tdtGxG: Genotypic TDT for Two-Way Interactions

Description

tdtGxG and colGxG perform the genotypic TDT for the interaction of two SNPs or of each pair of columns of a genotype matrix, respectively.

fastGxG provides a fast implementation for the genotypic TDT for two-way interactions when considering the simplest conditional logistic regression model only containing one parameter for the interaction effect. It thus leads to the same results as colGxG with test = "screen". In fastGxGrec, an analytic solution to the genotypic TDT based on the simplest model for testing a recessive x recessive model is implemented, which is even faster than fastGxG with model = "recessive". In future versions of this package, fastGxG and fastGxGrec will be joint with colGxG.

The genotypic TDT for testing two-way interactions makes use of the 16 possible genotypes that can be obtained from combining the parents' genotypes of the two considered SNPs. Thus, for each family, genotypes for one case (i.e. the affected offspring) and 15 pseudo-controls are used.

Usage

tdtGxG(snp1, snp2, test = c("epistatic", "lrt", "full", "screen"),  model = c("additive", "dominant", "recessive")) 
colGxG(mat.snp, test = c("epistatic", "lrt", "full", "screen"), genes = NULL, maf = FALSE, model = c("additive", "dominant", "recessive")) 
fastGxG(mat.snp, model = c("additive", "dominant", "recessive"),  genes = NULL, interval = c(-10, 10), tol = 10^-8, maxiter = 1000,  size = 20) 
fastGxGrec(mat.snp, genes = NULL, size = 20)

Arguments

snp1, snp2

numeric vectors of length $3 * t$ representing two SNPs genotyped at $t$ trios. Each of the $t$ blocks (i.e. snp1[1:3], snp1[4:6], ..., and snp2[1:3], snp2[4:6], ...) must consist of the genotypes of father, mother, and offspring (in this order). The genotypes must be coded by 0, 1, and 2. Missing values are allowed and need to be coded by NA. The vectors must thus have the same structure as the output of trio.check, or the genotype example data sets such as trio.gen1 (see data(trio.gen1)), and can be generated from a ped-file by, e.g., employing ped2geno.

mat.snp

a numeric matrix in which each column represents a SNP. Each of the SNPs must have the same structure as snp, and can, e.g., be generated from a ped-file by employing ped2geno.

test

character string naming the GxG test that should be performed. If test = "epistatic", then a conditional logistic regression version of the test proposed by Cordell (2002) is used to test for epistatistical interactions. If test = "full", a conditional logistic regression model containing one parameter for each SNP and one parameter for the interaction of these two SNPs will be fitted and a Wald test for the interaction term will be performed, where a genetic model specified by model is assumed for both SNPs. If test = "lrt", a likelihood ratio test is performed comparing the fit of this model with the fit of a conditional logistic regression model only containing the two parameters for the main effects of the SNPs. If test = "screen", a conditional logistic regression model only composed of one parameter for the interaction of the two SNPs will be fitted and a Wald test will be performed, where the genetic model specified by model is assumed for both SNPs.

genes

a character vector containing the names of the genes to which the SNPs belong. If specified, only the two-way interactions between SNPs from different genes are tested. If NULL, all two-way interactions between all possible pairs of SNPs are tested.

maf

logical indicating whether the minor allele frequency (computed by considering the genotypes of only the parents) should be added to the output.

model

type of model that should be considered. Abbreviations are allowed. Thus, e.g., model = "dom" will consider a dominant model for each of the respective two SNPs, and model = "r" an recessive model. Ignored if epistatic = TRUE.

interval

the end-points of the interval to be searched for the root. For details, see uniroot.

tol

the desired accuracy/convergence tolerance. For details, see uniroot.

maxiter

the maximum number of iterations. For details, see uniroot.

size

the number of interactions considered simultaneously when computing the parameter estimates.

Value

Depending on test, the output contains statistics and p-values either of a likelihood ratio test (test = "epistatic" or test = "lrt") or the Wald statistics and the corresponding p-values for the interaction term in the conditional logistic regression model (test = "full" or test = "screen"). If maf = TRUE, a vector maf containing the minor allele frequencies of each SNP and a matrix mat.maf with two columns containing the SNP-wise minor allele frequencies for each tested pair of SNPs are added to the output of colGxG.

References

Cordell, H. J. (2002). Epistasis: What it Means, what it Doesn't mean, and Statistical Methods to Detect it in Humans. Human Molecular Genetics, 11, 2463-2468.

Schwender, H., Taub, M.A., Beaty, T.H., Marazita, M.L., and Ruczinski, I. (2011). Rapid Testing of SNPs and Gene-Environment Interactions in Case-Parent Trio Data Based on Exact Analytic Parameter Estimation. Biometrics, 68, 766-773.

Examples

Run this code

# Load the simulated data.
data(trio.data)

# The interaction between a particular pair of SNPs
# (e.g., the ones in the first and second column of 
# mat.test) can be tested by
gxg.out <- tdtGxG(mat.test[,1], mat.test[,2])

# All pairs of SNPs in mat.test can be tested by
gxg.out2 <- colGxG(mat.test)

# By default, Cordell's likelihood ratio test for
# epistatistic interactions is used. This is the
# most sophisticated, but also most time-consuming
# test. If another test, e.g., the one considering
# a conditional logistic regression model only
# containing a term for the interaction, should
# be used, then this can be done by
gxg.out3 <- colGxG(mat.test, test = "screen")

# In this case, different modes of inheritance can
# be considered (by default, the additive mode is
# considered). If a dominant model (for both SNPs)
# should be tested, this can be done by
gxg.out4 <- colGxG(mat.test, test = "screen", model ="dom")

# If just a subset of all pairs of SNPs should be 
# tested, e.g., only pairs of SNPs belonging to different
# genes, then this can be done by first specifying a
# vector specifying which SNP belongs to which genes.
# If we, e.g., assume that the first two SNPs in mat.test 
# belong to gene G1 and the other four SNPs to G2, then
# this vector can be specified by
genes <- paste("G", rep(1:2, c(2,4)), sep="")

# and only the pairs of SNPs in which the two SNPs belong
# to different genes can be tested with Cordell's 
# likelihood ratio test by
gxg.out5 <- colGxG(mat.test, genes = genes)