Title: A Generalized Joint Location and Scale Framework for Association Testing
Version: 0.2.0
Description: An update to the Joint Location-Scale (JLS) testing framework that identifies associated SNPs, gene-sets and pathways with main and/or interaction effects on quantitative traits (Soave et al., 2015; <doi:10.1016/j.ajhg.2015.05.015>). The JLS method simultaneously tests the null hypothesis of equal mean and equal variance across genotypes, by aggregating association evidence from the individual location/mean-only and scale/variance-only tests using Fisher's method. The generalized joint location-scale (gJLS) framework has been developed to deal specifically with sample correlation and group uncertainty (Soave and Sun, 2017; <doi:10.1111/biom.12651>). The current release: gJLS2, include additional functionalities that enable analyses of X-chromosome genotype data through novel methods for location (Chen et al., 2021; <doi:10.1002/gepi.22422>) and scale (Deng et al., 2019; <doi:10.1002/gepi.22247>).
License: GPL (≥ 3)
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.1.1
Suggests: knitr, markdown
VignetteBuilder: knitr
Imports: methods, nlme, quantreg, MCMCpack, MASS, plyr, ggplot2, moments
Depends: R (≥ 3.6.0)
NeedsCompilation: no
Packaged: 2021-09-29 16:03:28 UTC; weideng
Author: Wei Deng [aut, cre], Lei Sun [aut]
Maintainer: Wei Deng <deng@utstat.toronto.edu>
Repository: CRAN
Date/Publication: 2021-09-30 09:00:05 UTC

X-chromosomal example using the 1000 Genomes Project data

Description

A dataset containing real genotypes of 5 X-chromosomal SNPs and simulated phenotype of 473 unrelated samples from the 1000 Genomes Project.

Usage

chrXdat

Format

A data frame with 473 rows and 11 variables:

FID

Family ID.

IID

Individual ID.

PAT

Paternal individual ID.

MAT

Maternal individual ID.

SEX

The genetic sex of a individual.

PHENOTYPE

The quantitative trait value, simulated from a standard normal distribution.

rs5983012_A

The genotype of SNP with MAF roughly equal to 0.1 in females.

rs4119090_G

The genotype of SNP with MAF roughly equal to 0.2 in females.

rs5911042_T

The genotype of SNP with MAF roughly equal to 0.3 in females.

rs986810_C

The genotype of SNP with MAF roughly equal to 0.4 in females.

rs180495_G

The genotype of SNP with MAF roughly equal to 0.45 in females.

Source

https://www.internationalgenome.org/data/

A Generalized Joint-Location-Scale (gJLS) Test

Description

This function takes as input the genotype of a SNP (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 and scale association p-values for each SNP, as well as the gJLS p-value, which provides the combined evidence via Fisher's method (Soave et al., 2015, 2017). To perform this analysis genome-wide, we recommend to use the R-plugin written for PLINK, see gJLSPLINK for more details.

Usage

gJLS2(
  GENO,
  Y,
  COVAR = NULL,
  SEX = NULL,
  Xchr = FALSE,
  transformed = TRUE,
  loc_alg = "LAD",
  related = FALSE,
  cov.structure = "corCompSymm",
  clust = NULL,
  genotypic = FALSE,
  origLev = FALSE,
  centre = "median",
  XchrMethod = 3
)

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 vector of quantitative traits, such as human height.

COVAR

optional: a vector or matrix of covariates that are used to reduce bias due to confounding, such as age.

SEX

optional: the genetic sex of individuals in the sample population, must be a vector of 1 and 2 following the default sex code is 1 for males and 2 for females in PLINK.

Xchr

a logical indicator for whether the analysis is for X-chromosome SNPs.

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 TRUE.

loc_alg

a character indicating the type of algorithm to compute the centre in stage 1; the value is either "OLS", corresponding to an ordinary linear regression under Gaussian assumptions to compute the mean, or "LAD", corresponding to a quantile regression to compute the median. The recommended default option is "LAD". For the quantile regression, the function calls quantreg::rq and the median is estimated using either the "br" (smaller samples) or "sfn" (larger samples and sparse problems) algorithm depending the sample size, for more details see ?quantreg::rq.

