LR2: Pairwise LR 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 LR is calculated for a pair of non-inbred individual as described in the paper
Egeland, Pinto and Amorim, FSI: Genetics (2017).
Usage
1
Arguments
g1
Genotype, two integers giving the alleles for individual 1.
g2
Genotype, two integers giving the alleles for individual 2.
n.num
Integer vector of length 4 giving the distance in number of meioses between
paternal, paternal-maternal, maternal-paternal alleles and maternal for numerator hypothesis.
n.den
Integer vector of length 4 giving the distance in number of meioses between
paternal, paternal-maternal, maternal-paternal alleles and maternal for denominator hypothesis.
p
Vector of real numbers summing to 1. Allele frequency vector.
M
Matrix of real numbers in [0,1] with lines summing to 1. Mutation matrix.
kappa.num
Vector of real numbers in [0,1] summing to 1 describing relationship for numerator hypothesis.
IBD parameters for 0,1,2 IBD alleles.
kappa.den
Vector of real numbers describing relationship for denominator hypothesis.
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, paternal-maternal,
maternal-paternal, and maternal-maternal.
theta
Real in [0,1]. Kinship coefficient.
silent
Logical, see below.
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.num,
the likelihood assuming kappa.den (typically unrelated) and the LR.
If silent=TRUE the last allele frequency of p
corresponds to the silent allele.
Value
numerator, denominator and LR=numerator/denominator.
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)
### The examples are from Egeland, Pinto and Amorim (2016)
### (referred to as the 'paper' below)
### Example 2.1.
### Consider a duo case and assume mutations are not possible.
p <- c(0.1,0.2,0.3,0.4)
M <- diag(c(1,1,1,1))
n.num <- c(2, 2, 2, 2)
n.den <- c(0, 0, 0, 0)
alpha <- c(1,1,1,1)/4
kappa.num <- c(0.25, 0.50, 0.25); kappa.den <- c(1,0,0); theta <- 0
# The next three LRs coincide with those found
# using exact formulae in the paper
LR2(c(1,2), c(3,4), n.num, n.den, p, M, kappa.num,
kappa.den, alpha, theta)$LR
LR2(c(1,2), c(1,3), n.num, n.den, p, M, kappa.num,
kappa.den, alpha, theta)$LR
LR2(c(1,2), c(1,2), n.num, n.den, p, M, kappa.num,
kappa.den, alpha, theta)$LR
### Example 2.2 Identifying parent-child with mutation
### "A father and a son are missing ..."
p <- 0.2; R <- 0.005; k <- R/(2*p*(1-p))
M <- rbind(c(1-k*(1-p),k*(1-p)),c(k*p,1-k*p))
n.num <- c(0, 1, 1, 0); kappa.num <- c(0, 1, 0)
n.den <- c(0, 0, 0, 0); kappa.den <- c(1, 0, 0)
alpha <- c(0, 0.5, 0.5, 0)
theta <- 0.0
# Below values coincide, this is no longer true if
# M is made unbalanced or theta>0
LR2(c(1,1), c(2,2), n.num, n.den, c(p, 1-p), M,
kappa.num, kappa.den, alpha, theta)$LR
LR2(c(2,2), c(1,1), n.num, n.den, c(p, 1-p), M,
kappa.num, kappa.den, alpha, theta)$LR
### Example 2.3
library(Familias)
persons <- c("Child", "Alleged father")
