# An adaptive sum of powered score (SPU) test for SNP-set (gene) and mutiple phenotypes Tests whether SNP-set (gene) is associated with multivariate outcomes; provides a series of p-values of GEE-SPU(pow, pow2) and GEEaSPUset tests. ```r 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) ``` ## Arguments - `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. ## Details Adaptive association tests for SNP-set (gene) and multiple phenotypes using GEE. ## Returns a vector of p-values from GEE-SPU(pow, pow2) tests and GEE-aSPUset test. ## References 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. ## Author(s) Junghi Kim and Wei Pan ## Note 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". ## Examples ```r # -- 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 ```

GEEaSPUset function