This vignette provides a description of how to use the GENESIS package to run genetic association tests. GENESIS uses mixed models for genetic association testing, as PC-AiR PCs can be used as fixed effect covariates to adjust for population stratification, and a kinship matrix (or genetic relationship matrix) estimated from PC-Relate can be used to account for phenotype correlation due to genetic similarity among samples.
fitNullMM function in the
GENESIS package reads sample data from either a standard
data.frame class object or a
ScanAnnotationDataFrame class object as created by the
GWASTools package. This object must contain all of the outcome and covariate data for all samples to be included in the mixed model analysis. Additionally, this object must include a variable called "scanID" which contains a unique identifier for each sample in the analysis. While a standard
data.frame can be used, we recommend using a
ScanAnnotationDataFrame object, as it can be paired with the genotype data (see below) to ensure matching of sample phenotype and genotype data. Through the use of
ScanAnnotationDataFrame class object can easily be created from a
data.frame class object. Example R code for creating a
ScanAnnotationDataFrame object is presented below. Much more detail can be found in the
GWASTools package reference manual.
library(GENESIS) library(GWASTools) # file path to GDS file gdsfile <- system.file("extdata", "HapMap_ASW_MXL_geno.gds", package="GENESIS") # read in GDS data HapMap_geno <- GdsGenotypeReader(filename = gdsfile) # create a GenotypeData class object HapMap_genoData <- GenotypeData(HapMap_geno) # load saved matrix of KING-robust estimates data("HapMap_ASW_MXL_KINGmat") # run PC-AiR mypcair <- pcair(genoData = HapMap_genoData, kinMat = HapMap_ASW_MXL_KINGmat, divMat = HapMap_ASW_MXL_KINGmat) # run PC-Relate mypcrel <- pcrelate(genoData = HapMap_genoData, pcMat = mypcair$vectors[,1], training.set = mypcair$unrels) # generate a phenotype set.seed(4) pheno <- 0.2*mypcair$vectors[,1] + rnorm(mypcair$nsamp, mean = 0, sd = 1)
# mypcair contains PCs from a previous PC-AiR analysis # mypcrel contains Kinship Estimates from a previous PC-Relate analysis # pheno is a vector of Phenotype values # make a data.frame mydat <- data.frame(scanID = mypcrel$sample.id, pc1 = mypcair$vectors[,1], pheno = pheno) head(mydat) # make ScanAnnotationDataFrame scanAnnot <- ScanAnnotationDataFrame(mydat) scanAnnot
assocTestMM function in the
GENESIS package reads genotype data from a
GenotypeData class object as created by the
GWASTools package. Through the use of
GenotypeData class object can easily be created from:
Example R code for creating a
GenotypeData object is presented below. Much more detail can be found in the
GWASTools package reference manual.
geno <- MatrixGenotypeReader(genotype = genotype, snpID = snpID, chromosome = chromosome, position = position, scanID = scanID) genoData <- GenotypeData(geno)
genotypeis a matrix of genotype values coded as 0 / 1 / 2, where rows index SNPs and columns index samples
snpIDis an integer vector of unique SNP IDs
chromosomeis an integer vector specifying the chromosome of each SNP
positionis an integer vector specifying the position of each SNP
scanIDis a vector of unique individual IDs
geno <- GdsGenotypeReader(filename = "genotype.gds") genoData <- GenotypeData(geno)
filenameis the file path to the GDS object
SNPRelate package provides the
snpgdsBED2GDS function to convert binary PLINK files into a GDS file.
snpgdsBED2GDS(bed.fn = "genotype.bed", bim.fn = "genotype.bim", fam.fn = "genotype.fam", out.gdsfn = "genotype.gds")
bed.fnis the file path to the PLINK .bed file
bim.fnis the file path to the PLINK .bim file
fam.fnis the file path to the PLINK .fam file
out.gdsfnis the file path for the output GDS file
Once the PLINK files have been converted to a GDS file, then a
GenotypeData object can be created as described above.
To demonstrate association testing with the
GENESIS package, we analyze SNP data from the Mexican Americans in Los Angeles, California (MXL) and African American individuals in the southwestern USA (ASW) population samples of HapMap 3. Mexican Americans and African Americans have a diverse ancestral background, and familial relatives are present in these data. Genotype data at a subset of 20K autosomal SNPs for 173 individuals are provided as a GDS file.
# read in GDS data gdsfile <- system.file("extdata", "HapMap_ASW_MXL_geno.gds", package="GENESIS") HapMap_geno <- GdsGenotypeReader(filename = gdsfile)
# create a GenotypeData class object with paired ScanAnnotationDataFrame HapMap_genoData <- GenotypeData(HapMap_geno, scanAnnot = scanAnnot) HapMap_genoData
A mixed model for genetic association testing typically includes a genetic relationship matrix (GRM) to account for genetic similarity among sample individuals. If we are using kinship coefficient estimates from PC-Relate to construct this GRM, then the function
pcrelateMakeGRM should be used to provide the matrix in the appropriate format for
myGRM <- pcrelateMakeGRM(mypcrel) myGRM[1:5,1:5]
Note that both the row and column names of this matrix are the same scanIDs as used in the scan annotation data.