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.

genotypic

a logical indicating whether the variance homogeneity should be tested with respect to an additively (linearly) coded or non-additively coded geno_one. The former has one less degree of freedom than the latter and is the default option. For dosage genotypes without genotypic probabilities, genotypic is forced to be FALSE.

origLev

a logical indicator for whether the reported p-values should also include original Levene's test.

centre

a character indicating whether the absolute deviation should be calculated with respect to "median" or "mean" in the traditional sex-specific and Fisher combined Levene's test p-values (three tests) for X-chromosome. The default value is "median". This option applies to sex-specific analysis using original Levene's test (i.e. when regression$$=$$TRUE).

XchrMethod

an integer taking values 0 (reports all models), 1.1, 1.2, 2, 3, for the choice of X-chromosome location association testing models; for more details, see locReg.

Value

a vector of location, scale and combined gJLS p-values for each SNP.

Note

For a genome-scan, we recommend to run this in PLINK via the plugin function gJLSPLINK, especially for large datasets and those with more than 20 covariates.

We highly recommend to quantile-normally transform Y for non-symmetrically distributed traits. This is typically done to avoid ‘scale-effect’ when the variance values tend to be proportional to mean values when stratified by GENO, as observed by Pare et al. (2010) and Yang et al. (2011).

For the moment, only quantitative trait Y is accepted as the subsequent generalized joint location scale (gJLS) analyses require the variance be calculated on quantitative traits. However, we are working on to include binary response for the generalized JLS analyses in the next update of gJLS.

Author(s)

Wei Q. Deng deng@utstat.toronto.edu, Lei Sun sun@utstat.toronto.edu

References

Soave D, Corvol H, Panjwani N, Gong J, Li W, Boëlle PY, Durie PR, Paterson AD, Rommens JM, Strug LJ, Sun L. (2015). A Joint Location-Scale Test Improves Power to Detect Associated SNPs, Gene Sets, and Pathways. American Journal of Human Genetics. 2015 Jul 2;97(1):125-38. doi: 10.1016/j.ajhg.2015.05.015. PMID: 26140448; PMCID: PMC4572492.

Examples

N <- 1000
genDAT <- rbinom(N, 2, 0.3)
sex <- rbinom(N, 1, 0.5)+1
y <- rnorm(N)
covar <- matrix(rnorm(N*10), ncol=10)

gJLS2(GENO=data.frame("SNP1" = genDAT, "aSNP1" = genDAT), SEX=sex, Y=y, COVAR=covar)

gJLS2(GENO=genDAT, SEX=sex, Y=y, COVAR=covar , Xchr=TRUE)

generalized Joint-Location-Scale (gJLS) test with summary statistics

Description

This function takes as input the gL and gS p-values for each SNP and combine to produce the gJLS p-values. It is used for genome-wide analysis where only the gL or gS p-values are available, caution should be exercised when combing gL and gS p-values obtained from separate datasets.

Usage

gJLS2s(gL, gS)

Arguments

gL

a vector of location p-values or a data.frame containing column names "SNP" and "gL".

gS

a vector of scale p-values or a data.frame containing column names "SNP" and "gS".

Value

a vector of combined gJLS p-values for each SNP.

Note

For a genome-scan, we recommend to run this in PLINK via the plugin function gJLSPLINK, especially for large datasets and those with more than 20 covariates.

We highly recommend to quantile-normally transform Y for non-symmetrically distributed traits. This is typically done to avoid ‘scale-effect’ when the variance values tend to be proportional to mean values when stratified by GENO, as observed by Pare et al. (2010) and Yang et al. (2011).

For the moment, only quantitative trait Y is accepted as the subsequent generalized joint location scale (gJLS) analyses require the variance be calculated on quantitative traits. However, we are working on to include binary response for the generalized JLS analyses in the next update of gJLS.

