| Title: | Genetic Data Handling (QC, GRM, LD, PCA) & Linear Mixed Models |
|---|---|
| Description: | Manipulation of genetic data (SNPs). Computation of GRM and dominance matrix, LD, heritability with efficient algorithms for linear mixed model (AIREML). Dandine et al <doi:10.1159/000488519>. |
| Authors: | Hervé Perdry [cre, aut, cph], Claire Dandine-Roulland [aut, cph], Deepak Bandyopadhyay [cph] (C++ gzstream class), Lutz Kettner [cph] (C++ gzstream class) |
| Maintainer: | Hervé Perdry <[email protected]> |
| License: | GPL-3 |
| Version: | 1.6 |
| Built: | 2024-12-02 07:01:38 UTC |
| Source: | CRAN |
Manipulation of genetic data (SNPs), computation of Genetic Relationship Matrix, Linkage Disequilibrium, etc. Efficient algorithms for Linear Mixed Model (AIREML, diagonalisation trick).
Gaston offers functions for efficient manipulation of large genotype (SNP) matrices, and state-of-the-art implementation of algorithms to fit Linear Mixed Models, that can be used to compute heritability estimates or to perform association tests.
Thanks to the packages Rcpp,
RcppParallel,
RcppEigen, gaston
functions are mainly written in C++.
Many functions are multithreaded;
the number of threads can be setted through RcppParallel
function setThreadOptions.
It is advised to try several values for the number of threads, as
using too many threads might be conterproductive due to an important
overhead.
Some functions have a verbose argument, which controls the
function verbosity. To mute all functions at once you can use
options(gaston.verbose = FALSE).
An S4 class for genotype matrices is defined, named bed.matrix.
Each row corresponds to an individual, and each column to a SNP. They can
be read from files using read.bed.matrix
and saved using write.bed.matrix. The function read.vcf reads
VCF files.
In first approach, a bed.matrix behaves as a "read-only" matrix containing only
0, 1, 2 and NAs, unless the genotypes are standardized (use standardize<-).
They are stored in a compact form, each genotype being coded on 2 bits (hence
4 genotypes per byte).
Bed.matrices can be converted to numerical matrices with as.matrix,
and multiplied with numeric vectors or matrices with %*% (this
feature can be used e.g. to simulate quantitative phenotypes, see a basic example in the example
section of association.test).
It is possible to subset bed.matrices just as base matrices, writing e.g.
x[1:100,] to extract the first 100 individuals, or x[1:100,1000:1999]
for extract the SNPs 1000 to 1999 for these 100 individuals. The use of logical
vectors for subsetting is allowed too. The functions
select.inds and select.snps can also be used for
subsetting with a nice syntax.
Some basic descriptive statistics can be added to a bed.matrix with set.stats (since
gaston 1.4, this function is called by default by all functions that create a bed.matrix, unless
options(gaston.auto.set.stats = FALSE) was set.
Hardy-Weinberg Equilibrium can be tested for all SNPs with set.hwe.
If is a standardized genotype matrix, a Genetic Relationship Matrix
(GRM) of the individuals can be computed as
where is the number of SNPs.
This computation is done by the function GRM. The eigen decomposition of the GRM produces
the Principal Components (PC) of the data set. If needed, the loadings
corresponding to the PCs can be retrieved using bed.loadings.
Doing the above crossproduct in the reverse order produces a moment estimate of the Linkage Disequilibrium:
where is the number of individuals. This computation is done by the function
LD (usually, only parts of the whole LD matrix is computed). This method is
also used by LD.thin to extract a set of SNPs in low linkage disequilibrium
(it is often recommended to perform this operation before computing the GRM).
lmm.aireml is a function for linear mixed models parameter estimation
and BLUP computations.
The model considered is of the form
with for and
.
Note that very often in genetics a mixed model is written as
with a standardized genotype matrix, and . In that case,
denoting ,
and letting we get a mixed model of the previous form.
When in the above general model (only one random term ), the likelihood
can be computed very efficiently using the eigen decomposition of
. This "diagonalization trick"
is used in lmm.diago.likelihood and lmm.diago, to compute
the likelihood and for parameter estimation, respectively.
Two small functions complete this set of functions: lmm.simu, to
simulate data under a linear mixed model, and random.pm, to generate
random positive matrices. Both are used in examples and can be useful for data simulation.
Hervé Perdry and Claire Dandine-Roulland
Maintainer: Hervé Perdry
These data have been extracted from the 1000 Genomes data.
The data set contains the genotype matrix AGT.gen, the pedigree matrix AGT.fam and a matrix AGT.bim,
corresponding to 503 individuals of European populations and 361 SNPs on chromosome 1, on a ~100kb segment
containing the Angiotensinogen gene. There is also a factor AGT.pop, which gives the population from which each
individual is drawn (CEU = Utah residents of Northern Western European ancestry, FIN = Finnish, GBR = England and Scottland,
IBS = Iberian, TSI = Toscani).
data(AGT)data(AGT)
There are three data objects in the dataset:
AGT.genGenotype matrix
AGT.fam Data frame containing all variables corresponding to a .fam file
AGT.bim Data frame containing all variables corresponding to a .bim file
AGT.popFactor giving the population from which each individual is drawn
The data were obtained from the 1000 Genomes project (see https://www.internationalgenome.org/).
McVean et al, 2012, An integrated map of genetic variation from 1,092 human genomes, Nature 491, 56-65 doi:10.1038/nature11632
data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) xdata(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) x
Creates a bed.matrix using a numeric matrix and two data frame for ped / snps slots
as.bed.matrix(x, fam, bim)as.bed.matrix(x, fam, bim)
x |
A numeric matrix |
fam |
(Optionnal) A data frame (the contents of a .fam file) |
bim |
(Optionnal) A data frame (the contents of a .bim file) |
The data frame fam should have columns named "famid", "id", "father", "mother", "sex" and "pheno".
The data frame bim should have columns named "chr", "id", "dist", "pos", "A1" and "A2".
A bed.matrix condensing all three arguments.
Hervé Perdry and Claire Dandine-Roulland
data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) xdata(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) x
Association tests between phenotype and SNPs.
association.test(x, Y = x@ped$pheno, X = matrix(1, nrow(x)), method = c("lm", "lmm"), response = c("quantitative", "binary"), test = c("score", "wald", "lrt"), K, eigenK, beg = 1, end = ncol(x), p = 0, tol = .Machine$double.eps^0.25, ...)association.test(x, Y = x@ped$pheno, X = matrix(1, nrow(x)), method = c("lm", "lmm"), response = c("quantitative", "binary"), test = c("score", "wald", "lrt"), K, eigenK, beg = 1, end = ncol(x), p = 0, tol = .Machine$double.eps^0.25, ...)
x |
|
Y |
The phenotype vector. Default is the column ( |
X |
A covariable matrix. The default is a column vector of ones, to include an intercept in the model |
method |
Method to use: |
response |
Is |
test |
Which test to use. For binary phenotypes, |
K |
A Genetic Relationship Matrix (as produced by |
eigenK |
Eigen decomposition of the Genetic Relationship Matrix (as produced by the function |
beg |
Index of the first SNP tested for association |
end |
Index of the last SNP tested for association |
p |
Number of Principal Components to include in the model with fixed effect (for |
tol |
Parameter for the likelihood maximization (as in |
... |
Additional parameters for |
Tests the association between the phenotype and requested SNPs in x.
If method = "lm" and response = "quantitative" are used, a simple linear regression
is performed to test each SNP in the considered interval. Precisely, the following model is
considered for each SNP,
with ,
the genotype vector of the SNP,
the covariates matrix, and the matrix of the first principal components.
A Wald test is performed, independently of the value of test.
Ifmethod = "lm" and response = "binary", a similar model is used for a logistic
regression (Wald test).
If method = "lmm" and response = "quantitative", the following model in considered for each SNP
with and .
is the genotype vector of the SNP, is a Genetic Relationship Matrix (GRM)
the covariates matrix, and the matrix of the first principal components.
If test = "score", all parameters are estimated with the same procedure as in
lmm.aireml and the argument K is used to specify the GRM matrix (or a list of GRM
matrices for inclusion of several random effects in the model). If p is positive, the paramater eigenK
needs to be given as well.
For Wald and LRT tests the procedure used is the same as in lmm.diago and eigenK is used to
specify the GRM matrix.
If method = "lmm" and response = "binary", the following model in considered for each SNP
with .
is the genotype vector of the SNP, is a Genetic Relationship Matrix (GRM),
the covariable matrix. A score test is performed, independently of the value of test.
All parameters under null model are estimated with the same procedure as in logistic.mm.aireml.
In case of convergence problems of the null problem, the user can try several starting values (in particular
with parameter tau, trying e.g. tau = 0.1 or another value).
It is possible to give a list of matrices in parameter K for inclusion of several random effects in the model.
If p is positive, the paramater eigenK needs to be given as well.
Note: this function is not multithreaded. Wald test with Linear Mixed Models are computationally intensive,
to run a GWAS with such tests consider using association.test.parallel in package gaston.utils
(on github). Association tests with dosages can be done with association.test.dosage and
association.test.dosage.parallel in the same package.