sex <- c("male", "male")
ped1 <- FamiliasPedigree(id=persons, dadid=c("Alleged father",NA),
momid=c(NA,NA), sex=c("male", "male"))
ped2 <- FamiliasPedigree(id=persons, dadid=c(NA,NA), momid=c(NA,NA),
sex=c("male", "male"))
pedigrees <- list(ped1,ped2)
R =.01; theta = 0.02
locus1 <- FamiliasLocus(frequencies=c(0.25,0.25,0.25,0.25),
name="L1", allelenames=c("1","2","3","4"),
MutationRate = R, MutationModel="Proportional")
loci <- list(locus1)
datamatrix <- data.frame(locus1.1=c("3","1"), locus1.2=c("4","2"))
datamatrix <- data.frame(locus1.1=c("1","3"), locus1.2=c("2","4")) #Swapped, same result
rownames(datamatrix) <- persons
result <- FamiliasPosterior(pedigrees, loci, datamatrix, ref=2, kinship=theta)
result$LR[1]
(1+2*theta)/(1-theta)*(4/3)*R
### Example 3.1 of paper, double first cousin example
p <- 0.2; q <- 1-p; R <- 0.005; k <- R/(2*p*(1-p))
k4 <- 1-(1-k)^4
m <- 1-k4*(1-p)
kappa0 <- 9/16; kappa1 <- 6/16; kappa2 <- 1/16
kappa0+kappa1*m/p+kappa2*m^2/p^2
# LR=3.759526 as confirmed by familias.name/DFC.SNP.fam
# Alternatively using library familias.name/mut.zip
alpha <- c(0,0.5,0.5, 0)
n.num <- c(0,4, 4, 0); n.den <- c(0,0,0,0)
kappaDFC <- c(kappa0, kappa1, kappa2)
LR2(c(1,1),c(1,1),n.num, n.den, M=M, p=c(p,1-p), kappa.num=kappaDFC,
alpha=alpha, theta=0, beta=0)$LR
# Four alleles
p <- c(0.1,0.2,0.3,0.4)
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= 1:length(p), MutationRate=R, MutationModel="Proportional")
M <- locus1$maleMutationMatrix
LR2(c(1,1), c(1,1),n.num, n.den, M=M, p=p, kappa.num=kappaDFC,
alpha=alpha, theta=0, beta=0)
# LR=10.15314 as confirmed by http://familias.name/DFC.4.fam (takes a few minutes)
# With ten alleles, all allele freq 0.1, and "Equal" mutation model
p <- rep(0.1,10)
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= 1:length(p), MutationRate=R, MutationModel="Equal")
M <- locus1$maleMutationMatrix
LR2(c(1,1), c(1,1),n.num, n.den, M=M, p=p, kappa.num=kappaDFC,
alpha=alpha, theta=0, beta=0)
# LR=10.24266 as confirmed by http://familias.name/DFC.10.fam (takes a few minutes)
### Example 3.2 of paper
library(paramlink)
library(Familias)
R <- 0.005; p <- c(0.01, 0.2, 0.3, 0.49)
g1 <- c(1,2); g2 <- c(1,3)
an <- 1:length(p)
nn1 <- nn2 <- 3; x <- doubleCousins(nn1, nn2)
v <- 3
kappa.num <- c((2^{2*v}-1)^2, 2*(2^{2*v}-1),1)/16^v
alpha <- c(0.5, 0, 0, 0.5)
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= an, MutationRate=R, MutationModel="Proportional")
M <- locus1$maleMutationMatrix
n1 <- nn1+nn2+2; n2 <- nn1+nn2+2
n.num <- c(n1, 0, 0, n2)
n.den <- c(0, 0, 0, 0)
kappa.den <- c(1,0,0)
myLR <- LR2(g1, g2, n.num, n.den, p, M, kappa.num, kappa.den, alpha, beta=0)
myLR$LR
#Exact
k <- R/(1-sum(p^2))
k10 <- 1-(1-k)^n2
kappa.num[1]+
kappa.num[2]*(p[3]*(k10*p[1]+(1-k10*(1-p[1]))) +
(p[1]*2*k10*p[3]))/(4*p[1]*p[3]) +
kappa.num[3]*2*((1-k10*(1-p[1]))*k10*p[3]+k10^2*p[1]*p[3])/(4*p[1]*p[3])
