lik2: Pairwise likelihood with mutation
In mut: Pairwise Likelihood Ratios
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
Detailed balance (DB) is assumed for the mutation model
and the likelihood is calculated for a pair of non-inbred individuals.
Usage
1
Arguments
g1
Genotype, two integers giving the alleles for individual 1.
g2
Genotype, two integers giving the alleles for individual 2.
n
Integer vector of length 4 giving the distance between
paternal, paternal-maternal, maternal-paternal alleles and maternal.
p
Vector of real numbers. Allele frequency vector.
M
Matrix of real numbers. Mutation matrix.
kappa
Vector of real numbers describing relationship.
IBD parameters for 0,1,2 IBD alleles.
alpha
Four probabilities, summing to 1, giving the probability,
in case IBD=1, that the alleles are paternal, paternal-maternal,
maternal-paternal, and maternal.
theta
Real in [0,1]. Kinship coefficient.
beta
Real in [0,1]. Probability of same parental origin when IBD=2.
Details
There are two non-inbred
individuals A and B, with genotypes a/b and c/d,
where the alleles may or may not differ.
We calculate
the likelihood assuming a relationship described by kappa.
Value
likelihood, real.
Author(s)
Thore Egeland <Thore.Egeland@nmbu.no>
References
Egeland, Pinto and Amorim, FSI:Genetics (2017), http://dx.doi.org/10.1016/j.fsigen.2017.04.018.
Examples
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library(expm)
library(Familias)
# Example 1. Paternity case. Silent allele, mutation
p <- c(0.2, 0.75, 0.05); R <- 0.005
locus1 <- FamiliasLocus(frequencies=p, name="L1", allelenames=c("1","2", "silent"),
femaleMutationRate = R, maleMutationRate =R,femaleMutationRange = 0.1,
maleMutationRange = 0.1,femaleMutationRate2 = 0, maleMutationRate2 = 0,
maleMutationModel="Proportional", femaleMutationModel="Proportional")
M <- locus1$maleMutationMatrix
theta <- 0.03
n <- c(0, 1, 1, 0); kappa.num <- c(0, 1, 0); kappa.den <- c(1, 0, 0);alpha <- c(0, 0.5, 0.5, 0)
t1 <- lik2(c(1,1), c(2,2), n, p, M, kappa.num, alpha, theta)
t2 <- lik2(c(1,3), c(2,2), n, p, M, kappa.num, alpha, theta)
t3 <- lik2(c(1,1), c(2,3), n, p, M, kappa.num, alpha, theta)
t4 <- lik2(c(1,3), c(2,3), n, p, M, kappa.num, alpha, theta)
u1 <- lik2(c(1,1), c(2,2), n, p, M, kappa.den, alpha, theta)
u2 <- lik2(c(1,3), c(2,2), n, p, M, kappa.den, alpha, theta)
u3 <- lik2(c(1,1), c(2,3), n, p, M, kappa.den, alpha, theta)
u4 <- lik2(c(1,3), c(2,3), n, p, M, kappa.den, alpha, theta)
num <- t1 + t2 + t3 + t4
den <- u1 + u2 + u3 + u4
LR1 <- num/den
# Below LR is checked using Familias
persons <- c("AF", "CH")
sex <- c("male", "male")