A data frame, giving for each considered SNP, its position, id, alleles, and
some of the following columns depending on the values of method and test:
score |
Score statistic for each SNP |
h2 |
Estimated value of |
beta |
Estimated value of |
sd |
Estimated standard deviation of the |
LRT |
Value of the Likelihood Ratio Test |
p |
The corresponding p-value |
qqplot.pvalues, manhattan, lmm.diago,
lmm.aireml, logistic.mm.aireml, optimize
# Load data data(TTN) x <- as.bed.matrix(TTN.gen, TTN.fam, TTN.bim) standardize(x) <- "p" # simulate quantitative phenotype with effect of SNP #631 set.seed(1) y <- x %*% c(rep(0,630),0.5,rep(0,ncol(x)-631)) + rnorm(nrow(x)) # association test with linear model test <- association.test(x, y, method="lm", response = "quanti") # a p-values qq plot qqplot.pvalues(test) # a small Manhattan plot # hihlighting the link between p-values and LD with SNP #631 lds <- LD(x, 631, c(1,ncol(x))) manhattan(test, col = rgb(lds,0,0), pch = 20) # use y to simulate a binary phenotype y1 <- as.numeric(y > mean(y)) # logistic regression t_binary <- association.test(x, y1, method = "lm", response = "binary") # another small Manhattan plot manhattan(t_binary, col = rgb(lds,0,0), pch = 20)# Load data data(TTN) x <- as.bed.matrix(TTN.gen, TTN.fam, TTN.bim) standardize(x) <- "p" # simulate quantitative phenotype with effect of SNP #631 set.seed(1) y <- x %*% c(rep(0,630),0.5,rep(0,ncol(x)-631)) + rnorm(nrow(x)) # association test with linear model test <- association.test(x, y, method="lm", response = "quanti") # a p-values qq plot qqplot.pvalues(test) # a small Manhattan plot # hihlighting the link between p-values and LD with SNP #631 lds <- LD(x, 631, c(1,ncol(x))) manhattan(test, col = rgb(lds,0,0), pch = 20) # use y to simulate a binary phenotype y1 <- as.numeric(y > mean(y)) # logistic regression t_binary <- association.test(x, y1, method = "lm", response = "binary") # another small Manhattan plot manhattan(t_binary, col = rgb(lds,0,0), pch = 20)
Compute the loadings corresponding to given PCs.
bed.loadings(x, pc)bed.loadings(x, pc)
x |
|
pc |
A matrix with Principal Components in columns |
A matrix with the corresponding loadings in columns.
Hervé Perdry and Claire Dandine-Roulland
# load chr2 data set (~10k SNPs in low LD) x <- read.bed.matrix( system.file("extdata", "chr2.bed", package="gaston") ) # Compute Genetic Relationship Matrix standardize(x) <- "p" K <- GRM(x) # Eigen decomposition eiK <- eigen(K) # deal with small negative eigen values eiK$values[ eiK$values < 0 ] <- 0 # Note: the eigenvectors are normalized, to compute 'true' PCs # multiply them by the square root of the associated eigenvalues PC <- sweep(eiK$vectors, 2, sqrt(eiK$values), "*") # Compute loadings for the 2 first PCs # one can use PC[,1:2] instead of eiK$vectors[,1:2] as well L <- bed.loadings(x, eiK$vectors[,1:2]) dim(L) head(L) # the loadings are normalized colSums(L**2) # Verify that these are loadings head( (x %*% L) / sqrt(ncol(x)-1) ) head( PC[,1:2] )# load chr2 data set (~10k SNPs in low LD) x <- read.bed.matrix( system.file("extdata", "chr2.bed", package="gaston") ) # Compute Genetic Relationship Matrix standardize(x) <- "p" K <- GRM(x) # Eigen decomposition eiK <- eigen(K) # deal with small negative eigen values eiK$values[ eiK$values < 0 ] <- 0 # Note: the eigenvectors are normalized, to compute 'true' PCs # multiply them by the square root of the associated eigenvalues PC <- sweep(eiK$vectors, 2, sqrt(eiK$values), "*") # Compute loadings for the 2 first PCs # one can use PC[,1:2] instead of eiK$vectors[,1:2] as well L <- bed.loadings(x, eiK$vectors[,1:2]) dim(L) head(L) # the loadings are normalized colSums(L**2) # Verify that these are loadings head( (x %*% L) / sqrt(ncol(x)-1) ) head( PC[,1:2] )
"bed.matrix"
S4 class for SNP genotype matrices
Objects can be created by calls of the form new("bed.matrix", ...).
ped:data.frame containing information for each individual: famid = Family ID,
id = Individual ID, father = Father ID, mother = Mother ID, sex = Sex and pheno = Phenotype.
Can also contain individuals statistic, for example: N0, N1 and N2 = Number of genotypes equal to 0, 1 and 2 respectively,
NAs = Number of missing genotypes, callrate = Individual callrate.
snps:data.frame containing information for each SNP: chr = Chromosome, id = SNP ID,
dist = Genetic Distance, pos = Physical position, A1 = Reference Allele, A2 = Alternative Allele.
Can also contain SNPs statistic, for example: N0, N1 and N2 = Number of genotypes equal to 0, 1 and 2 repectively,
NAs = Number of missing genotypes, callrate = SNP callrate, maf = Minor allele frequency), hz = heterozygosity
bed:externalptr (pointing to the genotype matrix).
p:vector or NULL for allelic frequencies (allèle A2).
mu:vector or NULL for genotype means (usually mu = 2*p).
sigma:vector or NULL for genotypic standard deviation
standardize_p:logical. If TRUE, the genotype matrix is standardized using means 2*p
and genotypic standard deviation sqrt(2*p*(1-p))
standardize_mu_sigma:logical. If TRUE, the genotype matrix is standardize using means
mu and genotypic standard deviation sigma.
For more details please check the vignette.
signature(x = "bed.matrix", i = "numeric" or "logical" or "missing",j = "numeric" or "logical" or "missing", drop = "missing"):
Extract a sub-matrix (a new bed.matrix).
signature(x = "bed.matrix", y = "matrix" or "vector"):
Right matrix multiplication of the genotype matrix (possibly centered and reduced) with a matrix or a vector.
signature(x = "matrix" or "vector", y = "bed.matrix"):
Left matrix multiplication of the genotype matrix with a matrix or a vector.
signature(x = "bed.matrix"):
Convert a bed.matrix into a matrix.
The resulting matrix can be huge, use this method only for a small bed.matrix!
signature(x = "bed.matrix"):
Get the standardize parameter of bed.matrix. Can be "none", "p" or "mu_sigma".
signature(x = "bed.matrix"):
Set the standardize parameter of a bed.matrix.
signature(x = "bed.matrix"):
Get the number of individuals (rows) and the number of SNPs (columns).
signature(x = "bed.matrix"):
Print the head of the genotype matrix of a bed.matrix object.
signature(x = "bed.matrix"):
Get the mu slot of a bed.matrix.
signature(x = "bed.matrix"):
Set the mu slot of a bed.matrix.
signature(x = "bed.matrix"):
Get the p slot of a bed.matrix.
signature(x = "bed.matrix"):
Set the p slot of a bed.matrix.
signature(object = "bed.matrix"):
Displays basic information about a bed.matrix.
signature(x = "bed.matrix"):
Get the sigma slot of a bed.matrix.
signature(x = "bed.matrix"):
Set the sigma slot of a bed.matrix.
signature(... = "bed.matrix"):
Combine a sequence of bed.matrix by columns.
signature(... = "bed.matrix"):
Combine a sequence of bed.matrix by rows.
Hervé Perdry and Claire Dandine-Roulland
read.bed.matrix, write.bed.matrix,
set.stats, select.snps, select.inds, GRM
showClass("bed.matrix") # Conversion example data(LCT) x1 <- as(LCT.gen, "bed.matrix") x1 head(x1@ped) head(x1@snps) # the function as.bed.matrix is an alternative x2 <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) x2 head(x2@ped) head(x2@snps)showClass("bed.matrix") # Conversion example data(LCT) x1 <- as(LCT.gen, "bed.matrix") x1 head(x1@ped) head(x1@snps) # the function as.bed.matrix is an alternative x2 <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) x2 head(x2@ped) head(x2@snps)
Compute the Dominance Matrix
DM(x, which.snps, autosome.only = TRUE, chunk = 1L)DM(x, which.snps, autosome.only = TRUE, chunk = 1L)
x |
|
which.snps |
Logical vector, giving which snps to use in the computation. The default is to use all autosomal SNPs |
autosome.only |
If |
chunk |
Parameter for the parallelization: how many SNPs are treated by each task |
The Dominance Matrix (DM) gives for each pair of individuals an estimation of their probability of sharing two alleles Identical By Descent.
It is computed by a moment estimator,
with the matrix with entries
, , according to the
values 0, 1, 2 in the genotype matrix x (here is the
frequency of the alternate allele, and is the number of SNPs
(ncol(x)).
A symmetric square matrix of dimension equal to the number of individuals. Each entry can be interpreted as an estimated probability of sharing two alleles IBD — as it is a moment estimator, the value can (and will) fall outside of the range (0,1).