### Example 3.3 HS or GP versus avuncular
p <- c(0.1, 0.2, 0.3, 0.4); R <-0.005
locus1 <- FamiliasLocus(frequencies=p, name="L1", allelenames=1:4,
femaleMutationRate = R, maleMutationRate =R,femaleMutationRange = 0.1,
maleMutationRange = 0.1,femaleMutationRate2 = 0, maleMutationRate2 = 0,
maleMutationModel="Proportional",femaleMutationModel="Proportional")
M <- locus1$maleMutationMatrix
kappa.num <- kappa.den <-c(0.5,0.5,0)
alpha <- c(1,0,0,0)
n1 <- c(2,0,0,0)
n2 <- c(3,0,0,0)
a <- 1; b<-2; c<-3; d<-4
g1 <- c(a,b); g2 <- c(c,d)
LR.1 <- LR2(g1, g2,n.num=n1, n.den=n2, p=p, M, kappa.num,
kappa.den, alpha, theta=0, beta=0)$LR
H <- 1-sum(p^2)
k <- R/H
k2 <- 1-(1-k)^2; k3 <- 1-(1-k)^3
# Case 1: a,b,c,d differ, no overlap in genotypes
LR.2 <- (1+k2)/(1+k3)
LR.1-LR.2#Equal
# Case 2 all a
g1 <- c(a,a); g2 <- c(a,a)
LR.1 <- LR2(g1, g2,n.num=n1, n.den=n2, p=p, M, kappa.num, kappa.den, alpha, theta=0)$LR
LR.2 <- (p[a]+1-k2*(1-p[a]))/(p[a]+1-k3*(1-p[a])) #all a
#Case 3 equal hetero
c <- 3; d <- 4
g1 <- c(c,d); g2 <- c(c,d)
LR.1 <- LR2(g1, g2,n.num=n1, n.den=n2, p=p, M, kappa.num, kappa.den, alpha, theta=0)$LR
num <- (4*p[c]*p[d]+p[d]*(1+k2*(2*p[c]-1))+p[c]*(1+k2*(2*p[d]-1)))
den <- (4*p[c]*p[d]+p[d]*(1+k3*(2*p[c]-1))+p[c]*(1+k3*(2*p[d]-1)))
LR.2 <- num/den
LR.1-LR.2
# Example QHFC Thompson p 22
p <- c(0.1, 0.9); R <- 0.005
kappa <-c(17,14,1)/32
alpha <- c(0.25,0.25,0.25,0.25)
n.num <- c(4,4,4,4); n.den <- c(0, 0, 0, 0)
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= 1:length(p), MutationRate=R, MutationModel="Proportional")
M <- locus1$maleMutationMatrix
LR2(c(1,2), c(1,1), n.num, n.den, M=M, p=p, kappa.num=kappa,
alpha=alpha, theta=0, beta=0.5)
#=2.562366 See familias.name/QHFC.fam
# Example Last line of Table 1 of old ms, to be balanced paper
data(NorwegianFrequencies)
d <- as.double(NorwegianFrequencies$D12S391)
names(d) <- 1:length(d) #21=16, 22=17 etct
n.num <- c(4,0,0,2); n.den <- c(0, 0, 0, 0)
alpha <- c(1/8,0,0, 7/8);kappa.num <- c(7/16,8/16,1/16)
line <-NULL
R <-0
locus1 <- FamiliasLocus(frequencies=d, name="locus1",
allelenames=1:length(d), MutationRate=R, MutationModel="Proportional")
M <- locus1$maleMutationMatrix
line <- c(line, LR2(c(16,17), c(18,19), n.num, n.den,
d, M, kappa.num, alpha=alpha)$numerator)
R <-0.0021
locus1 <- FamiliasLocus(frequencies=d, name="locus1",
allelenames=1:length(d), MutationRate=R, MutationModel="Proportional")
M <- locus1$maleMutationMatrix
line <- c(line,LR2(c(16,17),c(18,19),n.num, n.den ,d,M,kappa.num, alpha=alpha)$numerator)
locus1 <- FamiliasLocus(frequencies=d, name="locus1",
allelenames=1:length(d), MutationRate=R, MutationModel="Equal")
M <- locus1$maleMutationMatrix
line <- c(line,LR2(c(16,17),c(18,19), n.num, n.den, d, M, kappa.num, alpha=alpha)$numerator)
line <- c(line,LR2(c(18,19),c(16,17), n.den, n.den, d, M, kappa.num, alpha=alpha)$numerator)
names(line) <- paste("col",1:4,sep="")
p <- d[c(16,17,18,19)]
(7/16)*4*prod(p)# First column