#Define the alternative pedigrees
ped1 <- FamiliasPedigree(id=persons, dadid=c(NA,"AF"),
momid=c(NA,NA), sex=c("male", "male"))
ped2 <- FamiliasPedigree(id=persons, dadid=c(NA,NA),
momid=c(NA,NA), sex=c("male", "male"))
pedigrees <- list(ped1,ped2)
datamatrix <- data.frame(locus1.1=c(1,2), locus1.2=c(1,2))
rownames(datamatrix) <- persons
result <- FamiliasPosterior(pedigrees, locus1, datamatrix, ref=2, kinship = theta)
LR2 <- result$LR[1]
stopifnot(abs(LR1 - LR2) <1e-15)
###
library(Familias)
test <- function(a, b, c, d, R, model="Proportional",
p=c(0.1,0.2,0.3,0.3,0.1), theta=0){
anames <- 1:length(p)
datamatrix <- cbind(c(NA,NA,a,c,NA,NA),c(NA,NA,b,d,NA,NA))
persons <- c("FA","MO", "B1", "B2","EM","EF")
rownames(datamatrix) <- persons
seks <- c("male", "female", "male", "male","male","female")
ped1 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,"FA","FA",NA, NA),
momid=c(NA, NA,NA,NA,NA, NA), sex = seks)
ped2 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,"FA","FA",NA, NA),
momid=c(NA, NA,"MO","MO",NA, NA), sex =seks)
ped3 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,"B2",NA,NA, NA),
momid=c(NA, NA,NA,NA,NA, NA), sex =seks)
ped4 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,NA,NA,NA, NA),
momid=c(NA, NA,NA,NA,NA, NA), sex =seks)
ped5 <- FamiliasPedigree(id=persons, dadid=c("B1", NA,NA,"FA",NA, NA),
momid=c(NA, NA,NA,NA,NA, NA), sex =seks)
ped6 <- FamiliasPedigree(id=persons, dadid=c(NA, "B1",NA,"FA",NA, NA),
momid=c("MO", NA,NA,NA,NA, NA), sex =seks)
ped7 <- FamiliasPedigree(id=persons, dadid=c("EM", "EM","FA",NA,NA, NA),
momid=c("EF", "EF",NA,"MO",NA, NA), sex =seks)
ped8 <- FamiliasPedigree(id=persons, dadid=c("EM", "B1",NA,"FA",NA, NA),
momid=c(NA, NA,NA,NA,"MO", NA), sex =seks)
ped9 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,"FA","EM","FA", NA),
momid=c(NA, NA,"MO",NA,"MO", NA), sex =seks)
ped10 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,"FA","EM",NA, NA),
momid=c("EF", NA,"MO","MO","EF", NA), sex =seks)
peds <- list(HS=ped1,FS=ped2, PO=ped3, UNR=ped4,GP=ped5, GR=ped6,
CO=ped7,GGR=ped8,AVU=ped9,diff=ped10)
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= anames, MutationRate=R, MutationModel=model)
res <- FamiliasPosterior(peds, locus1, datamatrix)
M <- locus1$maleMutationMatrix
g1 <- c(a,b); g2 <- c(c,d)
l1 <- lik2(g1, g2, n=c(1,0,0,0),p,M,
kappa=c(0.5,0.5,0), alpha=c(1,0,0,0), theta)
l2 <- lik2(g1, g2, n=c(1,1,1,1), p, M,
kappa=c(0.25,0.5,0.25), alpha=c(1,1,1,1)/4, theta)
l3 <- lik2(g1, g2, n=c(1,1, 0,0),p, M,
kappa=c(0,1,0.0), alpha=c(0.5, 0.5, 0, 0), theta)
l4 <- lik2(g1, g2, n=c(0,0,0,0), p, M,
kappa=c(1,0,0.0), alpha=c(1,1,1,1)/4, theta)
