LD: Pairwise linkage disequilibrium between genetic markers.

Description

Compute pairwise linkage disequilibrium between genetic markers

Usage

LD(g1, ...)
# S3 method for genotype
LD(g1,g2,...)
# S3 method for data.frame
LD(g1,...)

Arguments

genotype object or dataframe containing genotype objects

genotype object (ignored if g1 is a dataframe)

…

optional arguments (ignored)

Value

LD.genotype returns a 5 element list:

call

the matched call

Linkage disequilibrium estimate

Dprime

Scaled linkage disequilibrium estimate

corr

Correlation coefficient

nobs

Number of observations

chisq

Chi-square statistic for linkage equilibrium (i.e., D=D'=corr=0)

p.value

Chi-square p-value for marker independence

LD.data.frame returns a list with the same elements, but each element is a matrix where the upper off-diagonal elements contain the estimate for the corresponding pair of markers. The other matrix elements are NA.

Details

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

LD.genotype estimates the extent of LD for a single pair of genotypes. LD.data.frame computes LD for all pairs of genotypes contained in a data frame. Before starting, LD.data.frame checks the class and number of alleles of each variable in the dataframe. If the data frame contains non-genotype objects or genotypes with more or less than 2 alleles, these will be omitted from the computation and a warning will be generated.

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]
$$D' = \frac{D}{D_{max} } $$
where, if D > 0: $$% D_{max} = \min( p_A p_b, p_a p_B ) % $$ or if D < 0: $$% D_{max} = \max{ -p_A p_B, -p_a p_b } % $$
r correlation coefficient between the markers
$$% r = \frac{-D}{\sqrt( p_A * p_a * p_B * p_b )} % $$

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.

Examples

Run this code

# NOT RUN {
g1 <- genotype( c('T/A',    NA, 'T/T',    NA, 'T/A',    NA, 'T/T', 'T/A',
                  'T/T', 'T/T', 'T/A', 'A/A', 'T/T', 'T/A', 'T/A', 'T/T',
                     NA, 'T/A', 'T/A',   NA) )

g2 <- genotype( c('C/A', 'C/A', 'C/C', 'C/A', 'C/C', 'C/A', 'C/A', 'C/A',
                  'C/A', 'C/C', 'C/A', 'A/A', 'C/A', 'A/A', 'C/A', 'C/C',
                  'C/A', 'C/A', 'C/A', 'A/A') )


g3 <- genotype( c('T/A', 'T/A', 'T/T', 'T/A', 'T/T', 'T/A', 'T/A', 'T/A',
                  'T/A', 'T/T', 'T/A', 'T/T', 'T/A', 'T/A', 'T/A', 'T/T',
                  'T/A', 'T/A', 'T/A', 'T/T') )

# Compute LD on a single pair

LD(g1,g2)

# Compute LD table for all 3 genotypes

data <- makeGenotypes(data.frame(g1,g2,g3))
LD(data)
# }