#Silent, mutation and kinship
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$maleMutationMatrix
persons <- c("AF", "CH")
sex <- c("male", "male")
H1 <- FamiliasPedigree(dadid=c(NA, "AF"), momid= c(NA,NA),
sex=sex, id=persons)
H2 <- FamiliasPedigree(dadid=c(NA, NA), momid= c(NA,NA),
sex=sex, id=persons)
dm <- rbind(c(1,1),
c(2,2))
rownames(dm) <- persons
theta <- 0.03
alpha <- c(0.5, 0.5, 0, 0)
n.num <- c(1, 1, 0, 0)
n.den <- c(0, 0, 0, 0)
pedigrees <- list(H1, H2)
LRfam <- FamiliasPosterior(pedigrees, locus1, dm, ref=2,
kinship = theta)$LRperMarker[1]
LR <- LR2(c(1,1), c(2,2), n.num,n.den, p, M, c(0,1,0), c(1,0,0),
alpha, theta, silent=TRUE)$LR #=0.1973758 as for Familias
# Example in Section 2.1.2. Duo with mutation and theta
R <- 0.01
theta <- 0.02
LR <- 4*(R/3)*(1+2*theta)/(1-theta) #Exact LR
g1 <- c(1,2); g2 <- c(3,4)
n.num <- c(1,0, 1,0); n.den <- c(0, 0, 0, 0)
p <- c(1, 1, 1, 1)/4
kappa.num <- c(0, 1, 0)
kappa.den <- c(1, 0, 0)
alpha <- c(0.5,0.0,0.5,0)
theta <- 0.02
silent <- 0
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= 1:4, MutationRate=R,
MutationModel="Proportional")
M <- locus1$maleMutationMatrix
LR2(g1, g2, n.num, n.den, p, M, kappa.num, kappa.den, alpha, theta, silent)
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 LR is calculated for a pair of non-inbred individual as described in the paper Egeland, Pinto and Amorim, FSI: Genetics (2017).
Usage
1 |
Arguments
g1 |
Genotype, two integers giving the alleles for individual 1. |
g2 |
Genotype, two integers giving the alleles for individual 2. |
n.num |
Integer vector of length 4 giving the distance in number of meioses between paternal, paternal-maternal, maternal-paternal alleles and maternal for numerator hypothesis. |
n.den |
Integer vector of length 4 giving the distance in number of meioses between paternal, paternal-maternal, maternal-paternal alleles and maternal for denominator hypothesis. |
p |
Vector of real numbers summing to 1. Allele frequency vector. |
M |
Matrix of real numbers in [0,1] with lines summing to 1. Mutation matrix. |
kappa.num |
Vector of real numbers in [0,1] summing to 1 describing relationship for numerator hypothesis. IBD parameters for 0,1,2 IBD alleles. |
kappa.den |
Vector of real numbers describing relationship for denominator hypothesis. 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, paternal-maternal, maternal-paternal, and maternal-maternal. |
theta |
Real in [0,1]. Kinship coefficient. |
silent |
Logical, see below. |
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.num,
the likelihood assuming kappa.den (typically unrelated) and the LR.
If silent=TRUE the last allele frequency of p
corresponds to the silent allele.
Value
numerator, denominator and LR=numerator/denominator.
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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 | library(expm)
library(Familias)
