,simumix(geno, ncontri = c(2, 0, 0)))

I For each mixture : an error is scored if the value of x thatmaximizes the likelihood is different from the true number ofcontributors.

> res<-sapply(Mix2,likestim,strusa,"Afri")

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Mixture simulated with African American allele frequencies

I DNA stains comprising 1 to 5 individuals belonging to thesame population : African Americans

x 1 2 3 4 5

Max. Likelihood 1 1 0.94 0.79 0.67Max. All. count. 1 1 0.99 0.45 0.05

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Other situations can be investigated

More functionalities available via other packages :

• Basic statistical inference

• Bayesian inference

• Familial analysis

• Population genetics

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How to get help

You are not familiar with :

Do not worry ! A detailed tutorial with practical and reproducibleexamples is available online :http://forensim.r-forge.r-project.org/

You are encountering problems using forensim :

I Post a message on forensim mailing list :[email protected].

I Contact me :[email protected]

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http://forensim.r-forge.r-project.org/

[email protected].

[email protected]



Contributions are greatly encouraged !

forensim is evolving, and you can participate !

I Suggestions ?

I Particular needs ?

I Contributions to the package : data, methods... are welcome !


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