Likelihood for mixtures with related contributors based on paramlink
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 noncontributors.
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 noncontributorsH)=P(R,T,VH)
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
1 2 3 4 
Arguments
x 

R 
Integers, mixture. 
id.U 
Integers indicating untyped contributors (e.g.,suspect(s)). 
id.V 
Integers indicating typed noncontributors. 
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, 
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 
eliminate 
A nonnegative integer, indicating the number of iterations in the internal genotypecompatibility algorithm. Positive values can save time if partialmarker is nonempty 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,VH)=Pr(RT,V,H)Pr(T,VH)= Pr(T,VH)sum_u Pr(U=u,T,VH)
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,VH) 
allLikelihoods 
Terms adding to above Pr(R,T,VH) 
Author(s)
Magnus Dehli Vigeland and Thore Egeland <Thore.Egeland@nmbu.no>
See Also
famMix
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43  #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(LR1exact)<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(LR123.125)<10^(6))
LR13=l1/l3
stopifnot(abs(LR13 2.355296)<10^(6))

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