l5 <- lik2(g1, g2, n=c(1,1,0,0), p, M,
kappa=c(0.5, 0.5,0.0), alpha=c(0.5, 0.5, 0, 0), theta)
l6 <- lik2(g1, g2, n=c(2,2,0,0), p, M,
kappa=c(0.75, 0.25,0.0), alpha=c(0.5, 0.5, 0, 0), theta)
l7 <- lik2(g1, g2, n=c(0,4,0,0), p, M,
kappa=c(0.75, 0.25,0.0), alpha=c(0, 1, 0, 0), theta)
l8 <- lik2(g1, g2, n=c(3,3,0,0), p, M,
kappa=c(7/8, 1/8,0.0), alpha=c(0.5, 0.5, 0, 0), theta)
l9 <- lik2(g1, g2, n=c(3,3,0,0), p, M,
kappa=c(0.5, 0.5,0.0), alpha=c(0.5, 0.5, 0, 0), theta)
l10 <- lik2(g1, g2, n=c(4,0,0,0), p, M,
kappa=c(7, 8, 1)/16, alpha=c(1,0, 0, 0), theta)
fam <- res$likelihoods
exact <- c(l1,l2,l3,l4,l5,l6,l7,l8,l9,l10)
z <- abs(res$likelihoods-exact)
check <- all(z< 1e-10)
res <- cbind(fam,exact)
colnames(res) <- c("Familias","Exact")
rownames(res) <- c("HS","FS","PO", "UNR","GP","GGP","CO","GGGP", "UNC","HS+")
list(res, check=check)
}
data(NorwegianFrequencies)
d <- NorwegianFrequencies$D12S391
names(d) <- 1:length(d) #21=16, 22=17 etct
foo3 <- test(16,17,18,19,R=0.00,"Proportional", p=as.double(d))
foo3 <- foo3[[1]]
foo4 <- test(16,17,18,19,R=0.0021,"Proportional", p=as.double(d))
foo4 <- foo4[[1]]
foo5 <- test(16,17,18,19,R=0.0021,"Equal", p=as.double(d))
foo5 <- foo5[[1]]
foo6 <- test(18,19,16,17,R=0.0021,"Equal", p=as.double(d))
foo6 <- foo6[[1]]
foo <- cbind(foo3,foo4,foo5,foo6)
foo <- foo[,c(1,3,5,7)]
kappa <- c("(0.5,0.5,0)","(0.25,0.5,0.25)","(0,1,0)","1,0,0)",
"(0.5,0.5,0)","(0.75,0.25,0)","(0.75,0.25,0)","(7/8,1/8,0)","(0.5,0.5,0)",
"(7/16,8/16,1/16)")
Table1 <- data.frame(kappa,foo)
colnames(Table1) <- c("kappa","R=0","R=0.0021","R=0.0021(Eq)","Swapped")
Table1
# Example First example of paper
foo1 <- test(1,1,2,2,R=0.005, model="Equal",p=c(0.1,0.9) )[[1]][3,1]
foo2 <- test(2,2,1,1,R=0.005, model="Equal",p=c(0.1,0.9) )[[1]][3,1]
foo1/foo2 #=9, i.e., no 1
foo1 <- test(1,1,2,2,R=0.005, model="Proportional",p=c(0.1,0.9) )[[1]][3,1]
foo2 <- test(2,2,1,1,R=0.005, model="Proportional",p=c(0.1,0.9) )[[1]][3,1]
foo1/foo2 # =1
#LR with general mutation matrix using Familias
library(Familias)
id <- c("I", "II")
I.II <- FamiliasPedigree(id, c(NA, "I"), c(NA, NA), c("male", "male"))
II.I <- FamiliasPedigree(id, c(NA, NA), c(NA, NA), c("male", "male"))
pedigrees <- list( I.II = I.II, II.I = II.I)
m12 <- 1/100; m21 <- 3/100
M <- rbind(c(1-m12,m12),c(m21,1-m21))
p1 <- m21/(m12+m21);p2 <- m12/(m12+m21); p <- c(p1,1-p1)
anames <- 1:length(p)
locus1 <-FamiliasLocus(frequencies = p,"locus1",
allelenames = anames,
MutationModel="Custom", MutationMatrix=M)
locus2 <-FamiliasLocus(frequencies = p,"locus2",
allelenames = anames,
MutationModel="Custom", MutationMatrix=M)
