| Title: | Adaptive Association Tests for Multiple Phenotypes using Generalized Estimating Equations (GEE) |
|---|---|
| Description: | Provides adaptive association tests for SNP level, gene level and pathway level analyses. |
| Authors: | Junghi Kim and Wei Pan |
| Maintainer: | Junghi Kim <[email protected]> |
| License: | GNU General Public License (>= 3) |
| Version: | 1.0.2 |
| Built: | 2024-11-12 06:29:20 UTC |
| Source: | CRAN |
Provides adaptive association tests for SNP level, gene level and pathway level analyses.
Functions for adaptive association tests including GEEaSPU, GEEaSPUset and GEEaSPUpath. These methods use a weighting scheme for testing associations with multiple phenotypes. GEEaSPU function computes a SNP level p value; GEEaSPUset function can be used for the SNP-set (gene) level association test, while GEEaSPUpath function is for the gene-set (pathway) level analysis.
Junghi Kim and Wei Pan
Kim J, Zhang Y, and Pan W (2016). "Powerful and adaptive testing for multi-trait and multi-SNP associations with GWAS and sequencing data." Genetics 203(2), 715–731.
Zhang Y, Xu Z, Shen, X and Pan W (2014). "Testing for association with multiple traits in generalized estimation equations, with application to neuroimaging data." NeuroImage 96, 309–325.
Tests whether a SNP is associated with multivariate outcomes; provides a series of p-values of GEE-SPU(pow) and GEE-aSPU tests.
GEEaSPU(pheno, geno, Z = NULL, model = "gaussian", corstr = "independence", pow = c(1:8, Inf), n.perm = 1000, null.type = "perm", score.test = FALSE)GEEaSPU(pheno, geno, Z = NULL, model = "gaussian", corstr = "independence", pow = c(1:8, Inf), n.perm = 1000, null.type = "perm", score.test = FALSE)
pheno |
a numeric phenotype matrix with each row as a different individual and each column as a separate phenotype. |
geno |
a numeric vector with each element for an individual genotype. |
Z |
a numeric covariate matrix with each row as a different individual and each column as a covariated to be adjested. |
model |
a character string specifying the model of the phenotypes. Models supported are "gaussian" for a quantitative trait and "binomial" for a binary trait (default = "gaussian"). |
corstr |
a character string specifying the correlation structure of phenotypes. The following are permitted: "independence", "fixed", "stat_M_dep", "non_stat_M_dep", "exchangeable", "AR-M" and "unstructured" (default = "independence"). |
pow |
a vector of the power weight to be used at a trait level (default = c(1:8, Inf)). |
n.perm |
a numeric value of number of null statistics (default = 1000). |
null.type |
a character string specifying how to generate null statistics; "perm" is used when null statistics are generated using permutations and "sim" is used when null statistics are generated using simulations (default = "perm"). |
score.test |
a logical value indicating whether to include GEEaSPU-Score test along with GEE-Score test (default = FALSE). If TRUE, it computes p-values of GEEaSPU-Score and GEE-Score as well as GEEaSPU test. |
Adaptive association tests for single SNP and multiple phenotypes using GEE.
a vector of p-values from GEE-SPU(pow) tests and GEE-aSPU test.
When large SNP-set (namely large gene size) or large number of phenotypes are included, the permuation based test (null.type = "perm") is recommended.
An option "binomial" model only supports the option, null.type = "sim".
Junghi Kim and Wei Pan
Kim J, Zhang Y, and Pan W (2016). "Powerful and adaptive testing for multi-trait and multi-SNP associations with GWAS and sequencing data." Genetics 203(2), 715–731.
Zhang Y, Xu Z, Shen, X and Pan W (2014). "Testing for association with multiple traits in generalized estimation equations, with application to neuroimaging data." NeuroImage, 96, 309–325.
