# Location (mean-based association) test This function takes as input the genotype of SNPs (`GENO`), the SEX (`SEX`), and a quantitative trait (`Y`) in a sample population, and possibly additional covariates, such as principal components. The function returns the location association **p**-values for each SNP. ```r locReg( GENO, Y, SEX = NULL, COVAR = NULL, Xchr = FALSE, XchrMethod = 3, transformed = FALSE, related = FALSE, cov.structure = "corCompSymm", clust = NULL ) ``` ## Arguments - `GENO`: a list of a genotype matrix/vector of SNPs, must contain values 0, 1, 2's coded for the number of reference allele. Alternatively, for imputed genotypes, it could either be a vector of dosage values between 0 and 2, or a list of matrix of genotype probabilities, numerically between 0 and 1 for each genotype. The length/dimension of `GENO` should match that of `Y`, and/or `SEX` and `COVAR`. - `Y`: a numeric vector of quantitative trait, such as human height. - `SEX`: the genetic sex of individuals in the sample population, must be a vector of 1's and 2's following PLINK default coding, where males are coded as 1 and females 2. Optional for analysis of autosomal SNPs, but required for X-chromosome. - `COVAR`: optional: a vector or a matrix of covariates, such as age or principal components. - `Xchr`: a logical indicator for whether the analysis is for X-chromosome SNPs, if `TRUE` then the following association testing model is used: Y~G+G_D+S+GxS; with p-value given by comparing Y~G+S+GxS vs. Y~S (G is the additive coded genotype; G_D is an indicator for female heterozygotes). - `XchrMethod`: an integer taking values 0 (reports all models), 1.1, 1.2, 2, 3, for the choice of X-chromosome association testing models: model 1,1: Y~G (females only) model 1.2: Y~G (males only) model 2: Y~G+S+GxSex; with p-value given by comparing Y~G+Sex+GxSex vs. Y~Sex (the additively coded G is robust to X-chromosome inactivation uncertainty). This is also the option for dosage genotypes. model 3 (recommended): Y~G+G_D+S+GxSex; with p-value given by comparing Y ~ G+G_D+Sex+GxSex vs. Y ~ Sex (G_D is an indicator for female heterozygotes, this model is robust to X-chromosome inactivation uncertainty and skewed inactivation). For imputed data in the form of genotypic probabilities, the model becomes: Y ~ G1 + G2 + G1xSex + Sex, where G1 and G2 are the genotypic probabilities for the heterozygote and alternative allele homozygote. - `transformed`: a logical indicating whether the quantitative response `Y` should be transformed using a rank-based method to resemble a normal distribution; recommended for traits with non-symmetric distribution. The default option is `FALSE`. - `related`: optional: a logical indicating whether the samples should be treated as related; if `TRUE` while no relatedness covariance information is given, it is then estimated under a `cov.structure` and assumes this structure among all within-group errors pertaining to the same pair/cluster if specified using `clust`. This option currently only applies to autosomal SNPs. - `cov.structure`: optional: should be one of standard classes of correlation structures listed in `corClasses` from `R` package `nlme`. See `?corClasses`. The most commonly used option is `corCompSymm` for a compound symmetric correlation structure. This option currently only applies to autosomal SNPs. - `clust`: optional: a factor indicating the grouping of samples; it should have at least two distinct values. It could be the family ID (FID) for family studies. This option currently only applies to autosomal SNPs. ## Returns a vector of location association **p**-values for each SNP. ## Note The choice to use a rank-based inverse normal transformation is left to the user's discretion. See XXX for a discussion on the pros and cons of quantile transformation with respect to location association. For X-chromosome markers, when the samples consist entirely of females or males, we report only results from model 1, regardless of the `XchrMethod` option. ## Examples ```r N <- 100 genDAT <- rbinom(N, 2, 0.3) sex <- rbinom(N, 1, 0.5)+1 y <- rnorm(N) COVAR <- matrix(rnorm(N*10), ncol=10) locReg(GENO=genDAT, SEX=sex, Y=y, COVAR=COVAR) # correlated example: library("MASS") yy <- mvrnorm(1, mu= rep(0, N), Sigma = matrix(0.3, N, N) + diag(0.7, N)) locReg(GENO=list("SNP1"= genDAT, "SNP2" = genDAT[sample(1:100)]), SEX=sex, Y=as.numeric(yy), COVAR=COVAR, related = TRUE, clust = rep(1, 100)) # sibpair example: pairedY <- mvrnorm(N/2,rep(0,2),matrix(c(1,0.2,0.2,1), 2)) yy <- c(pairedY[,1], pairedY[,2]) locReg(GENO=list("SNP1"= genDAT, "SNP2" = genDAT[sample(1:100)]), SEX=sex, Y=as.numeric(yy), COVAR=COVAR, related = TRUE, clust = rep(c(1:50), 2)) # Xchr data example: genDAT1 <- rep(NA, N) genDAT1[sex==1] <- rbinom(sum(sex==1), 1, 0.5) genDAT1[sex==2] <-rbinom(sum(sex==2), 2, 0.5) locReg(GENO=genDAT1, SEX=sex, Y=y, COVAR=COVAR, Xchr=TRUE) ``` ## References Chen B, Craiu RV, Sun L. (2020) Bayesian model averaging for the X-chromosome inactivation dilemma in genetic association study. **Biostatistics**. 21 (2):319-335. tools:::Rd_expr_doi("10.1093/biostatistics/kxy049") . PMID: 30247537. Chen B, Craiu RV, Strug LJ, Sun L. (2021) The X factor: A robust and powerful approach to X-chromosome-inclusive whole-genome association studies. **Genetic Epidemiology**. tools:::Rd_expr_doi("10.1002/gepi.22422") . PMID: 34224641. ## Author(s) Wei Q. Deng deng@utstat.toronto.edu , Lei Sun sun@utstat.toronto.edu

locReg function