There are two steps to performing genetic association testing with GENESIS. First, the null model (i.e. the model with no SNP genotype term) is fit using the
fitNullMM function. Second, the output of the null model fit is used in conjunction with the genotype data to quickly run SNP-phenotype association tests using the
assocTestMM function. There is a computational advantage to splitting these two steps into two function calls; the null model only needs to be fit once, and SNP association tests can be paralelized by chromosome or some other partitioning to speed up analyses (details below).
The first step for association testing with
GENESIS is to fit the mixed model under the null hypothesis that each SNP has no effect. This null model contains all of the covariates, including ancestry representative PCs, as well as any random effects, such as a polygenic effect due to genetic relatedness, but it does not include any SNP genotype terms as fixed effects.
fitNullMM function, random effects in the null model are specified via their covariance structures. This allows for the inclusion of a polygenic random effect using a kinship matrix or genetic relationship matrix (GRM).
A linear mixed model (LMM) should be fit when analyzing a quantitative phenotype. The example R code below fits a basic null mixed model.
# fit the null mixed model nullmod <- fitNullMM(scanData = scanAnnot, outcome = "pheno", covars = "pc1", covMatList = myGRM, family = gaussian)
scanDatais the class
data.frameobject containing the sample data
outcomespecifies the name of the outcome variable in
covarsspecifies the names of the covariates in
covMatListspecifies the covariance structures for the random effects included in the model
familyshould be gaussian for a quantitative phenotype, specifying a linear mixed model
The Average Information REML (AIREML) procedure is used to estimate the variance components of the random effects. When
verbose = TRUE, the variance component estimates, the log-likelihood, and the residual sum of squares in each iteration are printed to the R console (shown above). In this example,
Sigma^2_A is the variance component for the random effect specified in
Sigma^2_E is the residual variance component.
The model can be fit with multiple fixed effect covariates by setting
covars equal to vector of covariate names. For example, if we wanted to include the variables "pc1", "pc2", "sex", and "age" all as covariates in the model:
nullmod <- fitNullMM(scanData = scanAnnot, outcome = "pheno", covars = c("pc1","pc2","sex","age"), covMatList = myGRM, family = gaussian)
The model also can be fit with multiple random effects. This is done by setting
covMatList equal to a list of matrices. For example, if we wanted to include a polygenic random effect with covariance structure given by the matrix "myGRM" and a household random effect with covariance structure specified by the matrix "H":
nullmod <- fitNullMM(scanData = scanAnnot, outcome = "pheno", covars = "pc1" covMatList = list("GRM" = myGRM, "House" = H), family = gaussian)
The names of the matrices in
covMatList determine the names of the variance component parameters. Therefore, in this example, the output printed to the R console will include
Sigma^2_GRM for the random effect specified by "myGRM",
Sigma^2_House for the random effect specified by "H", and
Sigma^2_E for the residual variance component.
Note: the row and column names of each matrix used to specify the covariance structure of a random effect in the mixed model must be the unique scanIDs for each sample in the analysis.
LMMs are typically fit under an assumption of constant (homogeneous) residual variance for all observations. However, for some outcomes, there may be evidence that different groups of observations have different residual variances, in which case the assumption of homoscedasticity is violated.
group.var can be used in order to fit separate (heterogeneous) residual variance components by some grouping variable. For example, if we have a categorical variable "race" in our
scanData, then we can estimate a different residual variance component for each unique value of "race" by using the following code:
nullmod <- fitNullMM(scanData = scanAnnot, outcome = "pheno", covars = "pc1", covMatList = myGRM, family = gaussian, group.var = "race")
In this example, the residual variance component
Sigma^2_E is replaced with group specific residual variance components
Sigma^2_race2, ..., where "race1", "race2", ... are the unique values of the "race" variable.
Ideally, a generalized linear mixed model (GLMM) would be fit for a binary phenotype; however, fitting a GLMM is much more computationally demanding than fitting an LMM. To provide a compuationally efficient approach to fitting such a model,
fitNullMM uses the penalized quasi-likelihood (PQL) approximation to the GLMM (Breslow and Clayton). The implementation of this procedure in
GENESIS is the same as in GMMAT (Chen et al.), and more details can be found in that manuscript. If our outcome variable, "pheno", were binary, then the same R code could be used to fit the null model, but with
family = binomial.
nullmod <- fitNullMM(scanData = scanAnnot, outcome = "pheno", covars = "pc1", covMatList = myGRM, family = binomial)
Multiple fixed effect covariates and multiple random effects can be specified for binary phenotypes in the same way as they are for quantitative phenotypes.
group.var does not apply here.