# -- simulating phenotypes # -- n.subjects: number of subjects # -- n.traits: number of phenotypes # -- Sigma: covariance matrix of phenotypes (e.g. AR(1)) set.seed(136) n.subjects <- 100 n.traits <- 3 sigma <- 2; rho <- 0.5 Sigma0 <- diag(n.traits); Sigma <- sigma * rho^abs(row(Sigma0) - col(Sigma0)) eS <- eigen(Sigma, symmetric = TRUE) ev <- eS$values X <- matrix(rnorm(n.traits * n.subjects), n.subjects) pheno <- X %*% diag(sqrt(pmax(ev, 0)), ncol(Sigma)) %*% eS$vectors # -- simulating genotype geno <- rbinom(n = n.subjects, size = 2, prob = 0.2) # -- Computing the p-value of GEEaSPU test with the permutation based method Pvl <- GEEaSPU(pheno = pheno, geno = geno, Z = NULL, pow = c(1,2,4,Inf), n.perm = 1000, null.type = "perm", score.test = FALSE) # -- Each element of Pvl is a p value of GEE-SPU(pow) in order # -- The last element of Pvl is a p value of GEE-aSPU test Pvl Pvl[length(Pvl)] # > Pvl # SPU.1 SPU.2 SPU.4 SPU.Inf aSPU # 0.1890000 0.4070000 0.3520000 0.3040000 0.2917083 # > Pvl[length(Pvl)] # aSPU # 0.2917083# -- simulating phenotypes # -- n.subjects: number of subjects # -- n.traits: number of phenotypes # -- Sigma: covariance matrix of phenotypes (e.g. AR(1)) set.seed(136) n.subjects <- 100 n.traits <- 3 sigma <- 2; rho <- 0.5 Sigma0 <- diag(n.traits); Sigma <- sigma * rho^abs(row(Sigma0) - col(Sigma0)) eS <- eigen(Sigma, symmetric = TRUE) ev <- eS$values X <- matrix(rnorm(n.traits * n.subjects), n.subjects) pheno <- X %*% diag(sqrt(pmax(ev, 0)), ncol(Sigma)) %*% eS$vectors # -- simulating genotype geno <- rbinom(n = n.subjects, size = 2, prob = 0.2) # -- Computing the p-value of GEEaSPU test with the permutation based method Pvl <- GEEaSPU(pheno = pheno, geno = geno, Z = NULL, pow = c(1,2,4,Inf), n.perm = 1000, null.type = "perm", score.test = FALSE) # -- Each element of Pvl is a p value of GEE-SPU(pow) in order # -- The last element of Pvl is a p value of GEE-aSPU test Pvl Pvl[length(Pvl)] # > Pvl # SPU.1 SPU.2 SPU.4 SPU.Inf aSPU # 0.1890000 0.4070000 0.3520000 0.3040000 0.2917083 # > Pvl[length(Pvl)] # aSPU # 0.2917083
Tests whether gene-set (pathway) is associated with multivariate outcomes; provides a series of p-values of GEE-SPU(pow, pow2, pow3) and GEEaSPUpath tests.
GEEaSPUpath(pheno, geno, nSNPs, Z = NULL, corstr = "independence", pow = c(1,2,4,8), pow2 = c(1,2,4,8), pow3 = c(1,2,4,8), n.perm = 1000)GEEaSPUpath(pheno, geno, nSNPs, Z = NULL, corstr = "independence", pow = c(1,2,4,8), pow2 = c(1,2,4,8), pow3 = c(1,2,4,8), n.perm = 1000)
pheno |
a numeric phenotype matrix with each row as a different individual and each column as a separate phenotype. |
geno |
a numeric genotype matrix with each row as a different individual and each column as a snp; the SNPs (with the number stored in nSNPs) from one gene are stored consecutively from the first gene. |
nSNPs |
A numeric vector, whose length matches to the total number of genes; each element of vector indicate the number of SNPs in each gene. |
Z |
a numeric covariate matrix with each row as a different individual and each column as a covariated to be adjested. |
corstr |
a character string specifying the correlation structure of phenotypes. The following are permitted: "independence", "fixed", "stat_M_dep", "non_stat_M_dep", "exchangeable", "AR-M" and "unstructured" (default = "independence"). |
pow |
a vector of the power weight to be used at a SNP level (default = c(1,2,4,8)). |
pow2 |
a vector of the power weight to be used at a trait level (default = c(1,2,4,8)). |
pow3 |
a vector of the power weight to be used at a gene level (default = c(1,2,4,8)). |
n.perm |
a numeric value of number of null statistics (default = 1000). |
Adaptive association tests for gene-set (pathway) and multiple phenotypes using GEE.
a vector of p-values from GEE-SPU(pow, pow2, pow3) tests and GEE-aSPUpath test.