# load chr2 data set (~10k SNPs in low LD) x <- read.bed.matrix( system.file("extdata", "chr2.bed", package="gaston") ) # Compute Dominance Matrix D <- DM(x) dim(D)# load chr2 data set (~10k SNPs in low LD) x <- read.bed.matrix( system.file("extdata", "chr2.bed", package="gaston") ) # Compute Dominance Matrix D <- DM(x) dim(D)
SNP.rm.duplicates
The SNPs in this data frame are as follows:
Unduplicated SNP
Two duplicated SNPs with identical alleles
Two duplicated SNPs with swapped alleles
Two duplicated SNPs with flipped reference strand
Two duplicated SNPs with swapped alleles and flipped reference strand
Two duplicated SNPs with incompatible alleles
Two duplicated SNPs including one monomorphic SNP (one allele set to "0")
Three duplicated SNPs
Three duplicated SNPs with incompatible alleles
data(dupli)data(dupli)
There are three data objects in the dataset:
dupli.genGenotype matrix
dupli.ped Data frame containing all variables corresponding to a .fam file
dupli.bim Data frame containing all variables corresponding to a .bim file
data(dupli) x <- as.bed.matrix(dupli.gen, fam = dupli.ped, bim = dupli.bim)data(dupli) x <- as.bed.matrix(dupli.gen, fam = dupli.ped, bim = dupli.bim)
Compute the Genetic Relationship Matrix
GRM(x, which.snps, autosome.only = TRUE, chunk = 1L)GRM(x, which.snps, autosome.only = TRUE, chunk = 1L)
x |
|
which.snps |
Logical vector, giving which snps to use in the computation. The default is to use all autosomal SNPs |
autosome.only |
If |
chunk |
Parameter for the parallelization: how many SNPs are treated by each task |
The Genetic Relationship Matrix (GRM) is computed by the formula ,
with the standardized genotype matrix and the number of SNPs
(ncol(x)).
If x is not standardized before this computation, the function
will use standardize(x) <- "p" by default.
The GRM is a symmetric square matrix of dimension equal to the number of individuals. Each entry can be interpreted as an estimated kinship coefficient between individuals, although some authors might disagree. Note in particular that some entries will be negative.
Hervé Perdry and Claire Dandine-Roulland
DM, reshape.GRM, lmm.aireml, lmm.diago, standardize, bed.loadings
# load chr2 data set (~10k SNPs in low LD) x <- read.bed.matrix( system.file("extdata", "chr2.bed", package="gaston") ) # Compute Genetic Relationship Matrix K <- GRM(x) dim(K)# load chr2 data set (~10k SNPs in low LD) x <- read.bed.matrix( system.file("extdata", "chr2.bed", package="gaston") ) # Compute Genetic Relationship Matrix K <- GRM(x) dim(K)
Test if a chromosome id corresponds to an autosome or to X, Y, MT chromosomes
is.autosome(chr) is.chr.x(chr) is.chr.y(chr) is.chr.mt(chr)is.autosome(chr) is.chr.x(chr) is.chr.y(chr) is.chr.mt(chr)
chr |
A vector of chromosome ids |
These functions work by comparing the ids given in parameters with
the options gaston.autosomes, gaston.chr.x, gaston.chr.y,
gaston.chr.mt.
For example, is.autosome(chr) is a short cut for
chr %in% getOption("gaston.autosomes").
A logical vector.
Hervé Perdry
These data have been extracted from the 1000 Genomes data.
The data set contains the genotype matrix LCT.gen, the pedigree matrix LCT.fam and a matrix LCT.bim,
corresponding to 503 individuals of European populations and 607 SNPs on chromosome 2, on a ~300kb segment
containing the Lactase gene. There is also a factor LCT.pop, which gives the population from which each
individual is drawn (CEU = Utah residents of Northern Western European ancestry, FIN = Finnish, GBR = England and Scottland,
IBS = Iberian, TSI = Toscani).
Note that the SNP rs4988235 is associated with lactase persistence / lactose intolerence.
data(LCT)data(LCT)
There are three data objects in the dataset:
LCT.genGenotype matrix
LCT.fam Data frame containing all variables corresponding to a .fam file
LCT.bim Data frame containing all variables corresponding to a .bim file
LCT.popFactor giving the population from which each individual is drawn
The data were obtained from the 1000 Genomes project (see https://www.internationalgenome.org/).
McVean et al, 2012, An integrated map of genetic variation from 1,092 human genomes, Nature 491, 56-65 doi:10.1038/nature11632
data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) x which(x@snps$id == "rs4988235")data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) x which(x@snps$id == "rs4988235")
Compute Linkage Disequilibrium (LD) between given SNPs.
LD(x, lim, lim2, measure = c("r2", "r", "D"), trim = TRUE)LD(x, lim, lim2, measure = c("r2", "r", "D"), trim = TRUE)
x |
|
lim |
Range of SNPs for which the LD is computed |
lim2 |
(Optional) Second range of SNPs (see Details) |
measure |
The LD measure |
trim |
|
If lim2 is missing, the LD is computed between all SNPs with indices between lim[1] and lim[2];
else, the LD is computed between the SNPs in the range given by lim and those in the range given by lim2.
Note that the LD estimates are moment estimates (which are less precise than Maximum Likelihood Estimates).
If standardize(x) = "none", x will be standardized
using x@mu and x@sigma. If standardize(x) = "p", the moment estimates can produce
values outside of the range , hence the parameter trim. We recommend to set
standardize(x) <- "mu" (trimming can still be necessary due to rounding errors).
A matrix of LD values.
Hervé Perdry and Claire Dandine-Roulland
# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute LD ld.x <- LD(x, c(1,ncol(x))) # Plot a tiny part of the LD matrix LD.plot( ld.x[1:20,1:20], snp.positions = x@snps$pos[1:20] )# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute LD ld.x <- LD(x, c(1,ncol(x))) # Plot a tiny part of the LD matrix LD.plot( ld.x[1:20,1:20], snp.positions = x@snps$pos[1:20] )
Construct group of SNPs in LD with 'top associated SNPs'
LD.clump(x, p, r2.threshold, p.threshold, max.dist = 500e3)LD.clump(x, p, r2.threshold, p.threshold, max.dist = 500e3)
x |
|
p |
A vector of p-values, or a data frame including p-values, such as sent back by |
r2.threshold |
The maximum LD (measured by |
p.threshold |
The threshold used to define associated SNPs |
max.dist |
The maximum distance for which the LD is computed |
The p-values provided through argument p are assumed to correspond to the result of an association test with the SNPs of x.
The aim of the function is to construct cluster of SNPs in strong LD with associated SNPs.
The algorithm first seeks the SNP with the lowest p-value (below p.threshold) ; this SNP will be the 'index' of a cluster.
The corresponding cluster is constructed by aggregating SNPs that are in LD (above r2.threshold) with the index. The cluster's name
is the position of the index SNP.
The processus is repeated on the SNPs which are not yet attributed to a cluster, until there is no associated SNP
(ie SNP with a p-value below threshold) left.
The remaining SNPs are attributed to cluster 0.
The LD is computed only for SNP pairs for which distance is inferior to max.dist, expressed in number of bases: above this
distance it is assumed to be null.
If p was a data frame, then the function returns the same data frame with to extra columns, cluster and is.index.
If p was a vector of p-values, it returns a data frame with columns chr, id, pos, p, cluster
and is.index.
# Construct a bed matrix x <- as.bed.matrix(TTN.gen, TTN.fam, TTN.bim) standardize(x) <- "p" # simulate quantitative phenotype with effect of SNPs #108 and #631 beta <- numeric(ncol(x)) beta[c(108,631)] <- 0.5 set.seed(1) y <- x %*% beta + rnorm(nrow(x)) # association test with linear model test <- association.test(x, y, method="lm", response = "quanti") # LD clumping test <- LD.clump(x, test, r2.threshold = 0.25, p.threshold = 1e-8) # use as.factor for a quick-and-dirty cluster colouring on the manhattan plot manhattan(test, col = as.factor(test$cluster), pch = 20)# Construct a bed matrix x <- as.bed.matrix(TTN.gen, TTN.fam, TTN.bim) standardize(x) <- "p" # simulate quantitative phenotype with effect of SNPs #108 and #631 beta <- numeric(ncol(x)) beta[c(108,631)] <- 0.5 set.seed(1) y <- x %*% beta + rnorm(nrow(x)) # association test with linear model test <- association.test(x, y, method="lm", response = "quanti") # LD clumping test <- LD.clump(x, test, r2.threshold = 0.25, p.threshold = 1e-8) # use as.factor for a quick-and-dirty cluster colouring on the manhattan plot manhattan(test, col = as.factor(test$cluster), pch = 20)
Pretty plot of a Linkage Disequilibrium (LD) matrix
LD.plot(LD, snp.positions, max.dist = Inf, depth = nrow(LD), graphical.par = list(mar = c(0,0,0,0)), cex.ld, cex.snp, polygon.par = list(border = "white"), color.scheme = function(ld) rgb(1,1-abs(ld),1-abs(ld)), write.snp.id = TRUE, write.ld = function(ld) sprintf("%.2f", ld), draw.chr = TRUE, above.space = 1 + 2*write.snp.id + draw.chr, below.space = 1, pdf.file, finalize.pdf = TRUE)LD.plot(LD, snp.positions, max.dist = Inf, depth = nrow(LD), graphical.par = list(mar = c(0,0,0,0)), cex.ld, cex.snp, polygon.par = list(border = "white"), color.scheme = function(ld) rgb(1,1-abs(ld),1-abs(ld)), write.snp.id = TRUE, write.ld = function(ld) sprintf("%.2f", ld), draw.chr = TRUE, above.space = 1 + 2*write.snp.id + draw.chr, below.space = 1, pdf.file, finalize.pdf = TRUE)
LD |
A symmetric LD matrix (such as produced by |
snp.positions |
A vector of SNP positions |
max.dist |
Maximal distance above which the LD is not plotted |
depth |
Maximal number of neighbouring SNPs for which the LD is plotted |
graphical.par |
A list of graphical parameters for function |
cex.ld |
The magnification to be used for LD values (if missing, an ad-hoc value is computed) |
cex.snp |
The magnification to be used for SNPs ids (if missing, an ad-hoc value is computed) |
polygon.par |
A list of parameters for function |
color.scheme |
A function to set the background color of a cell |
write.snp.id |
|
write.ld |
|
draw.chr |
|
above.space |
Space above the plot (in user units = height of a cell) |
below.space |
Space below the plot (in user units = height of a cell) |
pdf.file |
The name of a pdf file in which to plot the LD matrix. If missing, current plot device will be used |
finalize.pdf |
|
This function displays a LD plot similar to Haploview plots.
