LD: Compute linkage disequilibrium (LD)

In DominikMueller64/LDtools: Tools for Linkage Disequilibrium Analysis

Description

Compute the linkage disequilibrium (LD) between a pair of loci.

Usage

LD(x, y, is_phased = TRUE, any_na = TRUE, r_only = FALSE, check = TRUE)

Arguments

x	A numeric vector. The haplotype/genotype data of the first locus. If they are phased, there must only contain 0 and 1. If they are unphased, they must only contain 0, 1, or 2, where 1 codes for the heterozygot.
y	A numeric vector. The haplotype/genotype data of the second locus.
is_phased	A logical. Are the data phased?
any_na	A logical. May some genotypes contain missing values? If not, computations are more efficient for phased genotypes.
r_only	Should only the r-statistic be computed? (Produces minimal output for saving memory and computation time.)
check	A logical. Should checks be performed?

Details

For computing LD among a large number of loci, please use LD_mult, which is much more efficient for that.

Linkage disequilibrium (LD) is the non-random association of marker alleles and can arise from marker proximity or from selection bias.

Three estimators of LD are computed:

• D raw difference in frequency between the observed number of AB pairs and the expected number:

  D = p(AB) - p(A)*p(B)

• D' scaled D spanning the range [-1,1]

  D' = D / Dmax

  where, if D > 0:

  Dmax = min( p(A)p(b), p(a)p(B) )

  or if D < 0:

  Dmax = max( -p(A)p(B), -p(a)p(b) )

• r correlation coefficient between the markers

  r = -D / sqrt( p(A) * p(a) * p(B) * p(b) )

where

• - p(A) is defined as the observed probability of allele 'A' for marker 1,

• - p(a) = 1-p(A) is defined as the observed probability of allele 'a' for marker 1,

• -p(B) is defined as the observed probability of allele 'B' for marker 2, and

• -p(b) = 1- p(B) is defined as the observed probability of allele 'b' for marker 2, and

• -p(AB) is defined as the probability of the marker allele pair 'AB'.

For genotype data, AB/ab cannot be distinguished from aB/Ab. Consequently, we estimate p(AB) using maximum likelihood and use this value in the computations.

Value

LD returns a list with the following components:

• D Linkage disequilibrium estimate

• Dprime Scaled linkage disequilibrium estimate

• r Correlation coefficient

• r2 Squared correlation coefficient

• n Number of observations

• chis2 Chi-square statistic for linkage equilibrium (i.e., D = Dprime = r = r2 = 0)

• pval Chi-square p-value for marker independence

Author(s)

Dominik Mueller ([e-mail]) The documentation is adapted from the LD function of the genetics package by Gregory Warnes.

See Also

transform_geno, LD_mult

Examples

# phased data
data('population', package = 'LDtools')
LD(x = X[, 1], y = X[, 2], is_phased = TRUE, any_na = FALSE)

# unphased data
tmp <- transform_geno(.gen_geno(n = 20L, m = 2L))
LD(x = tmp$geno[, 1], y = tmp$geno[, 2], is_phased = FALSE,
any_na = TRUE)

DominikMueller64/LDtools documentation built on May 6, 2019, 2:51 p.m.