### The examples are from Egeland, Pinto and Amorim (2016)
### (referred to as the 'paper' below)
### Example 2.1.
### Consider a duo case and assume mutations are not possible.
p <- c(0.1,0.2,0.3,0.4)
M <- diag(c(1,1,1,1))
n.num <- c(2, 2, 2, 2)
n.den <- c(0, 0, 0, 0)
alpha <- c(1,1,1,1)/4
kappa.num <- c(0.25, 0.50, 0.25); kappa.den <- c(1,0,0); theta <- 0
# The next three LRs coincide with those found
# using exact formulae in the paper
LR2(c(1,2), c(3,4), n.num, n.den, p, M, kappa.num,
kappa.den, alpha, theta)$LR
LR2(c(1,2), c(1,3), n.num, n.den, p, M, kappa.num,
kappa.den, alpha, theta)$LR
LR2(c(1,2), c(1,2), n.num, n.den, p, M, kappa.num,
kappa.den, alpha, theta)$LR
### Example 2.2 Identifying parent-child with mutation
### "A father and a son are missing ..."
p <- 0.2; R <- 0.005; k <- R/(2*p*(1-p))
M <- rbind(c(1-k*(1-p),k*(1-p)),c(k*p,1-k*p))
n.num <- c(0, 1, 1, 0); kappa.num <- c(0, 1, 0)
n.den <- c(0, 0, 0, 0); kappa.den <- c(1, 0, 0)
alpha <- c(0, 0.5, 0.5, 0)
theta <- 0.0
# Below values coincide, this is no longer true if
# M is made unbalanced or theta>0
LR2(c(1,1), c(2,2), n.num, n.den, c(p, 1-p), M,
kappa.num, kappa.den, alpha, theta)$LR
LR2(c(2,2), c(1,1), n.num, n.den, c(p, 1-p), M,
kappa.num, kappa.den, alpha, theta)$LR
### Example 2.3
library(Familias)
persons <- c("Child", "Alleged father")
sex <- c("male", "male")
ped1 <- FamiliasPedigree(id=persons, dadid=c("Alleged father",NA),
momid=c(NA,NA), sex=c("male", "male"))
ped2 <- FamiliasPedigree(id=persons, dadid=c(NA,NA), momid=c(NA,NA),
sex=c("male", "male"))
pedigrees <- list(ped1,ped2)
R =.01; theta = 0.02
locus1 <- FamiliasLocus(frequencies=c(0.25,0.25,0.25,0.25),
name="L1", allelenames=c("1","2","3","4"),
MutationRate = R, MutationModel="Proportional")
loci <- list(locus1)
datamatrix <- data.frame(locus1.1=c("3","1"), locus1.2=c("4","2"))
datamatrix <- data.frame(locus1.1=c("1","3"), locus1.2=c("2","4")) #Swapped, same result
rownames(datamatrix) <- persons
result <- FamiliasPosterior(pedigrees, loci, datamatrix, ref=2, kinship=theta)
result$LR[1]
(1+2*theta)/(1-theta)*(4/3)*R
### Example 3.1 of paper, double first cousin example
p <- 0.2; q <- 1-p; R <- 0.005; k <- R/(2*p*(1-p))
k4 <- 1-(1-k)^4
m <- 1-k4*(1-p)
kappa0 <- 9/16; kappa1 <- 6/16; kappa2 <- 1/16
kappa0+kappa1*m/p+kappa2*m^2/p^2
# LR=3.759526 as confirmed by familias.name/DFC.SNP.fam
# Alternatively using library familias.name/mut.zip
alpha <- c(0,0.5,0.5, 0)
n.num <- c(0,4, 4, 0); n.den <- c(0,0,0,0)
kappaDFC <- c(kappa0, kappa1, kappa2)
LR2(c(1,1),c(1,1),n.num, n.den, M=M, p=c(p,1-p), kappa.num=kappaDFC,
alpha=alpha, theta=0, beta=0)$LR
# Four alleles
p <- c(0.1,0.2,0.3,0.4)
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= 1:length(p), MutationRate=R, MutationModel="Proportional")
M <- locus1$maleMutationMatrix