To add anotations to the plot, it is useful to know that each cell has width and height equal
to one user unit, the first cell in the upper row being centered at coordinates (1.5, -0.5).
Hervé Perdry and Claire Dandine-Roulland
# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute LD ld.x <- LD(x, c(1,ncol(x))) # Plot a tiny part of the LD matrix LD.plot( ld.x[1:20,1:20], snp.positions = x@snps$pos[1:20] ) # Customize the plot LD.plot( ld.x[1:20,1:20], snp.positions = x@snps$pos[1:20], graphical.par = list(cex = 1.3, bg = "gray"), polygon.par = list(border = NA), write.ld = NULL ) ## Not run: # Plotting the whole matrix in X11 display is very long (lots of polygons) # but it is ok with a pdf file # (please uncomment to run) #LD.plot(ld.x, snp.positions = x@snps$pos, max.dist = 50e3, write.ld = NULL, pdf.file = "LDAGT.pdf") ## End(Not run)# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute LD ld.x <- LD(x, c(1,ncol(x))) # Plot a tiny part of the LD matrix LD.plot( ld.x[1:20,1:20], snp.positions = x@snps$pos[1:20] ) # Customize the plot LD.plot( ld.x[1:20,1:20], snp.positions = x@snps$pos[1:20], graphical.par = list(cex = 1.3, bg = "gray"), polygon.par = list(border = NA), write.ld = NULL ) ## Not run: # Plotting the whole matrix in X11 display is very long (lots of polygons) # but it is ok with a pdf file # (please uncomment to run) #LD.plot(ld.x, snp.positions = x@snps$pos, max.dist = 50e3, write.ld = NULL, pdf.file = "LDAGT.pdf") ## End(Not run)
Select SNPs in LD below a given threshold.
LD.thin(x, threshold, max.dist = 500e3, beg = 1, end = ncol(x), which.snps, dist.unit = c("bases", "indices", "cM"), extract = TRUE, keep = c("left", "right", "random"))LD.thin(x, threshold, max.dist = 500e3, beg = 1, end = ncol(x), which.snps, dist.unit = c("bases", "indices", "cM"), extract = TRUE, keep = c("left", "right", "random"))
x |
|
threshold |
The maximum LD (measured by |
max.dist |
The maximum distance for which the LD is computed |
beg |
The index of the first SNP to consider |
end |
The index of the last SNP to consider |
which.snps |
Logical vector, giving which SNPs are considerd. The default is to use all SNPs |
dist.unit |
Distance unit in |
extract |
A |
keep |
Which SNP is selected in a pair with LD above |
The SNPs to keep are selected by a greedy algorithm. The LD is computed only for SNP pairs for which distance is inferior to
max.dist, expressed in number of bases if dist.unit = "bases", in number of SNPs if dist.unit = "indices",
or in centiMorgan if dist.unit = "cM".
The argument which.snps allows to consider only a subset of SNPs.
The algorithm tries to keep the largest possible number of SNPs: it is not appropriate to select tag-SNPs.
If extract = TRUE, a bed.matrix extracted from x with SNPs in pairwise LD below the given threshold.
If extract = FALSE, a logical vector of length end - beg + 1, where TRUE indicates that
the corresponding SNPs is selected.
Hervé Perdry and Claire Dandine-Roulland
# Load data data(TTN) x <- as.bed.matrix(TTN.gen, TTN.fam, TTN.bim) # Select SNPs in LD r^2 < 0.4, max.dist = 500 kb y <- LD.thin(x, threshold = 0.4, max.dist = 500e3) y # Verifies that there is no SNP pair with LD r^2 > 0.4 # (note that the matrix ld.y has ones on the diagonal) ld.y <- LD( y, lim = c(1, ncol(y)) ) sum( ld.y > 0.4 )# Load data data(TTN) x <- as.bed.matrix(TTN.gen, TTN.fam, TTN.bim) # Select SNPs in LD r^2 < 0.4, max.dist = 500 kb y <- LD.thin(x, threshold = 0.4, max.dist = 500e3) y # Verifies that there is no SNP pair with LD r^2 > 0.4 # (note that the matrix ld.y has ones on the diagonal) ld.y <- LD( y, lim = c(1, ncol(y)) ) sum( ld.y > 0.4 )
Create a contour plot (superimposed with a heat map)
lik.contour(x, y, z, levels = NULL, nlevels = 11, heat = TRUE, col.heat = NULL, ...)lik.contour(x, y, z, levels = NULL, nlevels = 11, heat = TRUE, col.heat = NULL, ...)
x, y, z
|
As in |
levels |
As in |
nlevels |
As in |
heat |
If |
col.heat |
Vector of heat colors |
... |
Additional arguments to |
This function is a wrapper for contour, with a different method to compute
a default value for levels. If heat = TRUE, a heatmap produced by image is added to the plot.
See contour for details on parameters.
Hervé Perdry and Claire Dandine-Roulland
lmm.diago.likelihood, contour, image
data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix K <- GRM(x) # eigen decomposition of K eiK <- eigen(K) # simulate a phenotype set.seed(1) y <- 1 + lmm.simu(tau = 1, sigma2 = 2, eigenK = eiK)$y # Likelihood TAU <- seq(0.5,2.5,length=30) S2 <- seq(1,3,length=30) lik1 <- lmm.diago.likelihood(tau = TAU, s2 = S2, Y = y, eigenK = eiK) lik.contour(TAU, S2, lik1, heat = TRUE, xlab = "tau", ylab = "sigma^2")data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix K <- GRM(x) # eigen decomposition of K eiK <- eigen(K) # simulate a phenotype set.seed(1) y <- 1 + lmm.simu(tau = 1, sigma2 = 2, eigenK = eiK)$y # Likelihood TAU <- seq(0.5,2.5,length=30) S2 <- seq(1,3,length=30) lik1 <- lmm.diago.likelihood(tau = TAU, s2 = S2, Y = y, eigenK = eiK) lik.contour(TAU, S2, lik1, heat = TRUE, xlab = "tau", ylab = "sigma^2")
Estimate the parameters of a linear mixed model, using Average Information Restricted Maximum Likelihood (AIREML) algorithm.
lmm.aireml(Y, X = matrix(1, nrow = length(Y)), K, EMsteps = 0L, EMsteps_fail = 1L, EM_alpha = 1, min_tau, min_s2 = 1e-06, theta, constraint = TRUE, max_iter = 50L, eps = 1e-05, verbose = getOption("gaston.verbose", TRUE), contrast = FALSE, get.P = FALSE)lmm.aireml(Y, X = matrix(1, nrow = length(Y)), K, EMsteps = 0L, EMsteps_fail = 1L, EM_alpha = 1, min_tau, min_s2 = 1e-06, theta, constraint = TRUE, max_iter = 50L, eps = 1e-05, verbose = getOption("gaston.verbose", TRUE), contrast = FALSE, get.P = FALSE)
Y |
Phenotype vector |
X |
Covariable matrix. By default, a column of ones to include an intercept in the model |
K |
A positive definite matrix or a |
EMsteps |
Number of EM steps ran prior the AIREML |
EMsteps_fail |
Number of EM steps performed when the AIREML algorithm fail to improve the likelihood value |
EM_alpha |
Tweaking parameter for the EM (see Details) |
min_tau |
Minimal value for model parameter |
min_s2 |
Minimal value for model parameter |
theta |
(Optional) Optimization starting point |
constraint |
If |
max_iter |
Maximum number of iterations |
eps |
The algorithm stops when the gradient norm is lower than this parameter |
verbose |
If |
contrast |
If |
get.P |
If |
Estimate the parameters of the following linear mixed model, using AIREML algorithm:
with for and
.
The variance matrices , ..., , are specified through the parameter K.