Author(s)

Wei Q. Deng deng@utstat.toronto.edu, Lei Sun sun@utstat.toronto.edu

References

Soave D, Corvol H, Panjwani N, Gong J, Li W, Boëlle PY, Durie PR, Paterson AD, Rommens JM, Strug LJ, Sun L. (2015). A Joint Location-Scale Test Improves Power to Detect Associated SNPs, Gene Sets, and Pathways. American Journal of Human Genetics. 2015 Jul 2;97(1):125-38. doi: 10.1016/j.ajhg.2015.05.015. PMID: 26140448; PMCID: PMC4572492.

Examples

gL <- data.frame("SNP" = paste("rs", 1:100, sep=""), "gL"=runif(100))
gS <- runif(100)

gJLS2s(gL = gL, gS=gS)

The generalized Levene's test via a two-stage regression for variance homogeneity by SNP genotype (autosomes)

Description

This function takes as input the genotype of a SNP (GENO), a quantitative trait (Y) in a sample population, and possibly additional covariates, such as principal components. The function returns the scale association p-values for each autosomal SNP using the generalized Levene's test.

Usage

leveneRegA_per_SNP(
  geno_one,
  Y,
  COVAR = NULL,
  transformed = TRUE,
  loc_alg = "LAD",
  related = FALSE,
  cov.structure = "corCompSymm",
  clust = NULL,
  genotypic = FALSE
)

Arguments

geno_one

the genotype of a biallelic SNP, must be a vector of 0, 1, 2's coded for the number of reference allele. Alternatively, for imputed genotypes, it could be a matrix/vector of dosage values, numerically between 0 and 2. The length/dimension of geno_one should match that of Y, and/or SEX and COVAR.

Y

a vector of quantitative traits, such as human height.

COVAR

optional: a vector or matrix of covariates that are used to reduce bias due to confounding, such as age.

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 TRUE.

loc_alg

a character indicating the type of algorithm to compute the centre in stage 1; the value is either "OLS", corresponding to an ordinary linear regression under Gaussian assumptions to compute the mean, or "LAD", corresponding to a quantile regression to compute the median. The recommended default option is "LAD". For the quantile regression, the function calls quantreg::rq and the median is estimated using either the "fn" (smaller samples) or "sfn" (larger samples and sparse problems) algorithm depending the sample size, for more details see ?quantreg::rq.

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.

genotypic

optional: a logical indicating whether the variance homogeneity should be tested with respect to an additively (linearly) coded or non-additively coded geno_one. The former has one less degree of freedom than the latter and is the default option. For dosage data without genotypic probabilities, genotypic is forced to be FALSE.

Value

Levene's test regression p-values for autosomal SNPs according to the model specified.

Note

We recommend to quantile-normally transform Y to avoid ‘scale-effect’ where the variance values tend to be proportional to mean values when stratified by geno_one.

When the relatedness option is used, the computational time is expected to be longer for larger sample size ($$n > 1000$$), thus we recommend this option for smaller studies rather than large population based studies.

There is no explicit argument to supply SEX for autosomal SNPs, the user can choose to include the genetic sex of individuals as a column of the COVAR argument.

Author(s)

Wei Q. Deng deng@utstat.toronto.edu, Lei Sun sun@utstat.toronto.edu

References

Soave D, Sun L. (2017). A generalized Levene's scale test for variance heterogeneity in the presence of sample correlation and group uncertainty. Biometrics. 73(3):960-971. doi: 10.1111/biom.12651. PMID: 28099998.

