GiMat

This is an R package for testing the multiple phenotype associatin with gene-by-gene (GxG) interactions, which accounts for the relationship among the causal interaction effects on each of the phenotypes.

System requirements

GiMat could be installed with ease on versions of R > 4.0.2.

Installation

Before installing R package of GiMat, the following packages from CRAN are required:

install.packages("CompQuadForm")
install.packages("SKAT")
install.packages("copula")
install.packages("stats")

You can install the GitHub version of GiMat:

# install.packages("devtools")
devtools::install_github("SiruRooney/GiMat")

Example

Here's an example workflow using GiMat:

Data Preparation

First, prepare multiple dichotomous phenotypes and the common variant sets that are used for testing gene-by-gene interaction associations with these phenotypes. GiMat R package provides an example.

library(GiMat)
#> Warning: replacing previous import 'copula::profile' by 'stats::profile' when
#> loading 'GiMat'
#> Warning: replacing previous import 'copula::logLik' by 'stats::logLik' when
#> loading 'GiMat'
#> Warning: replacing previous import 'copula::confint' by 'stats::confint' when
#> loading 'GiMat'
#> Warning: replacing previous import 'copula::coef' by 'stats::coef' when loading
#> 'GiMat'

summary(Covariates)
#     sex              age       
# Min.   :0.0000   Min.   :38.58  
# 1st Qu.:0.0000   1st Qu.:45.99  
# Median :0.0000   Median :48.02  
# Mean   :0.4794   Mean   :48.03  
# 3rd Qu.:1.0000   3rd Qu.:50.05  
# Max.   :1.0000   Max.   :57.82 
apply(cbind(pheno1,pheno2),2,table)
#    pheno1          pheno2      
#0    4015            4011
#1    985             989

table(geno1)
#geno1
#   0    1    2 
# 6029 3310  661
table(geno2)
#geno2
#    0     1     2 
# 18525  5294  1181 

Then we construct the different kernels for modelling the phenotype covariates.

Y_mat=cbind(pheno1,pheno2)
# Heterogeneous (Het) kernel
Sigma_het=diag(2)
# Homogeneous (Hom) kernel
Sigma_hom=matrix(1,nrow=2,ncol=2)
# Phenotype covariance (PhC) kernel
Sigma_phc=binary_cov_matrix(Y_mat)
# Gene association with multi-trait (GAM) kernel
Sigma_gam=binary_cov_matrix(Y_mat)^2

Running

In this example, we assume that the genetic variants, geno1 and geno2, are not associated with both phenotypes but the gene-by-gene interactions are associated with phenotypes.

We conduct the null model under the null hypothesis that the gene-by-gene interactions have no effects on the phenotypes.

Inputted data for MPiG_SKAT_Null function

• Y_mat: Phenotype matrix. Each column refers to one dichotomous phenotype.

• X: Covariates including age, sex, PCs.

• G1: The first genotype matrix. Each column refers to one variant.

• G2: The second genotype matrix. Each column refers to one variant. By default, G2 is NULL.

• D: The environmental exposure. If we test the gene-by-env interactions associated with the environmental exposure, we input the individual-level environmental exposure and set G2 as NULL. By default, D is NULL.

• iG_with: An indicator which represents the gene-by-gene interactions or gene-by-env interactions. iG_with is set to "G" for gene-by-gene and "D" for gene-by-env. By default, iG_with is set to "G".

out<-MPiG_SKAT_Null(Y_mat,X=Covariates,G1=NULL,G2=NULL,D=NULL,iG_with="G")

Then we conduct the gene-by-gene interaction association tests under different kernel assumptions.

Inputted data for MPiG_SKAT_Fast_robust function

There are additional options in MPiG_SKAT_Fast_robust function except some overlapping inputted options appearing in MPiG_SKAT_Null function.

• W: The explainable variables in the null model. It contains intercept, covariates and genotype matrix (if the main genetic effects exist) and environment matrix (if main environmental effects exist).

• model: The complete output from the null model.

• res_model: Residuals under the null model.

• phi_model: Variance under the null model.

• mu_model: The fitted values (means) under the null model.

• Sigma_p: Phenotype covariance kernel.

• Is.Common: To indicate the variants are common or rare. If variants are common, Is.Common is TRUE. The current version is restricted to common variant interactions.

• weights_beta, weights_G and weights_V: The weights for allelic effect, variants and interactions. These options are applicable for gene-by-env interaction association tests. The current version is restricted to common variant interactions.

• impute.method: The imputed method for imputting missing values of the variants. By default, impute.method is set to "fixed".

• missing_cutoff: The threshold for variants having missing values. By default,missing_cutoff=0.15.

• max_MAF: The maximum of MAF. By default, max_MAF=0.5.

#Under heterogeneous (Het) kernel assumption
Gimat.het=MPiG_SKAT_Fast_robust(Y_mat,X=Covariates,G1=geno1,G2=geno2,D=NULL,W=out$W,model=out$model,res_model=out$res_model,phi_model=out$phi_model,mu_model=out$mu_model,Sigma_p=Sigma_het,iG_with="G",Is.Common=TRUE,weights_beta=c(1,25),weights_G=NULL,weights_V=NULL,impute.method="fixed",missing_cutoff=0.15,max_MAF=0.5)

#Under homogeneous (Hom) kernel assumption
Gimat.hom=MPiG_SKAT_Fast_robust(Y_mat,X=Covariates,G1=geno1,G2=geno2,D=NULL,W=out$W,model=out$model,res_model=out$res_model,phi_model=out$phi_model,mu_model=out$mu_model,Sigma_p=Sigma_hom,iG_with="G",Is.Common=TRUE,weights_beta=c(1,25),weights_G=NULL,weights_V=NULL,impute.method="fixed",missing_cutoff=0.15,max_MAF=0.5)

#Under the phenotype covariance (phc) kernel assumption
Gimat.phc=MPiG_SKAT_Fast_robust(Y_mat,X=Covariates,G1=geno1,G2=geno2,D=NULL,W=out$W,model=out$model,res_model=out$res_model,phi_model=out$phi_model,mu_model=out$mu_model,Sigma_p=Sigma_phc,iG_with="G",Is.Common=TRUE,weights_beta=c(1,25),weights_G=NULL,weights_V=NULL,impute.method="fixed",missing_cutoff=0.15,max_MAF=0.5)

#Under the gene association with multi-trait (GAM) kernel
Gimat.gam=MPiG_SKAT_Fast_robust(Y_mat,X=Covariates,G1=geno1,G2=geno2,D=NULL,W=out$W,model=out$model,res_model=out$res_model,phi_model=out$phi_model,mu_model=out$mu_model,Sigma_p=Sigma_gam,iG_with="G",Is.Common=TRUE,weights_beta=c(1,25),weights_G=NULL,weights_V=NULL,impute.method="fixed",missing_cutoff=0.15,max_MAF=0.5)

#Minimum P value‐based omnibus kernel tests

obj.list=list(Gimat.het,Gimat.hom,Gimat.phc,Gimat.gam)
#Extract the gene-by-gene or gene-by-env interactions
out.iG=MPiG_MAIN_Check_Z(G1=geno1,G2=geno2,D=NULL,nrow_G=NROW(geno1),iG_with="G",impute.method="fixed",missing_cutoff=0.15,max_MAF=0.5)

iG=out.iG$V
Gimat.minP=MPiG_minP_base(n.pheno=NCOL(Y_mat),n=NROW(Y_mat),res_model=out$res_model,obj.list=obj.list,Z1=iG,X=covariates, resample = 200)

Contact

We are very grateful to any questions, comments, or bugs reports; and please contact Siru Wang