If EMsteps is positive, the function will use this number of EM steps to compute a better starting point
for the AIREML algorithm. Setting EMsteps to a value higher than max_iter leads to an EM optimization.
It can happen that after an AIREML step, the likelihood did not increase: if this
happens, the functions falls back to EMsteps_fail EM steps. The parameter EM_alpha can be set to
a value higher than to attempt to accelerate EM convergence; this could also result in uncontrolled
behaviour and should be used with care.
After convergence, the function also compute Best Linear Unbiased Predictors (BLUPs) for
and , and an
estimation of the participation of the fixed effects to the variance of .
A named list with members:
sigma2 |
Estimate of the model parameter |
tau |
Estimate(s) of the model parameter(s) |
logL |
Value of log-likelihood |
logL0 |
Value of log-likelihood under the null model (without random effect) |
niter |
Number of iterations done |
norm_grad |
Last computed gradient's norm |
P |
Last computed value of matrix P (see reference) |
Py |
Last computed value of vector Py (see reference) |
BLUP_omega |
BLUPs of random effects |
BLUP_beta |
BLUPs of fixed effects |
varbeta |
Variance matrix for |
varXbeta |
Participation of fixed effects to variance of Y |
If get.P = TRUE, there is an additional member:
P |
The last matrix |
Hervé Perdry and Claire Dandine-Roulland
Gilmour, A. R., Thompson, R., & Cullis, B. R. (1995), Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models, Biometrics, 1440-1450
lmm.diago, logistic.mm.aireml, lmm.simu
# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix standardize(x) <- "p" K <- GRM(x) # Simulate a quantitative genotype under the LMM set.seed(1) y <- 1 + x %*% rnorm(ncol(x), sd = 1)/sqrt(ncol(x)) + rnorm(nrow(x), sd = sqrt(2)) # Estimates estimates <- lmm.aireml(y, K = K, verbose = FALSE) str(estimates)# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix standardize(x) <- "p" K <- GRM(x) # Simulate a quantitative genotype under the LMM set.seed(1) y <- 1 + x %*% rnorm(ncol(x), sd = 1)/sqrt(ncol(x)) + rnorm(nrow(x), sd = sqrt(2)) # Estimates estimates <- lmm.aireml(y, K = K, verbose = FALSE) str(estimates)
Estimate the parameters of a linear mixed model, using the "diagonalization trick".
lmm.diago(Y, X = matrix(1, nrow=length(Y)), eigenK, p = 0, method = c("newton", "brent"), min_h2 = 0, max_h2 = 1, verbose = getOption("gaston.verbose", TRUE), tol = .Machine$double.eps^0.25)lmm.diago(Y, X = matrix(1, nrow=length(Y)), eigenK, p = 0, method = c("newton", "brent"), min_h2 = 0, max_h2 = 1, verbose = getOption("gaston.verbose", TRUE), tol = .Machine$double.eps^0.25)
Y |
Phenotype vector |
X |
Covariable matrix |
eigenK |
Eigen decomposition of |
p |
Number of Principal Components included in the mixed model with fixed effect |
method |
Optimization method to use |
min_h2 |
Minimum admissible value |
max_h2 |
Maximum admissible value |
verbose |
If |
tol |
Accuracy of estimation |
Estimate the parameters of the following linear mixed model, computing the restricted likelihood as in lmm.diago.likelihood,
and using either a Newton algorithm, or Brent algorithm as in optimize:
with and
.
The matrix is given through its eigen decomposition, as produced by eigenK = eigen(K, symmetric = TRUE).
The matrix is the concatenation of the covariable matrix and
of the first eigenvectors of , included in the model with fixed effects.
If the parameter p is a scalar, a list with following elements :
sigma2 |
Estimate of the model parameter |
tau |
Estimate(s) of the model parameter(s) |
Py |
Last computed value of vector Py (see reference) |
BLUP_omega |
BLUPs of random effects |
BLUP_beta |
BLUPs of fixed effects |
Xbeta |
Estimate of |
varbeta |
Variance matrix for |
varXbeta |
Participation of fixed effects to variance of Y |
p |
Number of Principal Components included in the linear mixed model with fixed effect |
If the paramer p is a vector of length > 1, a list of lists as described above,
one for each value in p.
Hervé Perdry and Claire Dandine-Roulland
lmm.diago.likelihood, lmm.aireml, optimize
# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix K <- GRM(x) # eigen decomposition of K eiK <- eigen(K) # simulate a phenotype set.seed(1) y <- 1 + lmm.simu(tau = 1, sigma2 = 2, eigenK = eiK)$y # Estimations R <- lmm.diago(Y = y, eigenK = eiK, p = c(0,10)) str(R)# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix K <- GRM(x) # eigen decomposition of K eiK <- eigen(K) # simulate a phenotype set.seed(1) y <- 1 + lmm.simu(tau = 1, sigma2 = 2, eigenK = eiK)$y # Estimations R <- lmm.diago(Y = y, eigenK = eiK, p = c(0,10)) str(R)
Compute the Restricted or the Full Likelihood of a linear mixed model, using the "diagonalization trick".
lmm.diago.likelihood(tau, s2, h2, Y, X, eigenK, p = 0) lmm.diago.profile.likelihood(tau, s2, h2, Y, X, eigenK, p = 0)lmm.diago.likelihood(tau, s2, h2, Y, X, eigenK, p = 0) lmm.diago.profile.likelihood(tau, s2, h2, Y, X, eigenK, p = 0)
tau |
Value(s) of model parameter (see Details) |
s2 |
Value(s) of model parameter (see Details) |
h2 |
Value(s) of heritability (see Details) |
Y |
Phenotype vector |
X |
Covariable matrix |
eigenK |
Eigen decomposition of |
p |
Number of Principal Components included in the mixed model with fixed effect |
Theses function respectively compute the Restricted and the Profile Likelihood under the linear mixed model
with and
.
The matrix is given through its eigen decomposition, as produced by eigenK = eigen(K, symmetric = TRUE).
The matrix is the concatenation of the covariable matrix and
of the first eigenvectors of , included in the model with fixed effects.
If both tau and s2 (for ) are provided, lmm.diago.likelihood
computes the restricted
likelihood for these values of the parameters; if these parameters are vectors of length ,
then a matrix of likelihood values is computed.
The function lmm.diago.profile.likelihood computes the full likelihood, profiled for .
That is, the value which maximizes the full likelihood for the given values of
and is computed, and then the full likelihood is computed.
If h2 is provided, both functions compute and which
maximizes the likelihood under the constraint ,
and output these values as well as the likelihood value at this point.
If tau and s2 are provided, the corresponding likelihood values.
If tau or s2 are missing, and h2 is provided, a named list with members
tau |
Corresponding values of |
sigma2 |
Corresponding values of |
likelihood |
Corresponding likelihood values |
Hervé Perdry and Claire Dandine-Roulland
lmm.restricted.likelihood, lmm.profile.restricted.likelihood, lmm.diago, lmm.aireml
# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix K <- GRM(x) # eigen decomposition of K eiK <- eigen(K) # simulate a phenotype set.seed(1) y <- 1 + lmm.simu(tau = 1, sigma2 = 2, eigenK = eiK)$y # Likelihood TAU <- seq(0.5,1.5,length=30) S2 <- seq(1,3,length=30) lik1 <- lmm.diago.likelihood(tau = TAU, s2 = S2, Y = y, eigenK = eiK) H2 <- seq(0,1,length=51) lik2 <- lmm.diago.likelihood(h2 = H2, Y = y, eigenK = eiK) # Plotting par(mfrow=c(1,2)) lik.contour(TAU, S2, lik1, heat = TRUE, xlab = "tau", ylab = "sigma^2") lines(lik2$tau, lik2$sigma2) plot(H2, exp(lik2$likelihood), type="l", xlab="h^2", ylab = "likelihood")# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix K <- GRM(x) # eigen decomposition of K eiK <- eigen(K) # simulate a phenotype set.seed(1) y <- 1 + lmm.simu(tau = 1, sigma2 = 2, eigenK = eiK)$y # Likelihood TAU <- seq(0.5,1.5,length=30) S2 <- seq(1,3,length=30) lik1 <- lmm.diago.likelihood(tau = TAU, s2 = S2, Y = y, eigenK = eiK) H2 <- seq(0,1,length=51) lik2 <- lmm.diago.likelihood(h2 = H2, Y = y, eigenK = eiK) # Plotting par(mfrow=c(1,2)) lik.contour(TAU, S2, lik1, heat = TRUE, xlab = "tau", ylab = "sigma^2") lines(lik2$tau, lik2$sigma2) plot(H2, exp(lik2$likelihood), type="l", xlab="h^2", ylab = "likelihood")
Compute the Restricted or the Full Likelihood of a linear mixed model.
lmm.restricted.likelihood(Y, X = matrix(1, nrow = length(Y)), K, tau, s2) lmm.profile.restricted.likelihood(Y, X = matrix(1, nrow = length(Y)), K, h2)lmm.restricted.likelihood(Y, X = matrix(1, nrow = length(Y)), K, tau, s2) lmm.profile.restricted.likelihood(Y, X = matrix(1, nrow = length(Y)), K, h2)
Y |
Phenotype vector |
X |
Covariable matrix |
K |
A positive definite matrix or a |
tau |
Value(s) of parameter(s) |
s2 |
Value of parameter |
h2 |
Value(s) of heritability |
Theses function respectively compute the Restricted and the Profile Likelihood under the linear mixed model
with for and
.