LR2(c(1,1), c(1,1),n.num, n.den, M=M, p=p, kappa.num=kappaDFC,
alpha=alpha, theta=0, beta=0)
# LR=10.15314 as confirmed by http://familias.name/DFC.4.fam (takes a few minutes)
# With ten alleles, all allele freq 0.1, and "Equal" mutation model
p <- rep(0.1,10)
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= 1:length(p), MutationRate=R, MutationModel="Equal")
M <- locus1$maleMutationMatrix
LR2(c(1,1), c(1,1),n.num, n.den, M=M, p=p, kappa.num=kappaDFC,
alpha=alpha, theta=0, beta=0)
# LR=10.24266 as confirmed by http://familias.name/DFC.10.fam (takes a few minutes)
### Example 3.2 of paper
library(paramlink)
library(Familias)
R <- 0.005; p <- c(0.01, 0.2, 0.3, 0.49)
g1 <- c(1,2); g2 <- c(1,3)
an <- 1:length(p)
nn1 <- nn2 <- 3; x <- doubleCousins(nn1, nn2)
v <- 3
kappa.num <- c((2^{2*v}-1)^2, 2*(2^{2*v}-1),1)/16^v
alpha <- c(0.5, 0, 0, 0.5)
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= an, MutationRate=R, MutationModel="Proportional")
M <- locus1$maleMutationMatrix
n1 <- nn1+nn2+2; n2 <- nn1+nn2+2
n.num <- c(n1, 0, 0, n2)
n.den <- c(0, 0, 0, 0)
kappa.den <- c(1,0,0)
myLR <- LR2(g1, g2, n.num, n.den, p, M, kappa.num, kappa.den, alpha, beta=0)
myLR$LR
#Exact
k <- R/(1-sum(p^2))
k10 <- 1-(1-k)^n2
kappa.num[1]+
kappa.num[2]*(p[3]*(k10*p[1]+(1-k10*(1-p[1]))) +
(p[1]*2*k10*p[3]))/(4*p[1]*p[3]) +
kappa.num[3]*2*((1-k10*(1-p[1]))*k10*p[3]+k10^2*p[1]*p[3])/(4*p[1]*p[3])
### Example 3.3 HS or GP versus avuncular
p <- c(0.1, 0.2, 0.3, 0.4); R <-0.005
locus1 <- FamiliasLocus(frequencies=p, name="L1", allelenames=1:4,
femaleMutationRate = R, maleMutationRate =R,femaleMutationRange = 0.1,
maleMutationRange = 0.1,femaleMutationRate2 = 0, maleMutationRate2 = 0,
maleMutationModel="Proportional",femaleMutationModel="Proportional")
M <- locus1$maleMutationMatrix
kappa.num <- kappa.den <-c(0.5,0.5,0)
alpha <- c(1,0,0,0)
n1 <- c(2,0,0,0)
n2 <- c(3,0,0,0)
a <- 1; b<-2; c<-3; d<-4
g1 <- c(a,b); g2 <- c(c,d)
LR.1 <- LR2(g1, g2,n.num=n1, n.den=n2, p=p, M, kappa.num,
kappa.den, alpha, theta=0, beta=0)$LR
H <- 1-sum(p^2)
k <- R/H
k2 <- 1-(1-k)^2; k3 <- 1-(1-k)^3
# Case 1: a,b,c,d differ, no overlap in genotypes
LR.2 <- (1+k2)/(1+k3)
LR.1-LR.2#Equal
# Case 2 all a
g1 <- c(a,a); g2 <- c(a,a)
LR.1 <- LR2(g1, g2,n.num=n1, n.den=n2, p=p, M, kappa.num, kappa.den, alpha, theta=0)$LR
LR.2 <- (p[a]+1-k2*(1-p[a]))/(p[a]+1-k3*(1-p[a])) #all a
#Case 3 equal hetero
c <- 3; d <- 4
g1 <- c(c,d); g2 <- c(c,d)
LR.1 <- LR2(g1, g2,n.num=n1, n.den=n2, p=p, M, kappa.num, kappa.den, alpha, theta=0)$LR
num <- (4*p[c]*p[d]+p[d]*(1+k2*(2*p[c]-1))+p[c]*(1+k2*(2*p[d]-1)))
den <- (4*p[c]*p[d]+p[d]*(1+k3*(2*p[c]-1))+p[c]*(1+k3*(2*p[d]-1)))
LR.2 <- num/den
LR.1-LR.2
# Example QHFC Thompson p 22
p <- c(0.1, 0.9); R <- 0.005
kappa <-c(17,14,1)/32
alpha <- c(0.25,0.25,0.25,0.25)
n.num <- c(4,4,4,4); n.den <- c(0, 0, 0, 0)