The second step for association testing with
GENESIS is to use the fitted null model to test the SNPs in the
GenotypeData object for association with the specified outcome variable. This is done with the
assocTestMM function. Both (approximate) Wald and score tests are available, but the Wald test can only be performed when
family = gaussian in the null model. Otherwise, the use of
assocTestMM for running association tests with a quantitative or binary phenotype is identical.
The example R code below runs the association analyses using the null model we fit using
fitNullMM in the previous section.
assoc <- assocTestMM(genoData = HapMap_genoData, nullMMobj = nullmod, test = "Wald")
nullMMobjis the output from
testspecifies whether to use a "Wald" or "Score" test
By default, the function will perform association tests at all SNPs in the
genoData object. However, for computational reasons it may be practical to parallelize this step, partitioning SNPs by chromosome or some other pre-selected grouping. If we only want to test a pre-specified set of SNPs, this can be done by passing a vector of snpID values to the
# mysnps is a vector of snpID values for the SNPs we want to test assoc <- assocTestMM(genoData = HapMap_genoData, nullMMobj = nullmod, test = "Wald", snp.include = mysnps)
If we only want to test SNPs on chromosome 22, this can be done by specifying the
assoc <- assocTestMM(genoData = HapMap_genoData, nullMMobj = nullmod, test = "Wald", chromosome = 22)
Multiple chromosomes can be specified at once by setting
chromosome equal to a vector of integer values.
snp.include is specified, then the
chromosome argument is ignored.
fitNullMM function will return a list with a large amount of data. Some of the more useful output for the user includes:
varComp: the variance component estimates for the random effects
data.framewith point estimates, standard errors, test statistics, and p-values for each of the fixed effect covariates
fitted.values: the fitted values from the model
resid.conditional: the marginal and conditional residuals from the model
There are also metrics assessing model fit such as the log-likelihood (
logLik), restricted log-likelihood (
logLikR), and the Akaike information criterion (
AIC). Additionally, there are some objects such as the working outcome vector (
workingY) and the Cholesky decomposition of the inverse of the estimated phenotype covariance matrix (
cholSigmaInv) that are used by the
assocTestMM function for association testing. Further details describing all of the output can be found with the command
assocTestMM function will return a
data.frame with summary information from the association test for each SNP. Each row corresponds to a different SNP.
snpID: the unique snpID
chr: the chromosome
n: the number of samples analyzed at that SNP
MAF: the estimated minor allele frequency
minor.allele: which allele is the minor allele (either "A" or "B")
Est: the effect size estimate (beta) for that SNP
SE: the estimated standard error of the effect size estimate
Wald.Stat: the chi-squared Wald test statistic
Wald.pval: the p-value based on the Wald test statistic
test = "Score" in
assocTestMM (rather than
test = "Wald"), then
Wald.pval are replaced by:
Score: the value of the score function
Var: the variance of the score
Score.Stat: the chi-squared score test statistic
Score.pval: the p-value based on the score test statistic
Further details describing all of the output can be found with the command
It is often of interest to estimate the proportion of the total phenotype variability explained by the entire set of genotyped SNPs avaialable; this provides an estimate of the narrow sense heritability of the trait. One method for estimating heritability is to use the variance component estimates from the null mixed model.
GENESIS includes the
varCompCI function for computing the proportion of variance explained by each random effect along with 95% confidence intervals.
varCompCI(nullMMobj = nullmod, prop = TRUE)
nullMMobjis the output from
propis a logical indicator of whether the point estimates and confidence intervals should be returned as the proportion of total variability explained (TRUE) or on the orginal scale (FALSE)
When additional random effects are included in the model (e.g. a shared household effect),
varCompCI will also return the proportion of variability explained by each of these components.
varCompCI can not compute proportions of variance explained when heterogeneous residual variances are used in the null model (i.e.
group.var is used in
fitNullMM). Confidence intervals can still be computed for the variance component estimates on the original scale by setting
prop = FALSE.
Note: variance component estimates are not interpretable for binary phenotypes when fit using the PQL method implemented in
fitNullMM; proportions of variance explained should not be calculated for these models.
Breslow NE and Clayton DG. (1993). Approximate Inference in Generalized Linear Mixed Models. Journal of the American Statistical Association 88: 9-25.
Chen H, Wang C, Conomos MP, Stilp AM, Li Z, Sofer T, Szpiro AA, Chen W, Brehm JM, Celedon JC, Redline S, Papanicolaou GJ, Thornton TA, Laurie CC, Rice K and Lin X. Control for Population Structure and Relatedness for Binary Traits in Genetic Association Studies Using Logistic Mixed Models. (Submitted).
Gogarten, S.M., Bhangale, T., Conomos, M.P., Laurie, C.A., McHugh, C.P., Painter, I., ... & Laurie, C.C. (2012). GWASTools: an R/Bioconductor package for quality control and analysis of Genome-Wide Association Studies. Bioinformatics, 28(24), 3329-3331.
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