The variance matrices , ..., , are specified through the parameter K.
The parameter tau should be a vector of length .
The function lmm.restricted.likelihood computes the restricted
likelihood for the given values of and .
Whenever , it is similar to lmm.diago.likelihood(tau, s2, Y = Y, X = X, eigenK = eigen(K))
which should be prefered (with a preliminary computation of eigen(K)).
The function lmm.profile.restricted.likelihood computes a profile restricted
likelihood: the values of and which
maximizes the likelihood are computed under the constraint
,
and the profiled likelihood value for these parameters is computed.
Whenever , it is similar to lmm.diago.likelihood(h2 = h2, Y = Y, X = X, eigenK = eigen(K)).
The restricted likelihood value.
Hervé Perdry and Claire Dandine-Roulland
lmm.diago.likelihood, lmm.diago, lmm.aireml
# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix and its eigen decomposition K <- GRM(x) eiK <- eigen(K) # simulate a phenotype set.seed(1) y <- 1 + lmm.simu(tau = 1, sigma2 = 2, eigenK = eiK)$y # compute restricted likelihood for tau = 0.2 and s2 = 0.8 lmm.restricted.likelihood(y, K=K, tau = 0.2, s2 = 0.8) # compute profile restricted likelihood for h2 = 0.2 lmm.profile.restricted.likelihood(y, K=K, h2 = 0.2) # identity with the values computed with the diagonalisation trick lmm.diago.likelihood(tau = 0.2, s2 = 0.8, Y = y, eigenK = eiK) lmm.diago.likelihood(h2 = 0.2, Y = y, eigenK = eiK)# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix and its eigen decomposition K <- GRM(x) eiK <- eigen(K) # simulate a phenotype set.seed(1) y <- 1 + lmm.simu(tau = 1, sigma2 = 2, eigenK = eiK)$y # compute restricted likelihood for tau = 0.2 and s2 = 0.8 lmm.restricted.likelihood(y, K=K, tau = 0.2, s2 = 0.8) # compute profile restricted likelihood for h2 = 0.2 lmm.profile.restricted.likelihood(y, K=K, h2 = 0.2) # identity with the values computed with the diagonalisation trick lmm.diago.likelihood(tau = 0.2, s2 = 0.8, Y = y, eigenK = eiK) lmm.diago.likelihood(h2 = 0.2, Y = y, eigenK = eiK)
Simulate data under a linear mixed model, using the eigen decomposition of the variance matrix.
lmm.simu(tau, sigma2, K, eigenK = eigen(K), X, beta)lmm.simu(tau, sigma2, K, eigenK = eigen(K), X, beta)
tau |
Model parameter |
sigma2 |
Model parameter |
K |
(Optional) A positive symmetric matrix |
eigenK |
Eigen decomposition of |
X |
Covariable matrix |
beta |
Fixed effect vector of covariables |
The data are simulated under the following linear mixed model :
with and
.
The simulation uses only through its eigen decomposition; the parameter
K is therefore optional.
A named list with two members:
y |
Simulated value of |
omega |
Simulated value of |
Hervé Perdry and Claire Dandine-Roulland
# generate a random positive matrix set.seed(1) R <- random.pm(503) # simulate data with a "polygenic component" y <- lmm.simu(0.3, 1, eigenK = R$eigen) str(y)# generate a random positive matrix set.seed(1) R <- random.pm(503) # simulate data with a "polygenic component" y <- lmm.simu(0.3, 1, eigenK = R$eigen) str(y)
Estimate the parameters of a logistic linear mixed model using the Penalized Quasi-Likelihood with an AIREML step for the linear model.
logistic.mm.aireml(Y, X = matrix(1, nrow = length(Y)), K, min_tau, tau, beta, constraint = TRUE, max.iter = 50L, eps = 1e-5, verbose = getOption("gaston.verbose",TRUE), get.P = FALSE, EM = FALSE)logistic.mm.aireml(Y, X = matrix(1, nrow = length(Y)), K, min_tau, tau, beta, constraint = TRUE, max.iter = 50L, eps = 1e-5, verbose = getOption("gaston.verbose",TRUE), get.P = FALSE, EM = FALSE)
Y |
Binary phenotype vector |
X |
Covariable matrix. By default, a column of ones to include an intercept in the model |
K |
A positive definite matrix or a |
min_tau |
Minimal value for model parameter |
tau |
(Optional) Optimization starting point for variance component(s) |
beta |
(Optional) Optimization starting point for fixed effect(s) |
constraint |
If |
max.iter |
Maximum number of iterations |
eps |
The algorithm stops when the gradient norm is lower than this parameter |
verbose |
If |
get.P |
If |
EM |
If |
Estimate the parameters of the following logistic mixed model:
with for .
The estimation is based on the Penalized Quasi-Likelihood with an AIREML step for the linear model
(the algorithm is similar to the algorithm described in Chen et al 2016). If EM = TRUE
the AIREML step is replaced by an EM step. In this case the convergence will be much slower,
you're advised to use a large value of max.iter.
The variance matrices , ..., , are specified through the parameter K.
After convergence, the function also compute Best Linear Unbiased Predictors (BLUPs) for
and .
A named list with members:
tau |
Estimate(s) of the model parameter(s) |
niter |
Number of iterations done |
P |
Last computed value of matrix P (see reference) |
BLUP_omega |
BLUPs of random effects |
BLUP_beta |
BLUPs of fixed effects |
varbeta |
Variance matrix for |
If get.P = TRUE, there is an additional member:
P |
The last matrix |
Gilmour, A. R., Thompson, R., & Cullis, B. R. (1995), Average information REML: an efficient algorithm for variance parameter estimation in linear mixed models, Biometrics, 1440-1450
Chen, Han et al. (2016), Control for Population Structure and Relatedness for Binary Traits in Genetic Association Studies via Logistic Mixed Models, The American Journal of Human Genetics, 653–666
lmm.aireml, lmm.diago, lmm.simu
# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix standardize(x) <- "p" K <- GRM(x) # Simulate a quantitative genotype under the LMM set.seed(1) mu <- 1 + x %*% rnorm(ncol(x), sd = 2)/sqrt(ncol(x)) pi <- 1/(1+exp(-mu)) y <- 1*( runif(length(pi))<pi ) # Estimates estimates <- logistic.mm.aireml(y, K = K, verbose = FALSE) str(estimates)# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) # Compute Genetic Relationship Matrix standardize(x) <- "p" K <- GRM(x) # Simulate a quantitative genotype under the LMM set.seed(1) mu <- 1 + x %*% rnorm(ncol(x), sd = 2)/sqrt(ncol(x)) pi <- 1/(1+exp(-mu)) y <- 1*( runif(length(pi))<pi ) # Estimates estimates <- logistic.mm.aireml(y, K = K, verbose = FALSE) str(estimates)
Draws a Manhattan plot
manhattan(x, bty = "n", chrom.col = c("black", "gray50"), thinning = TRUE, ... )manhattan(x, bty = "n", chrom.col = c("black", "gray50"), thinning = TRUE, ... )
x |
A data.frame with columns named |
bty |
Type of box to draw about the plot. Default is to draw none. |
thinning |
|
chrom.col |
Alternating colors for chromosomes. |
... |
Graphical parameters to be passed to |
If there is only one chromosome value in x$chr, the x-axis will be labeled with the SNP
position. In the general case, the x-axis is labeled with the chromosome name and the color
of the points alternates between the colors in chrom.col.
The default value bty = "n" should give the best result for GWAS Manhattan plots.
See par for other possible values of bty and their meaning.
The thinning procedure suppress some points to avoid generating too heavy graphs. The user
should check that setting thinning = FALSE does not change the final aspect of the
plot.
An invisible copy of x is returned, in which a column coord has been added
if there is more than one chromosome value in x$chr. This column contains the x-coordinates of each
SNP on the plot, and should prove helpful to annotate it.
association.test, qqplot.pvalues,
par, plot.default, points.default
Draws a QQ plot of p-values
qqplot.pvalues(p, col.abline = "red", CB = TRUE, col.CB = "gray80", CB.level = 0.95, thinning = TRUE, ...)qqplot.pvalues(p, col.abline = "red", CB = TRUE, col.CB = "gray80", CB.level = 0.95, thinning = TRUE, ...)
p |
A vector of p-values, or a data.frame with a column named |
col.abline |
Color of the line of slope 1. Set to |
CB |
|
col.CB |
The color of the confidence band. |
CB.level |
The level of the confidence band. |
thinning |
|
... |
Graphical parameters to be passed to |
The QQ plot is on the scale, as is usual when reporting
GWAS results.
The confidence band is not a global confidence region: it is the mere juxtaposition
of confidence intervals for each quantile. Moreover it assumes independance of the
p-values, an hypothesis hich is false for the p-values resulting from an association
test in presence of linkage disequilibrium. Therefore, the probability that some of the
points lie outsite of this band is greater that CB.level.