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= 1:length(p), MutationRate=R, MutationModel="Proportional")
M <- locus1$maleMutationMatrix
LR2(c(1,2), c(1,1), n.num, n.den, M=M, p=p, kappa.num=kappa,
alpha=alpha, theta=0, beta=0.5)
#=2.562366 See familias.name/QHFC.fam
# Example Last line of Table 1 of old ms, to be balanced paper
data(NorwegianFrequencies)
d <- as.double(NorwegianFrequencies$D12S391)
names(d) <- 1:length(d) #21=16, 22=17 etct
n.num <- c(4,0,0,2); n.den <- c(0, 0, 0, 0)
alpha <- c(1/8,0,0, 7/8);kappa.num <- c(7/16,8/16,1/16)
line <-NULL
R <-0
locus1 <- FamiliasLocus(frequencies=d, name="locus1",
allelenames=1:length(d), MutationRate=R, MutationModel="Proportional")
M <- locus1$maleMutationMatrix
line <- c(line, LR2(c(16,17), c(18,19), n.num, n.den,
d, M, kappa.num, alpha=alpha)$numerator)
R <-0.0021
locus1 <- FamiliasLocus(frequencies=d, name="locus1",
allelenames=1:length(d), MutationRate=R, MutationModel="Proportional")
M <- locus1$maleMutationMatrix
line <- c(line,LR2(c(16,17),c(18,19),n.num, n.den ,d,M,kappa.num, alpha=alpha)$numerator)
locus1 <- FamiliasLocus(frequencies=d, name="locus1",
allelenames=1:length(d), MutationRate=R, MutationModel="Equal")
M <- locus1$maleMutationMatrix
line <- c(line,LR2(c(16,17),c(18,19), n.num, n.den, d, M, kappa.num, alpha=alpha)$numerator)
line <- c(line,LR2(c(18,19),c(16,17), n.den, n.den, d, M, kappa.num, alpha=alpha)$numerator)
names(line) <- paste("col",1:4,sep="")
p <- d[c(16,17,18,19)]
(7/16)*4*prod(p)# First column
#Silent, mutation and kinship
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$maleMutationMatrix
persons <- c("AF", "CH")
sex <- c("male", "male")
H1 <- FamiliasPedigree(dadid=c(NA, "AF"), momid= c(NA,NA),
sex=sex, id=persons)
H2 <- FamiliasPedigree(dadid=c(NA, NA), momid= c(NA,NA),
sex=sex, id=persons)
dm <- rbind(c(1,1),
c(2,2))
rownames(dm) <- persons
theta <- 0.03
alpha <- c(0.5, 0.5, 0, 0)
n.num <- c(1, 1, 0, 0)
n.den <- c(0, 0, 0, 0)
pedigrees <- list(H1, H2)
LRfam <- FamiliasPosterior(pedigrees, locus1, dm, ref=2,
kinship = theta)$LRperMarker[1]
LR <- LR2(c(1,1), c(2,2), n.num,n.den, p, M, c(0,1,0), c(1,0,0),
alpha, theta, silent=TRUE)$LR #=0.1973758 as for Familias
# Example in Section 2.1.2. Duo with mutation and theta
R <- 0.01
theta <- 0.02
LR <- 4*(R/3)*(1+2*theta)/(1-theta) #Exact LR
g1 <- c(1,2); g2 <- c(3,4)
n.num <- c(1,0, 1,0); n.den <- c(0, 0, 0, 0)
p <- c(1, 1, 1, 1)/4
kappa.num <- c(0, 1, 0)
kappa.den <- c(1, 0, 0)
alpha <- c(0.5,0.0,0.5,0)
theta <- 0.02
silent <- 0
locus1 <- FamiliasLocus(frequencies=p, name="locus1",
allelenames= 1:4, MutationRate=R,
MutationModel="Proportional")
M <- locus1$maleMutationMatrix
LR2(g1, g2, n.num, n.den, p, M, kappa.num, kappa.den, alpha, theta, silent)
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