snpgdsPairIBD {SNPRelate} | R Documentation

## Calculate Identity-By-Descent (IBD) Coefficients

### Description

Calculate the three IBD coefficients (k0, k1, k2) for non-inbred individual pairs by Maximum Likelihood Estimation (MLE) or PLINK Method of Moment (MoM).

### Usage

    snpgdsPairIBD(geno1, geno2, allele.freq,
        method=c("EM", "downhill.simplex", "MoM", "Jacquard"),
        kinship.constraint=FALSE, max.niter=1000L, reltol=sqrt(.Machine$double.eps),
        coeff.correct=TRUE, out.num.iter=TRUE, verbose=TRUE)

### Arguments

`geno1` | the SNP genotypes for the first individual, 0 – BB, 1 – AB, 2 – AA, other values – missing
`geno2` | the SNP genotypes for the second individual, 0 – BB, 1 – AB, 2 – AA, other values – missing
`allele.freq` | the allele frequencies
`method` | "EM", "downhill.simplex", "MoM" or "Jacquard", see details
`kinship.constraint` | if TRUE, constrict IBD coefficients ($k_0,k_1,k_2$) in the genealogical region ($2 k_0 k_1 >= k_2^2$)
`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
`verbose` | if TRUE, show information

### Details

If `method = "MoM"`, then PLINK Method of Moment without a allele-count-based correction factor is conducted. Otherwise, two numeric approaches for maximum likelihood estimation 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.

### Value

Return a `data.frame`:

`k0` | IBD coefficient, the probability of sharing ZERO IBD
`k1` | IBD coefficient, the probability of sharing ONE IBD
`loglik` | the value of log likelihood
`niter` | the number of iterations

### Author(s)

Xiuwen Zheng

### 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.

Purcell S, Neale B, Todd-Brown K, Thomas L, Ferreira MAR, Bender D, Maller J, Sklar P, de Bakker PIW, Daly MJ & Sham PC. 2007. PLINK: a toolset for whole-genome association and population-based linkage analysis. American Journal of Human Genetics, 81.

### See Also

`snpgdsPairIBDMLELogLik`, `snpgdsIBDMLE`, `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"]

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

    # the number of samples
    n <- 25

    # specify allele frequencies
    RF <- snpgdsSNPRateFreq(genofile, sample.id=YRI.id, snp.id=snpset,
        with.id=TRUE)
    summary(RF$AlleleFreq)

    subMLE <- snpgdsIBDMLE(genofile, sample.id=YRI.id[1:n], snp.id=RF$snp.id,
        allele.freq=RF$AlleleFreq)
    subMoM <- snpgdsIBDMoM(genofile, sample.id=YRI.id[1:n], snp.id=RF$snp.id,
        allele.freq=RF$AlleleFreq)
    subJac <- snpgdsIBDMLE(genofile, sample.id=YRI.id[1:n], snp.id=RF$snp.id,
        allele.freq=RF$AlleleFreq, method="Jacquard")

    ########################

    # genotype matrix
    mat <- snpgdsGetGeno(genofile, sample.id=YRI.id[1:n], snp.id=snpset,
        snpfirstdim=TRUE)

    rv <- NULL
    for (i in 2:n)
    {
        rv <- rbind(rv, snpgdsPairIBD(mat[,1], mat[,i], RF$AlleleFreq, "EM"))
        print(snpgdsPairIBDMLELogLik(mat[,1], mat[,i], RF$AlleleFreq,
            relatedness="unrelated", verbose=TRUE))
    }
    rv
    summary(rv$k0 - subMLE$k0[1, 2:n])
    summary(rv$k1 - subMLE$k1[1, 2:n])
    # ZERO

    rv <- NULL
    for (i in 2:n)
        rv <- rbind(rv, snpgdsPairIBD(mat[,1], mat[,i], RF$AlleleFreq, "MoM"))
    rv
    summary(rv$k0 - subMoM$k0[1, 2:n])
    summary(rv$k1 - subMoM$k1[1, 2:n])
    # ZERO

    rv <- NULL
    for (i in 2:n)
        rv <- rbind(rv, snpgdsPairIBD(mat[,1], mat[,i], RF$AlleleFreq, "Jacquard"))
    rv
    summary(rv$D1 - subJac$D1[1, 2:n])
    summary(rv$D2 - subJac$D2[1, 2:n])
    # ZERO

    # close the genotype file
    snpgdsClose(genofile)

[Package SNPRelate version 1.12.2 Index]