The thinning procedure suppress some points to avoid generating too heavy graphs. The user
should check that setting thinning = FALSE does not change the final aspect of the
QQ plot.
association.test, manhattan, qqplot,
plot.default, points.default
# a vector of uniform p-values p <- runif(1e6) qqplot.pvalues(p) # if we don't thin the points, using pch = "." is advised qqplot.pvalues(p, pch = ".", cex = 2, thinning = FALSE)# a vector of uniform p-values p <- runif(1e6) qqplot.pvalues(p) # if we don't thin the points, using pch = "." is advised qqplot.pvalues(p, pch = ".", cex = 2, thinning = FALSE)
Generate a random definite positive matrix with specified dimension
random.pm(n, values)random.pm(n, values)
n |
Dimension of matrix |
values |
(Optional) A numeric vector of dimension n : the eigenvalues of the matrix |
If values isn't given, it is chosen (deterministically)
so that the eigenvalues of the resulting matrix are
similar to eigenvalues observed on Genetic Relationship Matrices.
The random matrix is generated as
with a random orthogonal matrix.
A named list with members:
K |
A |
eigen |
The eigen decomposition of |
# generate a random positive matrix set.seed(1) R <- random.pm(500) str(R)# generate a random positive matrix set.seed(1) R <- random.pm(500) str(R)
bed.matrix Create a bed.matrix from a .bed file, and either
a .rds file or a .bim and a .fam file.
read.bed.matrix(basename, bed = paste(basename, ".bed", sep=""), fam = paste(basename, ".fam", sep=""), bim = paste(basename, ".bim", sep=""), rds = paste(basename, ".rds", sep=""), verbose = getOption("gaston.verbose",TRUE))read.bed.matrix(basename, bed = paste(basename, ".bed", sep=""), fam = paste(basename, ".fam", sep=""), bim = paste(basename, ".bim", sep=""), rds = paste(basename, ".rds", sep=""), verbose = getOption("gaston.verbose",TRUE))
basename |
Basename of all files |
bed |
Name of the |
fam |
Name of the |
bim |
Name of the |
rds |
Name of the |
verbose |
If |
The .bed, .fam and .bim files follow the PLINK specifications
(http://zzz.bwh.harvard.edu/plink/binary.shtml).
If a .rds file exists (created by write.bed.matrix),
the .fam and .bim files will be ignored.
To ignore an existing .rds file, set rds = NULL.
If the .bed file does not exist, and basename ends by ".bed",
the function will try to generate a new basename by trimming the extension out. This
allows to write read.bed.matrix("file.bed") instead of read.bed.matrix("file").
If the option gaston.auto.set.stats is set to TRUE (the default),
the function set.stats will be called before returning the bed.matrix,
unless a .rds file is present: in this case, the bed.matrix obtained
is identical to the bed.matrix saved with write.bed.matrix.
Hervé Perdry and Claire Dandine-Roulland
# Read RDS and bed files x <- read.bed.matrix( system.file("extdata", "LCT.bed", package="gaston") ) x# Read RDS and bed files x <- read.bed.matrix( system.file("extdata", "LCT.bed", package="gaston") ) x
bed.matrix from VCF files Create a bed.matrix from a .vcf file.
read.vcf(file, max.snps, get.info = FALSE, convert.chr = TRUE, verbose = getOption("gaston.verbose",TRUE))read.vcf(file, max.snps, get.info = FALSE, convert.chr = TRUE, verbose = getOption("gaston.verbose",TRUE))
file |
The name of the VCF file to read |
max.snps |
The maximal number of SNPs to read |
get.info |
If |
convert.chr |
If |
verbose |
If |
The vcf format is described in https://github.com/samtools/hts-specs
In addition to the usual data in the slot @snps, the bed.matrices produced by read.vcf have
@snps$quality and @snps$filter columns corresponding to the QUAL and FILTER fields in the VCF
file. If get.info = TRUE, an additionnal column @snps$info is added, corresponding to the
INFO field.
The information about individuals in VCF files is incomplete: in the slot @ped, the columns
@ped$famid and @ped$id will both contain the sample id; sex and phenotypes will be set
to unknown.
The function currently assumes that the GT field is the first field in the genotypes format.
If it is not the case, the variants are discarded.
Hervé Perdry and Claire Dandine-Roulland
## Read vcf file (from file name) filepath <-system.file("extdata", "LCT.vcf.gz", package="gaston") x1 <- read.vcf( filepath ) x1## Read vcf file (from file name) filepath <-system.file("extdata", "LCT.vcf.gz", package="gaston") x1 <- read.vcf( filepath ) x1
Reshapes a GRM into a data frame listing relationship of (possibly all) pairs of individuals. Options are provided to specify ranges of relationship values to include or exclude. This is useful in the Quality Control process.
reshape.GRM(K, include = c(-Inf, +Inf), exclude)reshape.GRM(K, include = c(-Inf, +Inf), exclude)
K |
A symmetric matrix (such as produced by |
include |
Range of values to include (default is to include all values) |
exclude |
Range of values to exclude (default it to exclude nothing) |
The relationship between individuals and is the coefficient
in the matrix . The functions lists all pair with and
in the range defined by include and outside the range defined by exclude.
A data frame with three columns named i, j, k.
Hervé Perdry and Claire Dandine-Roulland
# load chr2 data set (~10k SNPs in low LD) x <- read.bed.matrix( system.file("extdata", "chr2.bed", package="gaston") ) # Compute Genetic Relationship Matrix K <- GRM(x) # List all pairs if individuals with a relationship above 0.07 pairs <- reshape.GRM(K, exclude = c(-Inf, 0.07)) # Exclude first individual from each such pair x1 <- x[ -pairs$i, ]# load chr2 data set (~10k SNPs in low LD) x <- read.bed.matrix( system.file("extdata", "chr2.bed", package="gaston") ) # Compute Genetic Relationship Matrix K <- GRM(x) # List all pairs if individuals with a relationship above 0.07 pairs <- reshape.GRM(K, exclude = c(-Inf, 0.07)) # Exclude first individual from each such pair x1 <- x[ -pairs$i, ]
Score Test for association between covariates and phenotype.
score.fixed.linear(x, Y, X = matrix(1, length(Y)), K, ...) score.fixed.logistic(x, Y, X = matrix(1, length(Y)), K, ...)score.fixed.linear(x, Y, X = matrix(1, length(Y)), K, ...) score.fixed.logistic(x, Y, X = matrix(1, length(Y)), K, ...)
x |
A matrix of covariates |
Y |
The phenotype vector |
X |
A covariable matrix. The default is a column vector of ones, to include an intercept in the model |
K |
A positive definite matrix or a |
... |
Optional arguments used to fit null model in |
The function score.fixed.linear considers the linear mixed model
whereas the score.fixed.logistic function considers the following logistic model
with where are Genetic Relationship Matrix (GRM),
and fixed effects and .
The two functions give score test for
: vs : .
In this aim, all parameters under null model are estimated with lmm.aireml or logistic.mm.aireml.
A named list of values:
score |
Estimated score |
p |
The corresponding p-value |
log.p |
The logarithm of corresponding p-value |
Hervé Perdry and Claire Dandine-Roulland
lmm.aireml, logistic.mm.aireml
# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) standardize(x) <- "p" # Calculate GRM et its eigen decomposition k <- GRM(x) eig <- eigen(k) eig$values <- round(eig$values, 5) # generate covariate matrix set.seed(1) X <- cbind( rbinom(nrow(x), 1, prob=1/2), rnorm(nrow(x)) ) # simulate quantitative phenotype with polygenic component and covariate effects y <- X %*% c(-1,0.5) + lmm.simu(0.3,1,eigenK=eig)$y t <- score.fixed.linear(X, y, K=k, verbose=FALSE) str(t) # simulate binary phenotype with polygenic component and covariate effects mu <- X %*% c(-1,0.5) + lmm.simu(1, 0, eigenK=eig)$y pi <- 1/(1+exp(-mu)) y <- 1*( runif(length(pi))<pi ) tt <- score.fixed.logistic(X, y, K=k, verbose=FALSE) str(tt)# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) standardize(x) <- "p" # Calculate GRM et its eigen decomposition k <- GRM(x) eig <- eigen(k) eig$values <- round(eig$values, 5) # generate covariate matrix set.seed(1) X <- cbind( rbinom(nrow(x), 1, prob=1/2), rnorm(nrow(x)) ) # simulate quantitative phenotype with polygenic component and covariate effects y <- X %*% c(-1,0.5) + lmm.simu(0.3,1,eigenK=eig)$y t <- score.fixed.linear(X, y, K=k, verbose=FALSE) str(t) # simulate binary phenotype with polygenic component and covariate effects mu <- X %*% c(-1,0.5) + lmm.simu(1, 0, eigenK=eig)$y pi <- 1/(1+exp(-mu)) y <- 1*( runif(length(pi))<pi ) tt <- score.fixed.logistic(X, y, K=k, verbose=FALSE) str(tt)
Test if a variance component is significaly different from 0 using score test in a Linear or Logistic Mixed Model.
score.variance.linear(K0, Y, X = matrix(1, length(Y)), K, acc_davies=1e-10, ...) score.variance.logistic(K0, Y, X = matrix(1, length(Y)), K, acc_davies=1e-10, ...)score.variance.linear(K0, Y, X = matrix(1, length(Y)), K, acc_davies=1e-10, ...) score.variance.logistic(K0, Y, X = matrix(1, length(Y)), K, acc_davies=1e-10, ...)