Gastwirth JL, Gel YR, Miao W. (2009). The Impact of Levene's Test of Equality of Variances on Statistical Theory and Practice." Statistical Science. 24(3) 343 - 360, doi: 10.1214/09-STS301

Examples

N <- 100
genDAT <- rbinom(N, 2, 0.3)
Y <- rnorm(N)
covar <- matrix(rnorm(N*10), ncol=10)

# vanilla example:
leveneRegA_per_SNP(geno_one=genDAT, Y=Y, COVAR=covar)

# relatedness samples:
leveneRegA_per_SNP(geno_one=genDAT, Y=Y, COVAR=covar,
related=TRUE)
leveneRegA_per_SNP(geno_one=genDAT, Y=Y, COVAR=covar,
related=TRUE, clust = factor(rbinom(N, 2, 0.6)))


# dosage genotypes example:
library("MCMCpack")
a <- 0.3
geno <- rbinom(N, 2, 0.3)
a <- 0.3 ## uncertainty
genPP <- rbind(rdirichlet(sum(geno==0),c(a,(1-a)/2,(1-a)/2)),
               rdirichlet(sum(geno==1),c((1-a)/2,a,(1-a)/2)),
               rdirichlet(sum(geno==2),c((1-a)/2,(1-a)/2,a)))

leveneRegA_per_SNP(geno_one=genPP, Y=Y, COVAR=covar)
leveneRegA_per_SNP(geno_one=genPP, Y=Y, COVAR=covar,
genotypic=TRUE)

# dosage and related samples:
leveneRegA_per_SNP(geno_one=genPP, Y=Y, COVAR=covar,
related=TRUE, clust = factor(rbinom(N, 1, 0.3)))
leveneRegA_per_SNP(geno_one=genPP, Y=Y, COVAR=covar,
related=TRUE, clust = factor(rbinom(N, 1, 0.3)), genotypic=TRUE)

Levene's regression tests for variance homogeneity by SNP genotype (X-chromosome specific)

Description

This function takes as input the genotype of a SNP (geno_one), the genetic sex (SEX), a quantitative trait (Y) in a sample population, and possibly additional covariates, such as principal components. The function returns the scale association p-values for each X-chromosome SNP using the generalized Levene's test designed for X-chromosome biallelic markers.

Usage

leveneRegX_per_SNP(
  geno_one,
  SEX,
  Y,
  COVAR = NULL,
  genotypic = FALSE,
  transformed = TRUE,
  loc_alg = "LAD"
)

Arguments

geno_one

the genotype of a biallelic SNP, must be a vector of 0, 1, 2's coded for the number of reference allele. Alternatively, for imputed genotypes, it could be a matrix/vector of dosage values, numerically between 0 and 2. The length/dimension of geno_one should match that of Y, and/or SEX and COVAR.

SEX

optional: the genetic sex of individuals in the sample population, must be a vector of 1 and 2 following the default sex code is 1 for males and 2 for females in PLINK.

Y

a vector of quantitative traits, such as human height.

COVAR

optional: a vector or matrix of covariates that are used to reduce bias due to confounding, such as age.

genotypic

optional: a logical indicating whether the variance homogeneity should be tested with respect to an additively (linearly) coded or non-additively coded geno_one. The former has one less degree of freedom than the latter and is the default option. For dosage genotypes without genotypic probabilities, genotypic is forced to be FALSE.

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 TRUE.

loc_alg

a character indicating the type of algorithm to compute the centre in stage 1; the value is either "OLS", corresponding to an ordinary linear regression under Gaussian assumptions to compute the mean, or "LAD", corresponding to a quantile regression to compute the median. The recommended default option is "LAD". For the quantile regression, the function calls quantreg::rq and the median is estimated using either the "fn" (smaller samples) or "sfn" (larger samples and sparse problems) algorithm depending the sample size, for more details see ?quantreg::rq.

Value

the Levene's test regression p-value according to the model specified.

Note

We recommend to quantile-normally transform Y to avoid ‘scale-effect’ where the variance values tend to be proportional to mean values when stratified by geno_one.