datamatrix <- data.frame(locus1.1=c(1,2), locus1.2=c(1,2), locus2.1=c(2,1),locus2.2=c(2,1))
rownames(datamatrix) <- c("I","II")
myloci <- list(locus1,locus2)
LRs <- FamiliasPosterior(pedigrees,myloci, datamatrix,ref=2)$LRperMarker[,1]
#Both above:
m12+m21
#Example 3 Stationarity not enough
library(Familias)
id <- c("I", "II")
I.II <- FamiliasPedigree(id, c(NA, "I"), c(NA, NA), c("male", "male"))
II.I <- FamiliasPedigree(id, c(NA, NA), c(NA, NA), c("male", "male"))
pedigrees <- list( I.II = I.II, II.I = II.I)
R <- 0.1
M <- rbind(c(1-2*R,3*R/2,R/2),c(R/2,1-R,R/2),c(R/2,R/2,1-R))
p <- c(3,7,5)/15
anames <- 1:length(p)
locus1 <-FamiliasLocus(frequencies = p,"locus1",
allelenames = anames,
MutationModel="Custom", MutationMatrix=M)
locus2 <-FamiliasLocus(frequencies = p,"locus2",
allelenames = anames,
MutationModel="Custom", MutationMatrix=M)
datamatrix <- data.frame(locus1.1=c(1,2), locus1.2=c(1,2), locus2.1=c(2,1),locus2.2=c(2,1))
rownames(datamatrix) <- c("I","II")
myloci <- list(locus1,locus2)
result1 <- FamiliasPosterior(pedigrees,myloci, datamatrix,ref=2)
result1$LRperMarker
result1$LRperMarker[1]-45*R/14
result1$LRperMarker[2]-35*R/14
for (i in 1:10000) p <- p
p
# Example 3
# Exact calculation with SNP-s for an example of the paper
example2 <- function(p=0.4,R=0.005){
k <- R/(2*p*(1-p))
m11 <- 1-k*(1-p)
m22 <- 1- k*p
HS <- 0.5*p^4+0.5*p^3*(m11^2+k^2*p*(1-p))
UNC <- 0.5*p^4+0.5*p^3*(m11^3+2*k^2*p*(1-p)*m11+k^2*(1-p)*p)
GGP <- 0.75*p^4+0.25*p^3*(m11^3+2*k^2*p*(1-p)*m11+k^2*(1-p)*p)
list(HS.GP=HS,UNC=UNC, GGP=GGP)
}
p <- 0.4; R <- 0.005
example2(p,R)
test(1,1,1,1,R=R,"Proportional", p=c(p,1-p))[[1]][c(1,5,9,6),1]
#Example 4
data(NorwegianFrequencies)
p<-as.double(NorwegianFrequencies$D12S391)
k <- 0.0021/sum(p*(1-p))
#Example 5
#Same mother, father brothers
rm(list=ls())
a <- 1;b <- 2; c <- 1;d <- 3
persons <- c("FA","MO", "B1", "B2","EM","EF","EM2")
seks <- c("male", "female", "male", "male","male","female","male")
R <- 0.0021; model <- "Proportional"; p <- c(0.1,0.2,0.3,0.3,0.1)
anames <- 1:length(p)
ped11 <- FamiliasPedigree(id=persons, dadid=c("EM2", NA,"FA","EM","EM2", NA,NA),
momid=c("EF", NA,"MO","MO","EF", NA, NA), sex =seks)
datamatrix <- cbind(c(NA,NA,a,c,NA,NA,NA),c(NA,NA,b,d,NA,NA,NA))
rownames(datamatrix) <- persons
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= anames, MutationRate=R, MutationModel=model)
res <- FamiliasPosterior(ped11, locus1, datamatrix)
M <- locus1$maleMutationMatrix
l11 <- lik2(c(a,b),c(c,d), n = c(4,0,0,2), p,M,
kappa=c(3/8,4/8,1/8), alpha=c(1/4,0,0,3/4), theta=0)
c(res$likelihoodsPerSystem,l11)
mut documentation built on May 2, 2019, 11:10 a.m.