GEEaSPUpath function only supports a case for a quantitative trait (model = "gaussian") and a permutation based test (null.type = "perm").
Junghi Kim and Wei Pan
Kim J, Zhang Y, and Pan W (2016). "Powerful and adaptive testing for multi-trait and multi-SNP associations with GWAS and sequencing data." Genetics, 203(2), 715–731.
# -- simulating phenotypes # -- n.subjects: number of subjects # -- n.traits: number of phenotypes # -- Sigma: covariance matrix of phenotypes (e.g. AR(1)) set.seed(136) n.subjects <- 100 n.traits <- 3 sigma <- 2; rho <- 0.5 Sigma0 <- diag(n.traits) Sigma <- sigma * rho^abs(row(Sigma0) - col(Sigma0)) eS <- eigen(Sigma, symmetric = TRUE) ev <- eS$values X <- matrix(rnorm(n.subjects * n.traits), n.subjects) pheno <- X %*% diag(sqrt(pmax(ev, 0)), ncol(Sigma)) %*% eS$vectors # -- simulating genotype # -- Assume we have two genes each of which has 3 and 5 SNPs respectively. # -- n.geno1: number of SNPs included in the gene1 # -- n.geno2: number of SNPs included in the gene2 # -- nSNPs <- c(3,5) n.geno1 <- 3 n.geno2 <- 5 maf1 <- 0.2 maf2 <- 0.4 gene1 <- matrix(rbinom(n = n.subjects*n.geno1, size = 2, prob = maf1), ncol = n.geno1) gene2 <- matrix(rbinom(n = n.subjects*n.geno2, size = 2, prob = maf2), ncol = n.geno2) geno <- cbind(gene1, gene2) # -- Computing the p-value of GEEaSPUpath test Pvl <- GEEaSPUpath(pheno = pheno, geno = geno, nSNPs = c(3,5), Z = NULL, corstr = "independence", pow = c(1,4,8), pow2 = c(1,4,8), pow3 = c(1,4,8), n.perm = 1000) # -- Each element of Pvl is a p value of GEE-SPU(pow,pow2,pow3) in order # -- The last element of Pvl is a p value of GEE-aSPUpath test Pvl Pvl[length(Pvl)] # > Pvl # SPU.1.1.1 SPU.1.1.4 SPU.1.1.8 SPU.1.4.1 SPU.1.4.4 SPU.1.4.8 SPU.1.8.1 SPU.1.8.4 # 0.00900000 0.05600000 0.07000000 0.06200000 0.08300000 0.11200000 0.06100000 0.08200000 # SPU.1.8.8 SPU.4.1.1 SPU.4.1.4 SPU.4.1.8 SPU.4.4.1 SPU.4.4.4 SPU.4.4.8 SPU.4.8.1 # 0.10600000 0.58100000 0.54300000 0.49200000 0.62400000 0.64000000 0.62700000 0.64900000 # SPU.4.8.4 SPU.4.8.8 SPU.8.1.1 SPU.8.1.4 SPU.8.1.8 SPU.8.4.1 SPU.8.4.4 SPU.8.4.8 # 0.67100000 0.67500000 0.58300000 0.53700000 0.48100000 0.63400000 0.64600000 0.63800000 # SPU.8.8.1 SPU.8.8.4 SPU.8.8.8 aSPUpath # 0.66000000 0.68100000 0.67900000 0.04395604 # > Pvl[length(Pvl)] # aSPUpath # 0.04395604# -- simulating phenotypes # -- n.subjects: number of subjects # -- n.traits: number of phenotypes # -- Sigma: covariance matrix of phenotypes (e.g. AR(1)) set.seed(136) n.subjects <- 100 n.traits <- 3 sigma <- 2; rho <- 0.5 Sigma0 <- diag(n.traits) Sigma <- sigma * rho^abs(row(Sigma0) - col(Sigma0)) eS <- eigen(Sigma, symmetric = TRUE) ev <- eS$values X <- matrix(rnorm(n.subjects * n.traits), n.subjects) pheno <- X %*% diag(sqrt(pmax(ev, 0)), ncol(Sigma)) %*% eS$vectors # -- simulating genotype # -- Assume we have two genes each of which has 3 and 5 SNPs respectively. # -- n.geno1: number of SNPs included in the gene1 # -- n.geno2: number of SNPs included in the gene2 # -- nSNPs <- c(3,5) n.geno1 <- 3 n.geno2 <- 5 maf1 <- 0.2 maf2 <- 0.4 gene1 <- matrix(rbinom(n = n.subjects*n.geno1, size = 2, prob = maf1), ncol = n.geno1) gene2 <- matrix(rbinom(n = n.subjects*n.geno2, size = 2, prob = maf2), ncol = n.geno2) geno <- cbind(gene1, gene2) # -- Computing the p-value of GEEaSPUpath test Pvl <- GEEaSPUpath(pheno = pheno, geno = geno, nSNPs = c(3,5), Z = NULL, corstr = "independence", pow = c(1,4,8), pow2 = c(1,4,8), pow3 = c(1,4,8), n.perm = 1000) # -- Each element of Pvl is a p value of GEE-SPU(pow,pow2,pow3) in order # -- The last element of Pvl is a p value of GEE-aSPUpath test Pvl Pvl[length(Pvl)] # > Pvl # SPU.1.1.1 SPU.1.1.4 SPU.1.1.8 SPU.1.4.1 SPU.1.4.4 SPU.1.4.8 SPU.1.8.1 SPU.1.8.4 # 0.00900000 0.05600000 0.07000000 0.06200000 0.08300000 0.11200000 0.06100000 0.08200000 # SPU.1.8.8 SPU.4.1.1 SPU.4.1.4 SPU.4.1.8 SPU.4.4.1 SPU.4.4.4 SPU.4.4.8 SPU.4.8.1 # 0.10600000 0.58100000 0.54300000 0.49200000 0.62400000 0.64000000 0.62700000 0.64900000 # SPU.4.8.4 SPU.4.8.8 SPU.8.1.1 SPU.8.1.4 SPU.8.1.8 SPU.8.4.1 SPU.8.4.4 SPU.8.4.8 # 0.67100000 0.67500000 0.58300000 0.53700000 0.48100000 0.63400000 0.64600000 0.63800000 # SPU.8.8.1 SPU.8.8.4 SPU.8.8.8 aSPUpath # 0.66000000 0.68100000 0.67900000 0.04395604 # > Pvl[length(Pvl)] # aSPUpath # 0.04395604
Tests whether SNP-set (gene) is associated with multivariate outcomes; provides a series of p-values of GEE-SPU(pow, pow2) and GEEaSPUset tests.
GEEaSPUset(pheno, geno, Z = NULL, model = "gaussian", corstr = "independence", pow = c(1,2,4,8), pow2 = c(1,2,4,8), n.perm = 1000, null.type = "perm", score.test = FALSE)GEEaSPUset(pheno, geno, Z = NULL, model = "gaussian", corstr = "independence", pow = c(1,2,4,8), pow2 = c(1,2,4,8), n.perm = 1000, null.type = "perm", score.test = FALSE)
pheno |
a numeric phenotype matrix with each row as a different individual and each column as a separate phenotype. |
geno |
a numeric genotype matrix with each row as a different individual and each column as a snp. |
Z |
a numeric covariate matrix with each row as a different individual and each column as a covariated to be adjested. |
model |
a character string specifying the model of the phenotypes. Models supported are "gaussian" for a quantitative trait and "binomial" for a binary trait (default = "gaussian"). |
corstr |
a character string specifying the correlation structure of phenotypes. The following are permitted: "independence", "fixed", "stat_M_dep", "non_stat_M_dep", "exchangeable", "AR-M" and "unstructured" (default = "independence"). |
pow |
a vector of the power weight to be used at a SNP level (default = c(1,2,4,8)). |
pow2 |
a vector of the power weight to be used at a trait level (default = c(1,2,4,8)). |
n.perm |
a numeric value of number of null statistics (default = 1000). |
null.type |
a character string specifying how to generate null statistics; "perm" is used when null statistics are generated using permutations and "sim" is used when null statistics are generated using simulations (default = "perm"). |
score.test |
a logical value indicating whether to include GEEaSPU-Score test along with GEE-Score test (default = FALSE). If TRUE, it computes p-values of GEEaSPU-Score and GEE-Score as well as GEEaSPU test. |
Adaptive association tests for SNP-set (gene) and multiple phenotypes using GEE.
a vector of p-values from GEE-SPU(pow, pow2) tests and GEE-aSPUset test.
