SNPRelate (version 1.6.4)

snpgdsIBDMLE: Maximum likelihood estimation (MLE) for the Identity-By-Descent (IBD) Analysis

Description

Calculate the three IBD coefficients (k0, k1, k2) for non-inbred individual pairs by Maximum Likelihood Estimation.

Usage

snpgdsIBDMLE(gdsobj, sample.id=NULL, snp.id=NULL, autosome.only=TRUE, remove.monosnp=TRUE, maf=NaN, missing.rate=NaN, kinship=FALSE, kinship.constraint=FALSE, allele.freq=NULL, method=c("EM", "downhill.simplex", "Jacquard"), max.niter=1000L, reltol=sqrt(.Machine$double.eps), coeff.correct=TRUE, out.num.iter=TRUE, num.thread=1, verbose=TRUE)

Arguments

gdsobj

an object of class SNPGDSFileClass, a SNP GDS file

sample.id

a vector of sample id specifying selected samples; if NULL, all samples are used

snp.id

a vector of snp id specifying selected SNPs; if NULL, all SNPs are used

autosome.only

if TRUE, use autosomal SNPs only; if it is a numeric or character value, keep SNPs according to the specified chromosome

remove.monosnp

if TRUE, remove monomorphic SNPs

maf

to use the SNPs with ">= maf" only; if NaN, no any MAF threshold

missing.rate

to use the SNPs with "

kinship

if TRUE, output the estimated kinship coefficients

kinship.constraint

if TRUE, constrict IBD coefficients ($k_0,k_1,k_2$) in the geneloical region ($2 k_0 k_1 >= k_2^2$)

allele.freq

to specify the allele frequencies; if NULL, determine the allele frequencies from gdsobj using the specified samples; if snp.id is specified, allele.freq should have the same order as snp.id

method

"EM", "downhill.simplex", "Jacquard", see details

max.niter

the maximum number of iterations

reltol

relative convergence tolerance; the algorithm stops if it is unable to reduce the value of log likelihood by a factor of $reltol * (abs(log likelihood with the initial parameters) + reltol)$ at a step.

coeff.correct

TRUE by default, see details

out.num.iter

if TRUE, output the numbers of iterations

num.thread

the number of (CPU) cores used; if NA, detect the number of cores automatically

verbose

if TRUE, show information

Value

Return a snpgdsIBDClass object, which is a list:

sample.id

the sample ids used in the analysis

snp.id

the SNP ids used in the analysis

afreq

the allele frequencies used in the analysis

k0

IBD coefficient, the probability of sharing ZERO IBD, if method="EM" or "downhill.simplex"

k1

IBD coefficient, the probability of sharing ONE IBD, if method="EM" or "downhill.simplex"

D1, ..., D8

Jacquard's coefficients, if method="Jacquard"

kinship

the estimated kinship coefficients, if the parameter kinship=TRUE

Details

The minor allele frequency and missing rate for each SNP passed in snp.id are calculated over all the samples in sample.id.

The PLINK moment estimates are used as the initial values in the algorithm of searching maximum value of log likelihood function. Two numeric approaches can be used: one is Expectation-Maximization (EM) algorithm, and the other is Nelder-Mead method or downhill simplex method. Generally, EM algorithm is more robust than downhill simplex method. "Jacquard" refers to the estimation of nine Jacquard's coefficients.

If coeff.correct is TRUE, the final point that is found by searching algorithm (EM or downhill simplex) is used to compare the six points (fullsib, offspring, halfsib, cousin, unrelated), since any numeric approach might not reach the maximum position after a finit number of steps. If any of these six points has a higher value of log likelihood, the final point will be replaced by the best one.

Although MLE estimates are more reliable than MoM, MLE is much more computationally intensive than MoM, and might not be feasible to estimate pairwise relatedness for a large dataset.

References

Milligan BG. 2003. Maximum-likelihood estimation of relatedness. Genetics 163:1153-1167.

Weir BS, Anderson AD, Hepler AB. 2006. Genetic relatedness analysis: modern data and new challenges. Nat Rev Genet. 7(10):771-80.

Choi Y, Wijsman EM, Weir BS. 2009. Case-control association testing in the presence of unknown relationships. Genet Epidemiol 33(8):668-78.

Jacquard, A. Structures Genetiques des Populations (Masson & Cie, Paris, 1970); English translation available in Charlesworth, D. & Chalesworth, B. Genetics of Human Populations (Springer, New York, 1974).

See Also

snpgdsIBDMLELogLik, snpgdsIBDMoM

Examples

# open an example dataset (HapMap)
genofile <- snpgdsOpen(snpgdsExampleFileName())

YRI.id <- read.gdsn(index.gdsn(genofile, "sample.id"))[
    read.gdsn(index.gdsn(genofile, "sample.annot/pop.group"))=="YRI"]
YRI.id <- YRI.id[1:30]

# SNP pruning
set.seed(10)
snpset <- snpgdsLDpruning(genofile, sample.id=YRI.id, maf=0.05,
    missing.rate=0.05)
snpset <- sample(unlist(snpset), 250)
mibd <- snpgdsIBDMLE(genofile, sample.id=YRI.id, snp.id=snpset)
names(mibd)

# select a set of pairs of individuals
d <- snpgdsIBDSelection(mibd, kinship.cutoff=1/8)
head(d)


# log likelihood

loglik <- snpgdsIBDMLELogLik(genofile, mibd)
loglik0 <- snpgdsIBDMLELogLik(genofile, mibd, relatedness="unrelated")

# likelihood ratio test
p.value <- pchisq(loglik - loglik0, 1, lower.tail=FALSE)


flag <- lower.tri(mibd$k0)
plot(NaN, xlim=c(0,1), ylim=c(0,1), xlab="k0", ylab="k1")
lines(c(0,1), c(1,0), col="red", lty=3)
points(mibd$k0[flag], mibd$k1[flag])

# specify the allele frequencies
afreq <- snpgdsSNPRateFreq(genofile, sample.id=YRI.id,
    snp.id=snpset)$AlleleFreq
subibd <- snpgdsIBDMLE(genofile, sample.id=YRI.id[1:25], snp.id=snpset,
    allele.freq=afreq)
summary(c(subibd$k0 - mibd$k0[1:25, 1:25]))
# ZERO
summary(c(subibd$k1 - mibd$k1[1:25, 1:25]))
# ZERO


# close the genotype file
snpgdsClose(genofile)