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Description Usage Arguments Details Value Author(s) References Examples
Description
Detailed balance (DB) is assumed for the mutation model and the likelihood is calculated for a pair of non-inbred individuals.
Usage
1 |
Arguments
g1 |
Genotype, two integers giving the alleles for individual 1. |
g2 |
Genotype, two integers giving the alleles for individual 2. |
n |
Integer vector of length 4 giving the distance between paternal, paternal-maternal, maternal-paternal alleles and maternal. |
p |
Vector of real numbers. Allele frequency vector. |
M |
Matrix of real numbers. Mutation matrix. |
kappa |
Vector of real numbers describing relationship. IBD parameters for 0,1,2 IBD alleles. |
alpha |
Four probabilities, summing to 1, giving the probability, in case IBD=1, that the alleles are paternal, paternal-maternal, maternal-paternal, and maternal. |
theta |
Real in [0,1]. Kinship coefficient. |
beta |
Real in [0,1]. Probability of same parental origin when IBD=2. |
Details
There are two non-inbred individuals A and B, with genotypes a/b and c/d, where the alleles may or may not differ. We calculate the likelihood assuming a relationship described by kappa.
Value
likelihood, real.
Author(s)
Thore Egeland <Thore.Egeland@nmbu.no>
References
Egeland, Pinto and Amorim, FSI:Genetics (2017), http://dx.doi.org/10.1016/j.fsigen.2017.04.018.
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 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 | library(expm)
library(Familias)
# Example 1. Paternity case. Silent allele, mutation
p <- c(0.2, 0.75, 0.05); R <- 0.005
locus1 <- FamiliasLocus(frequencies=p, name="L1", allelenames=c("1","2", "silent"),
femaleMutationRate = R, maleMutationRate =R,femaleMutationRange = 0.1,
maleMutationRange = 0.1,femaleMutationRate2 = 0, maleMutationRate2 = 0,
maleMutationModel="Proportional", femaleMutationModel="Proportional")
M <- locus1$maleMutationMatrix
theta <- 0.03
n <- c(0, 1, 1, 0); kappa.num <- c(0, 1, 0); kappa.den <- c(1, 0, 0);alpha <- c(0, 0.5, 0.5, 0)
t1 <- lik2(c(1,1), c(2,2), n, p, M, kappa.num, alpha, theta)
t2 <- lik2(c(1,3), c(2,2), n, p, M, kappa.num, alpha, theta)
t3 <- lik2(c(1,1), c(2,3), n, p, M, kappa.num, alpha, theta)
t4 <- lik2(c(1,3), c(2,3), n, p, M, kappa.num, alpha, theta)
u1 <- lik2(c(1,1), c(2,2), n, p, M, kappa.den, alpha, theta)
u2 <- lik2(c(1,3), c(2,2), n, p, M, kappa.den, alpha, theta)
u3 <- lik2(c(1,1), c(2,3), n, p, M, kappa.den, alpha, theta)
u4 <- lik2(c(1,3), c(2,3), n, p, M, kappa.den, alpha, theta)
num <- t1 + t2 + t3 + t4
den <- u1 + u2 + u3 + u4
LR1 <- num/den
