Likelihood for mixtures with related contributors based on paramlink

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Description

A DNA mixture (R) has been observed and some individuals may have been typed. Some of these typed individuals are known contributors to the mixture, some are known non-contributors. In addition, there may be specified untyped individuals that have contributed to the mixture. Individuals can be specified as members of a pedigree defined by a linkdat object x corresponding to a hypothesis H. Relevant individuals unrelated to all others, are defined using singleton.The likelihood

Pr(mixture,Typed contributors,Typed non-contributors|H)=P(R,T,V|H)

is calculated; the notation on the right hand side corresponds to that of Curran, Gill and Bill (2005). A plot is also produced summarising the essential information. Compared to previous literature and methods, including a series of papers by Fung and Hu, we generalise calculations to allow for general, possibly inbred, pedigrees. Typically calculations are performed for competing hypotheses and the ratio of likelihoods, the likelihood ratio LR is calculated and reported. Previous methods have assumed the relationships between typed contributors to be same for the competing hypotheses. This restriction does not apply for our approach. The calculation may also be used for identification cases where a mixture and reference samples are available. Likelihood calculations are performed using the likelihood of paramlink. The function checkInput checks input to paraMix.

Usage

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paraMix(x, R, id.U, id.V = NULL, alleles, afreq = NULL, 
Xchrom= FALSE, known_genotypes = list(), loop_breakers =NULL, 
eliminate = 0, check = TRUE, plot = TRUE, title= NULL)
checkInput(x, R, id.U, id.V, alleles, all_typed, K, R_not_masked)

Arguments

x

linkdat object, or a list of such (if disconnected), describing the claimed relationship.

R

Integers, mixture.

id.U

Integers indicating untyped contributors (e.g.,suspect(s)).

id.V

Integers indicating typed non-contributors.

alleles

Integers indicating alleles for marker.

afreq

A numerical vector with allele frequencies. An error is given if they don't sum to 1 (rounded to 3 decimals).

Xchrom

Logical, FALSE for autosomal marker.

known_genotypes

List, each element a triplet of integers corresponding to (id,allele1,allele2)

loop_breakers

A numeric containing IDs of individuals to be used as loop breakers. Relevant only if the pedigree has loops. See breakLoops.

eliminate

A non-negative integer, indicating the number of iterations in the internal genotype-compatibility algorithm. Positive values can save time if partialmarker is non-empty and the number of alleles is large.

check

If TRUE check of input is performed and calculations stop if they are likely to take too much time

plot

If TRUE a plot is produced

title

Title of the plot

all_typed

An integer vector identifying typed individuals

K

Known alleles in contrib_typed

R_not_masked

Unexplained alleles

Details

The required likelihood Pr(R,T,V|H)=Pr(R|T,V,H)Pr(T,V|H)= Pr(T,V|H)sum_u Pr(U=u,T,V|H) where the sum extends over u among persons specified by id.U so that the union of u,T, V is R. The likelihoohd for each u and the sum is returned. Assumes alleles to be numbered 1,2,...

Value

likelihod

The likelood Pr(R,T,V|H)

allLikelihoods

Terms adding to above Pr(R,T,V|H)

Author(s)

Magnus Dehli Vigeland and Thore Egeland <Thore.Egeland@nmbu.no>

See Also

famMix

Examples

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#Example 1: Motivating example Egeland et al. (2013)
require(paramlink)
y1=swapSex(nuclearPed(3),c(3,4))
p=c(0.1,0.2,0.3,0.4)
alleles=1:length(p)
T1=c(1,1)
T2=c(2,2)
R=1:2
known=list(c(3,T1),c(4,T2))
l1=paraMix(y1,R,id.U=5,alleles=alleles,afreq=p,known_genotypes=known)
y2=swapSex(nuclearPed(1),3)
y2=addOffspring(y2,mother=2,noff=1,sex=2)
y2=relabel(y2,c(1:3,6,4),1:5)
l2=paraMix(y2,R,id.U=6,alleles=alleles,afreq=p,known_genotypes=known)
LR1=l1$lik/l2$lik
exact=1/(2*(p[1]+p[2]))
stopifnot(abs(LR1-exact)<10^(-6)) 

#Example 2. Example 1 in Egeland et al. (2013) based on Fung and Hu (2008)
#Data:
#Mixture 1/2/3
#Suspect=4, genotype 3/3
#Victim=10, genotype 1/2
#H1: Contributors were the suspect  and victim (unrelated)
#H2: Contributors were the father of suspect  and victim (unrelated)
#H3: Contributors were the brother of suspect  and victim (unrelated)
afreq=c(0.044,0.166,0.110,0.680)
alleles=1:length(afreq)
R=1:3 #Mixture
man_ped=nuclearPed(2)
victim = singleton(id=10, sex=2)
known = list(c(4,3,3),c(10,1,2)) #individual 4 is 3/3, and 10 (the victim) is 1/2.
#The likelihoods corresponding to H1,H2 and H3
l1=paraMix(list(man_ped, victim), R, id.U=NULL, id.V=NULL, 
alleles=alleles, afreq=afreq, known_genotypes=known)$lik
l2=paraMix(list(man_ped, victim), R, id.U=1, id.V=4, 
alleles=alleles, afreq=afreq, known_genotypes=known)$lik
l3=paraMix(list(man_ped, victim), R, id.U=3, id.V=4, 
alleles=alleles, afreq=afreq, known_genotypes=known)$lik
LR12=l1/l2
stopifnot(abs(LR12-3.125)<10^(-6)) 
LR13=l1/l3
stopifnot(abs(LR13- 2.355296)<10^(-6))