Author(s)

Wei Q. Deng deng@utstat.toronto.edu, Lei Sun sun@utstat.toronto.edu

References

Deng WQ, Mao S, Kalnapenkis A, Esko T, Magi R, Pare G, Sun L. (2019) Analytical strategies to include the X-chromosome in variance heterogeneity analyses: Evidence for trait-specific polygenic variance structure. Genet Epidemiol. 43(7):815-830. doi: 10.1002/gepi.22247. PMID:31332826.

Gastwirth JL, Gel YR, Miao W. (2009). The Impact of Levene's Test of Equality of Variances on Statistical Theory and Practice. Statistical Science. 24(3) 343-360, doi: 10.1214/09-STS301.

Examples

N <- 1000
sex <- rbinom(N, 1, 0.5)+1
Y <- rnorm(N)
genDAT <- NA
genDAT[sex==2] <- rbinom(sum(sex==2), 2, 0.3)
table(genDAT, sex)
genDAT[sex==1] <- rbinom(sum(sex==1), 1, 0.3)
table(genDAT, sex)

leveneRegX_per_SNP(geno_one=genDAT, SEX=sex, Y=Y)
leveneRegX_per_SNP(geno_one=genDAT, SEX=sex, Y=Y, genotypic=TRUE)
leveneRegX_per_SNP(geno_one=genDAT, SEX=sex, Y=Y, loc_alg="OLS")

Levene's test for variance homogeneity by SNP genotypes (sex-specific p-values)

Description

This function takes as input the genotype of a SNP (geno_one), the genetic sex (SEX), a quantitative trait (Y) in a sample population. The function then returns the variance heterogeneity p-values for each sex and the overall variance heterogeneity signal using Fisher's method by combining the sex-specific results.

Usage

leveneTests_per_SNP(
  geno_one,
  SEX = NULL,
  Y,
  centre = "median",
  transformed = TRUE
)

Arguments

geno_one

the genotype of a bi-allelic SNP, must be a vector of 0, 1, 2's coded for the number of reference allele. Alternatively, for imputed genotypes, it could be a matrix/vector of dosage values, numerically between 0 and 2. The length/dimension of geno_one should match that of Y, and/or SEX and COVAR.

SEX

optional: the genetic sex of individuals in the sample population, must be a vector of 1 and 2 following the default sex code is 1 for males and 2 for females in PLINK.

Y

a vector of quantitative traits, such as human height.

centre

a character indicating whether the absolute deviation should be calculated with respect to "median" or "mean", the default option is "median".

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 TRUE.

Value

a vector of Levene's test p-values according to levels specified by geno_one in each sex and the Fisher's method to combine the sex-specific Levene's test p-values.

Note

We recommend to quantile-normally transform Y to avoid ‘scale-effect’ where the variance values tend to be proportional to mean values when stratified by G.

Author(s)

Wei Q. Deng deng@utstat.toronto.edu, Lei Sun sun@utstat.toronto.edu

References

Levene H. (1960) Robust tests for equality of variances. In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling eds:I. Olkin, S.G. Ghurye, W. Hoeffding, W.G. Madow & H.B.Mann, pp.278-292. Stanford: Stanford University Press.

Examples

N <- 5000
sex <- rbinom(N, 1, 0.5)+1
genDAT <- rbinom(N, 2, 0.3)
y <- rnorm(N);

genDAT[sex==2] <- rbinom(sum(sex==2), 1, 0.3)
table(genDAT, sex)
leveneTests_per_SNP(geno_one=genDAT, SEX=sex, Y=y^2, transform=TRUE)

genDAT[sex==2] <- rbinom(sum(sex==2), 1, 0.01)
table(genDAT, sex)
leveneTests_per_SNP(geno_one=genDAT, SEX=sex, Y=y^2, transform=FALSE)

leveneTests_per_SNP(geno_one=rep(0, N), SEX=sex, Y=y^2, transform=TRUE)
leveneTests_per_SNP(geno_one=rep(0, N), Y=y^2, transform=TRUE)

Location (mean-based association) test

Description

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.

Usage

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.

Value

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.