# Below LR is checked using Familias
persons <- c("AF", "CH")
sex <- c("male", "male")
#Define the alternative pedigrees
ped1 <- FamiliasPedigree(id=persons, dadid=c(NA,"AF"),
momid=c(NA,NA), sex=c("male", "male"))
ped2 <- FamiliasPedigree(id=persons, dadid=c(NA,NA),
momid=c(NA,NA), sex=c("male", "male"))
pedigrees <- list(ped1,ped2)
datamatrix <- data.frame(locus1.1=c(1,2), locus1.2=c(1,2))
rownames(datamatrix) <- persons
result <- FamiliasPosterior(pedigrees, locus1, datamatrix, ref=2, kinship = theta)
LR2 <- result$LR[1]
stopifnot(abs(LR1 - LR2) <1e-15)
###
library(Familias)
test <- function(a, b, c, d, R, model="Proportional",
p=c(0.1,0.2,0.3,0.3,0.1), theta=0){
anames <- 1:length(p)
datamatrix <- cbind(c(NA,NA,a,c,NA,NA),c(NA,NA,b,d,NA,NA))
persons <- c("FA","MO", "B1", "B2","EM","EF")
rownames(datamatrix) <- persons
seks <- c("male", "female", "male", "male","male","female")
ped1 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,"FA","FA",NA, NA),
momid=c(NA, NA,NA,NA,NA, NA), sex = seks)
ped2 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,"FA","FA",NA, NA),
momid=c(NA, NA,"MO","MO",NA, NA), sex =seks)
ped3 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,"B2",NA,NA, NA),
momid=c(NA, NA,NA,NA,NA, NA), sex =seks)
ped4 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,NA,NA,NA, NA),
momid=c(NA, NA,NA,NA,NA, NA), sex =seks)
ped5 <- FamiliasPedigree(id=persons, dadid=c("B1", NA,NA,"FA",NA, NA),
momid=c(NA, NA,NA,NA,NA, NA), sex =seks)
ped6 <- FamiliasPedigree(id=persons, dadid=c(NA, "B1",NA,"FA",NA, NA),
momid=c("MO", NA,NA,NA,NA, NA), sex =seks)
ped7 <- FamiliasPedigree(id=persons, dadid=c("EM", "EM","FA",NA,NA, NA),
momid=c("EF", "EF",NA,"MO",NA, NA), sex =seks)
ped8 <- FamiliasPedigree(id=persons, dadid=c("EM", "B1",NA,"FA",NA, NA),
momid=c(NA, NA,NA,NA,"MO", NA), sex =seks)
ped9 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,"FA","EM","FA", NA),
momid=c(NA, NA,"MO",NA,"MO", NA), sex =seks)
ped10 <- FamiliasPedigree(id=persons, dadid=c(NA, NA,"FA","EM",NA, NA),
momid=c("EF", NA,"MO","MO","EF", NA), sex =seks)
peds <- list(HS=ped1,FS=ped2, PO=ped3, UNR=ped4,GP=ped5, GR=ped6,
CO=ped7,GGR=ped8,AVU=ped9,diff=ped10)
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= anames, MutationRate=R, MutationModel=model)
res <- FamiliasPosterior(peds, locus1, datamatrix)
M <- locus1$maleMutationMatrix
g1 <- c(a,b); g2 <- c(c,d)
l1 <- lik2(g1, g2, n=c(1,0,0,0),p,M,
kappa=c(0.5,0.5,0), alpha=c(1,0,0,0), theta)
l2 <- lik2(g1, g2, n=c(1,1,1,1), p, M,
kappa=c(0.25,0.5,0.25), alpha=c(1,1,1,1)/4, theta)
l3 <- lik2(g1, g2, n=c(1,1, 0,0),p, M,
kappa=c(0,1,0.0), alpha=c(0.5, 0.5, 0, 0), theta)
l4 <- lik2(g1, g2, n=c(0,0,0,0), p, M,