When large SNP-set (namely large gene size) or large number of phenotypes are included, the permuation based test (null.type = "perm") is recommended.
An option "binomial" model only supports the option, null.type="sim".
Junghi Kim and Wei Pan
Kim J, Zhang Y, and Pan W (2016). "Powerful and adaptive testing for multi-trait and multi-SNP associations with GWAS and sequencing data." Genetics, 203(2), 715–731.
# -- simulating phenotypes # -- n.subjects: number of subjects # -- n.traits: number of phenotypes # -- Sigma: covariance matrix of phenotypes (e.g. AR(1)) set.seed(136) n.subjects <- 100 n.traits <- 3 sigma <- 2; rho <- 0.5 Sigma0 <- diag(n.traits); Sigma <- sigma * rho^abs(row(Sigma0) - col(Sigma0)) eS <- eigen(Sigma, symmetric = TRUE) ev <- eS$values X <- matrix(rnorm(n.subjects * n.traits), n.subjects) pheno <- X %*% diag(sqrt(pmax(ev, 0)), ncol(Sigma)) %*% eS$vectors # -- simulating genotype # -- n.geno: number of SNPs included in the SNP set/gene n.geno <- 3 maf <- 0.2 geno <- matrix(rbinom(n = n.subjects * n.geno, size = 2, prob = maf), ncol = n.geno) # -- Computing the p-value of GEEaSPUpath test with the permutation based method Pvl <- GEEaSPUset(pheno = pheno, geno = geno, Z = NULL, model = "gaussian", corstr = "independence", pow = c(1,4,Inf), pow2 = c(1,4,Inf), n.perm = 1000, null.type = "perm", score.test = FALSE) # -- Each element of Pvl is a p value of GEE-SPU(pow,pow2) in order # -- The last element of Pvl is a p value of GEE-aSPUset test Pvl Pvl[length(Pvl)] # > Pvl # SPU.1.1 SPU.1.4 SPU.1.Inf SPU.4.1 SPU.4.4 SPU.4.Inf SPU.Inf.1 # 0.01400000 0.08800000 0.07200000 0.53000000 0.41000000 0.32100000 0.55100000 # SPU.Inf.4 SPU.Inf.Inf aSPUset # 0.48700000 0.41000000 0.04095904 # > Pvl[length(Pvl)] # aSPUset # 0.04095904# -- simulating phenotypes # -- n.subjects: number of subjects # -- n.traits: number of phenotypes # -- Sigma: covariance matrix of phenotypes (e.g. AR(1)) set.seed(136) n.subjects <- 100 n.traits <- 3 sigma <- 2; rho <- 0.5 Sigma0 <- diag(n.traits); Sigma <- sigma * rho^abs(row(Sigma0) - col(Sigma0)) eS <- eigen(Sigma, symmetric = TRUE) ev <- eS$values X <- matrix(rnorm(n.subjects * n.traits), n.subjects) pheno <- X %*% diag(sqrt(pmax(ev, 0)), ncol(Sigma)) %*% eS$vectors # -- simulating genotype # -- n.geno: number of SNPs included in the SNP set/gene n.geno <- 3 maf <- 0.2 geno <- matrix(rbinom(n = n.subjects * n.geno, size = 2, prob = maf), ncol = n.geno) # -- Computing the p-value of GEEaSPUpath test with the permutation based method Pvl <- GEEaSPUset(pheno = pheno, geno = geno, Z = NULL, model = "gaussian", corstr = "independence", pow = c(1,4,Inf), pow2 = c(1,4,Inf), n.perm = 1000, null.type = "perm", score.test = FALSE) # -- Each element of Pvl is a p value of GEE-SPU(pow,pow2) in order # -- The last element of Pvl is a p value of GEE-aSPUset test Pvl Pvl[length(Pvl)] # > Pvl # SPU.1.1 SPU.1.4 SPU.1.Inf SPU.4.1 SPU.4.4 SPU.4.Inf SPU.Inf.1 # 0.01400000 0.08800000 0.07200000 0.53000000 0.41000000 0.32100000 0.55100000 # SPU.Inf.4 SPU.Inf.Inf aSPUset # 0.48700000 0.41000000 0.04095904 # > Pvl[length(Pvl)] # aSPUset # 0.04095904