snpgdsIBDMLE: Maximum likelihood estimation (MLE) for the...
In SNPRelate: Parallel Computing Toolset for Genome-Wide Association Studies (GWAS)

Description Usage Arguments Details Value Author(s) References See Also Examples

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

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"),
	max.niter=1000, reltol=sqrt(.Machine$double.eps), coeff.correct=TRUE,
	out.num.iter=TRUE, num.thread=1, verbose=TRUE)

`gdsobj`	a GDS file object (`gds.class`)
`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
`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 "<= missing.rate" only; if NaN, no any missing threshold
`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
`method`	"EM", "downhill.simplex", 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
`verbose`	if TRUE, show information

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.

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.

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
`k1`	IBD coefficient, the probability of sharing ONE IBD
`kinship`	the estimated kinship coefficients, if the parameter `kinship=TRUE`

Xiuwen Zheng

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.

snpgdsIBDMLELogLik, snpgdsIBDMoM

# open an example dataset (HapMap)
genofile <- openfn.gds(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
closefn.gds(genofile)