kappa=c(1,0,0.0), alpha=c(1,1,1,1)/4, theta)
l5 <- lik2(g1, g2, n=c(1,1,0,0), p, M,
kappa=c(0.5, 0.5,0.0), alpha=c(0.5, 0.5, 0, 0), theta)
l6 <- lik2(g1, g2, n=c(2,2,0,0), p, M,
kappa=c(0.75, 0.25,0.0), alpha=c(0.5, 0.5, 0, 0), theta)
l7 <- lik2(g1, g2, n=c(0,4,0,0), p, M,
kappa=c(0.75, 0.25,0.0), alpha=c(0, 1, 0, 0), theta)
l8 <- lik2(g1, g2, n=c(3,3,0,0), p, M,
kappa=c(7/8, 1/8,0.0), alpha=c(0.5, 0.5, 0, 0), theta)
l9 <- lik2(g1, g2, n=c(3,3,0,0), p, M,
kappa=c(0.5, 0.5,0.0), alpha=c(0.5, 0.5, 0, 0), theta)
l10 <- lik2(g1, g2, n=c(4,0,0,0), p, M,
kappa=c(7, 8, 1)/16, alpha=c(1,0, 0, 0), theta)
fam <- res$likelihoods
exact <- c(l1,l2,l3,l4,l5,l6,l7,l8,l9,l10)
z <- abs(res$likelihoods-exact)
check <- all(z< 1e-10)
res <- cbind(fam,exact)
colnames(res) <- c("Familias","Exact")
rownames(res) <- c("HS","FS","PO", "UNR","GP","GGP","CO","GGGP", "UNC","HS+")
list(res, check=check)
}
data(NorwegianFrequencies)
d <- NorwegianFrequencies$D12S391
names(d) <- 1:length(d) #21=16, 22=17 etct
foo3 <- test(16,17,18,19,R=0.00,"Proportional", p=as.double(d))
foo3 <- foo3[[1]]
foo4 <- test(16,17,18,19,R=0.0021,"Proportional", p=as.double(d))
foo4 <- foo4[[1]]
foo5 <- test(16,17,18,19,R=0.0021,"Equal", p=as.double(d))
foo5 <- foo5[[1]]
foo6 <- test(18,19,16,17,R=0.0021,"Equal", p=as.double(d))
foo6 <- foo6[[1]]
foo <- cbind(foo3,foo4,foo5,foo6)
foo <- foo[,c(1,3,5,7)]
kappa <- c("(0.5,0.5,0)","(0.25,0.5,0.25)","(0,1,0)","1,0,0)",
"(0.5,0.5,0)","(0.75,0.25,0)","(0.75,0.25,0)","(7/8,1/8,0)","(0.5,0.5,0)",
"(7/16,8/16,1/16)")
Table1 <- data.frame(kappa,foo)
colnames(Table1) <- c("kappa","R=0","R=0.0021","R=0.0021(Eq)","Swapped")
Table1
# Example First example of paper
foo1 <- test(1,1,2,2,R=0.005, model="Equal",p=c(0.1,0.9) )[[1]][3,1]
foo2 <- test(2,2,1,1,R=0.005, model="Equal",p=c(0.1,0.9) )[[1]][3,1]
foo1/foo2 #=9, i.e., no 1
foo1 <- test(1,1,2,2,R=0.005, model="Proportional",p=c(0.1,0.9) )[[1]][3,1]
foo2 <- test(2,2,1,1,R=0.005, model="Proportional",p=c(0.1,0.9) )[[1]][3,1]
foo1/foo2 # =1
#LR with general mutation matrix using Familias
library(Familias)
id <- c("I", "II")
I.II <- FamiliasPedigree(id, c(NA, "I"), c(NA, NA), c("male", "male"))
II.I <- FamiliasPedigree(id, c(NA, NA), c(NA, NA), c("male", "male"))
pedigrees <- list( I.II = I.II, II.I = II.I)
m12 <- 1/100; m21 <- 3/100
M <- rbind(c(1-m12,m12),c(m21,1-m21))
p1 <- m21/(m12+m21);p2 <- m12/(m12+m21); p <- c(p1,1-p1)
anames <- 1:length(p)
locus1 <-FamiliasLocus(frequencies = p,"locus1",
allelenames = anames,
MutationModel="Custom", MutationMatrix=M)
locus2 <-FamiliasLocus(frequencies = p,"locus2",
allelenames = anames,
MutationModel="Custom", MutationMatrix=M)