Author(s)

Wei Q. Deng deng@utstat.toronto.edu, Lei Sun sun@utstat.toronto.edu

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. 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. doi: 10.1002/gepi.22422. PMID: 34224641.

Examples

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)

Scale (variance-based association) test

Description

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 scale association p-values for each SNP.

Usage

scaleReg(
  GENO,
  Y,
  COVAR = NULL,
  SEX = NULL,
  Xchr = FALSE,
  transformed = FALSE,
  loc_alg = "LAD",
  related = FALSE,
  cov.structure = "corCompSymm",
  clust = NULL,
  genotypic = FALSE,
  origLev = FALSE,
  centre = "median"
)

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 vector of quantitative traits, such as human height.

COVAR

optional: a vector or matrix of covariates that are used to reduce bias due to confounding, such as age.

SEX

optional: the genetic sex of individuals in the sample population, must be a vector of 1 and 2 following the default sex code is 1 for males and 2 for females in PLINK.

Xchr

a logical indicator for whether the analysis is for X-chromosome SNPs.

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.

loc_alg

a character indicating the type of algorithm to compute the centre in stage 1; the value is either "OLS", corresponding to an ordinary linear regression under Gaussian assumptions to compute the mean, or "LAD", corresponding to a quantile regression to compute the median. The recommended default option is "LAD". For the quantile regression, the function calls quantreg::rq and the median is estimated using either the "br" (smaller samples) or "sfn" (larger samples and sparse problems) algorithm depending the sample size, for more details see ?quantreg::rq.

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.

genotypic

a logical indicating whether the variance homogeneity should be tested with respect to an additively (linearly) coded or non-additively coded geno_one. The former has one less degree of freedom than the latter and is the default option. For dosage genotypes without genotypic probabilities, genotypic is forced to be FALSE.

origLev

a logical indicator for whether the reported p-values should also include original Levene's test.

centre

a character indicating whether the absolute deviation should be calculated with respect to "median" or "mean" in the traditional sex-specific and Fisher combined Levene's test p-values (three tests) for X-chromosome. The default value is "median". This option applies to sex-specific analysis using original Levene's test (i.e. when regression$$=$$TRUE).

Value

a vector of Levene's test regression p-values according to the models specified.

Note

We recommend to quantile-normally transform Y to avoid ‘scale-effect’ where the variance values tend to be proportional to mean values when stratified by GENO.

Author(s)

Wei Q. Deng deng@utstat.toronto.edu, Lei Sun sun@utstat.toronto.edu

References

Deng WQ, Mao S, Kalnapenkis A, Esko T, Magi R, Pare G, Sun L. (2019) Analytical strategies to include the X-chromosome in variance heterogeneity analyses: Evidence for trait-specific polygenic variance structure. Genet Epidemiol. 43(7):815-830. doi: 10.1002/gepi.22247. PMID:31332826.

Gastwirth JL, Gel YR, Miao W. (2009). The Impact of Levene's Test of Equality of Variances on Statistical Theory and Practice." Statistical Science. 24(3) 343-360, doi: 10.1214/09-STS301.

Soave D, Sun L. (2017). A generalized Levene's scale test for variance heterogeneity in the presence of sample correlation and group uncertainty. Biometrics. 73(3):960-971. doi: 10.1111/biom.12651. PMID:28099998.

Examples

N <- 1000
genoDAT <- rbinom(N, 2, 0.3)
sex <- rbinom(N, 1, 0.5)+1
Y <- rnorm(N)
covar <- matrix(rnorm(N*10), ncol=10)

# vanilla example:
scaleReg(GENO=list(genoDAT, genoDAT), Y=Y, COVAR=covar)
scaleReg(GENO=list(genoDAT, genoDAT), Y=Y, COVAR=covar, genotypic=TRUE)
scaleReg(GENO=list(genoDAT, genoDAT), Y=Y, COVAR=covar, origLev = TRUE)
scaleReg(GENO=list(genoDAT, genoDAT), Y=Y, COVAR=covar, origLev = TRUE, SEX=sex)