datamatrix <- data.frame(locus1.1=c(1,2), locus1.2=c(1,2), locus2.1=c(2,1),locus2.2=c(2,1))
rownames(datamatrix) <- c("I","II")
myloci <- list(locus1,locus2)
LRs <- FamiliasPosterior(pedigrees,myloci, datamatrix,ref=2)$LRperMarker[,1]
#Both above:
m12+m21
#Example 3 Stationarity not enough
library(Familias)
id <- c("I", "II")
I.II <- FamiliasPedigree(id, c(NA, "I"), c(NA, NA), c("male", "male"))
II.I <- FamiliasPedigree(id, c(NA, NA), c(NA, NA), c("male", "male"))
pedigrees <- list( I.II = I.II, II.I = II.I)
R <- 0.1
M <- rbind(c(1-2*R,3*R/2,R/2),c(R/2,1-R,R/2),c(R/2,R/2,1-R))
p <- c(3,7,5)/15
anames <- 1:length(p)
locus1 <-FamiliasLocus(frequencies = p,"locus1",
allelenames = anames,
MutationModel="Custom", MutationMatrix=M)
locus2 <-FamiliasLocus(frequencies = p,"locus2",
allelenames = anames,
MutationModel="Custom", MutationMatrix=M)
datamatrix <- data.frame(locus1.1=c(1,2), locus1.2=c(1,2), locus2.1=c(2,1),locus2.2=c(2,1))
rownames(datamatrix) <- c("I","II")
myloci <- list(locus1,locus2)
result1 <- FamiliasPosterior(pedigrees,myloci, datamatrix,ref=2)
result1$LRperMarker
result1$LRperMarker[1]-45*R/14
result1$LRperMarker[2]-35*R/14
for (i in 1:10000) p <- p
p
# Example 3
# Exact calculation with SNP-s for an example of the paper
example2 <- function(p=0.4,R=0.005){
k <- R/(2*p*(1-p))
m11 <- 1-k*(1-p)
m22 <- 1- k*p
HS <- 0.5*p^4+0.5*p^3*(m11^2+k^2*p*(1-p))
UNC <- 0.5*p^4+0.5*p^3*(m11^3+2*k^2*p*(1-p)*m11+k^2*(1-p)*p)
GGP <- 0.75*p^4+0.25*p^3*(m11^3+2*k^2*p*(1-p)*m11+k^2*(1-p)*p)
list(HS.GP=HS,UNC=UNC, GGP=GGP)
}
p <- 0.4; R <- 0.005
example2(p,R)
test(1,1,1,1,R=R,"Proportional", p=c(p,1-p))[[1]][c(1,5,9,6),1]
#Example 4
data(NorwegianFrequencies)
p<-as.double(NorwegianFrequencies$D12S391)
k <- 0.0021/sum(p*(1-p))
#Example 5
#Same mother, father brothers
rm(list=ls())
a <- 1;b <- 2; c <- 1;d <- 3
persons <- c("FA","MO", "B1", "B2","EM","EF","EM2")
seks <- c("male", "female", "male", "male","male","female","male")
R <- 0.0021; model <- "Proportional"; p <- c(0.1,0.2,0.3,0.3,0.1)
anames <- 1:length(p)
ped11 <- FamiliasPedigree(id=persons, dadid=c("EM2", NA,"FA","EM","EM2", NA,NA),
momid=c("EF", NA,"MO","MO","EF", NA, NA), sex =seks)
datamatrix <- cbind(c(NA,NA,a,c,NA,NA,NA),c(NA,NA,b,d,NA,NA,NA))
rownames(datamatrix) <- persons
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= anames, MutationRate=R, MutationModel=model)
res <- FamiliasPosterior(ped11, locus1, datamatrix)
M <- locus1$maleMutationMatrix
l11 <- lik2(c(a,b),c(c,d), n = c(4,0,0,2), p,M,
kappa=c(3/8,4/8,1/8), alpha=c(1/4,0,0,3/4), theta=0)
c(res$likelihoodsPerSystem,l11)
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