K0 |
A positive definite matrix |
Y |
The phenotype vector |
X |
A covariate matrix. The default is a column vector of ones, to include an intercept in the model |
K |
A positive definite matrix or a |
acc_davies |
Accuracy in Davies method used to compute p-value |
... |
Optional arguments used to fit null model with |
In score.variance.linear, we consider the linear mixed model
or, in score.variance.logistic, we consider the following logistic model
with , ,
.
and are Genetic Relationship Matrix (GRM).
score.variance.linear and score.variance.logistic functions permit to test
with, for linear mixed model, the score
or, for logistic mixed model, the score
where is the last matrix computed in the optimization process for null model and the vector of fitted values under null logistic model.
The associated p-value is computed with Davies method.
In this aim, all parameters under null model are estimated with lmm.aireml or logistic.mm.aireml.
The p-value corresponding to the estimated score is computed using Davies method implemented in 'CompQuadForm' R package.
A named list of values:
score |
Estimated score |
p |
The corresponding p-value |
Hervé Perdry and Claire Dandine-Roulland
Davies R.B. (1980) Algorithm AS 155: The Distribution of a Linear Combination of chi-2 Random Variables, Journal of the Royal Statistical Society. Series C (Applied Statistics), 323-333
lmm.aireml, logistic.mm.aireml
# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) standardize(x) <- "p" # Calculate GRM et its eigen decomposition K0 <- GRM(x) eig <- eigen(K0) eig$values <- round(eig$values, 5) # generate an other positive matrix (to play the role of the second GRM) set.seed(1) R <- random.pm(nrow(x)) # simulate quantitative phenotype with two polygenic components y <- lmm.simu(0.1,1,eigenK=eig)$y + lmm.simu(0.2,0,eigenK=R$eigen)$y t <- score.variance.linear(K0, y, K=R$K, verbose=FALSE) str(t) # simulate binary phenotype with two polygenic components mu <- lmm.simu(0.1,0.5,eigenK=eig)$y + lmm.simu(0.2,0,eigenK=R$eigen)$y pi <- 1/(1+exp(-mu)) y <- 1*(runif(length(pi))<pi) tt <- score.variance.logistic(K0, y, K=R$K, verbose=FALSE) str(tt)# Load data data(AGT) x <- as.bed.matrix(AGT.gen, AGT.fam, AGT.bim) standardize(x) <- "p" # Calculate GRM et its eigen decomposition K0 <- GRM(x) eig <- eigen(K0) eig$values <- round(eig$values, 5) # generate an other positive matrix (to play the role of the second GRM) set.seed(1) R <- random.pm(nrow(x)) # simulate quantitative phenotype with two polygenic components y <- lmm.simu(0.1,1,eigenK=eig)$y + lmm.simu(0.2,0,eigenK=R$eigen)$y t <- score.variance.linear(K0, y, K=R$K, verbose=FALSE) str(t) # simulate binary phenotype with two polygenic components mu <- lmm.simu(0.1,0.5,eigenK=eig)$y + lmm.simu(0.2,0,eigenK=R$eigen)$y pi <- 1/(1+exp(-mu)) y <- 1*(runif(length(pi))<pi) tt <- score.variance.logistic(K0, y, K=R$K, verbose=FALSE) str(tt)
bed.matrix Returns subset of individuals satisfying a condition.
select.inds(x, condition)select.inds(x, condition)
x |
|
condition |
Condition used to select individuals |
The conditions can involve global variables and all variables defined
in the data frame x@ped, in particular
famid, id, father, mother, sex, pheno
If basic stats have been computed (see set.stats),
N0, N1, N2, NAs, callrate, etc.
If some condition evaluate to NA (e.g. sex == 1 when sex is undefined for some individuals),
a warning is issued and the corresponding individuals are removed.
A bed.matrix similar to x, containing the selected individuals only
Hervé Perdry and Claire Dandine-Roulland
# Load data data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) # Select individuals with a call rate > 95% # and more than 5% of heterozygous genotypes y <- select.inds(x, callrate > 0.95 & N1/(N0+N1+N2) > 0.05) y# Load data data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) # Select individuals with a call rate > 95% # and more than 5% of heterozygous genotypes y <- select.inds(x, callrate > 0.95 & N1/(N0+N1+N2) > 0.05) y
bed.matrix Returns subset of SNPs satisfying a condition.
select.snps(x, condition)select.snps(x, condition)
x |
|
condition |
Condition used to select SNPs |
The conditions can involve global variables and all variables defined
in the data frame x@snps, in particular
chr, id, dist, pos, A1, A2
If basic stats have been computed (see set.stats), N0, N1, N2, NAs, callrate, maf, hz, etc.
If Hardy-Weinberg Equilibrium test has been performed (see set.hwe), hwe.
If some condition evaluate to NA (e.g. maf > 0 when maf is undefined for some SNPs),
a warning is issued and the corresponding SNPs are removed.
A bed.matrix similar to x, containing the selected SNPs only
Hervé Perdry and Claire Dandine-Roulland
select.snps, set.stats, set.hwe
# Load data data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) # Select SNPs with a maf > 5% y <- select.snps(x, maf > 0.05) y# Load data data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) # Select SNPs with a maf > 5% y <- select.snps(x, maf > 0.05) y
Returns an updated bed.matrix with genetic
distances in centimorgan computed from the variant positions
set.dist(x, map, verbose = getOption("gaston.verbose", TRUE))set.dist(x, map, verbose = getOption("gaston.verbose", TRUE))
x |
|
map |
The genetic map, given by a list of data frames (see Details) |
verbose |
If |
A map is a list of data frames, with names corresponding to chromosomes.
Each of these data frames must have columns pos and dist corresponding
to positions in bp and cM, respectively.
Such maps are too large to be included in a CRAN package. You can get two genetic
maps for the Human Genome (build 36 and 37) in the package HumanGeneticMap
on GitHub.
To install this package, run
install.packages("HumanGeneticMap", repos="https://genostats.github.io/R/")
You can then use this function with set.dist(x, HumanGeneticMap::genetic.map.b36)
for example, for positions on the build 36. Use map = HumanGeneticMap::genetic.map.b37)
for the build 37.
A bed.matrix similar to x, with updated values in x@snps$dist.
Returns an updated bed.matrix with a new variable for the genomic sex
of each individual.
set.genomic.sex(x, plot = FALSE, verbose = getOption("gaston.verbose",TRUE))set.genomic.sex(x, plot = FALSE, verbose = getOption("gaston.verbose",TRUE))
x |
|
plot |
If |
verbose |
If |
For each individual, the function uses the hetorozygosity rate for SNPs on X chromosome,
and the call rate for SNPs on the Y chromosomes (both statistics computed by set.stats),
to cluster the individuals using kmeans.
If plot = TRUE, a plot is produced with the two variables used and the clusters
determined by kmeans.
A bed.matrix similar to x, with a new variable x@ped$genomic.sex
containing the genomic sex for each individual.
Hervé Perdry
Returns an updated bed.matrix with a new variable for the -values of an
Hardy-Weinberg Equilibrium test.
set.hwe(x, method = c("chisquare", "exact"), verbose = getOption("gaston.verbose", TRUE))set.hwe(x, method = c("chisquare", "exact"), verbose = getOption("gaston.verbose", TRUE))
x |
|
method |
The method to use, either "chisquare" or "exact" |
verbose |
If |
Two tests of Hardy-Weinberg Equilibrium are proposed:
if method = "chisquare", the good old Chi-square test
if method = "exact", Haldane's exact test (see Wigginton et al)
The function set.stats will be called first if necessary.
The -value is set to for SNPs on chromosomes Y and MT. For SNPs on
chromosomes X, currently, the test is performed using only the genotypic counts of women.
A bed.matrix similar to x, with a new variable x@snps$hwe
containing the -values for each SNP.
Hervé Perdry and Claire Dandine-Roulland
Wigginton, J. E., Cutler, D. J., & Abecasis, G. R. (2005). A note on exact tests of Hardy-Weinberg equilibrium. The American Journal of Human Genetics, 76(5), 887-893
# Load data data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) # Compute Hardy-Weinberg p-values x <- set.hwe(x) head( x@snps[,c("id","hwe")] )# Load data data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) # Compute Hardy-Weinberg p-values x <- set.hwe(x) head( x@snps[,c("id","hwe")] )
bed.matrix Return an updated bed.matrix with new variables for
several basic statistics.
set.stats(x, set.p = TRUE, set.mu_sigma = TRUE, verbose = getOption("gaston.verbose",TRUE)) set.stats.snps(x, set.p = TRUE, set.mu_sigma = TRUE, verbose = getOption("gaston.verbose",TRUE)) set.stats.ped(x, verbose = getOption("gaston.verbose",TRUE))set.stats(x, set.p = TRUE, set.mu_sigma = TRUE, verbose = getOption("gaston.verbose",TRUE)) set.stats.snps(x, set.p = TRUE, set.mu_sigma = TRUE, verbose = getOption("gaston.verbose",TRUE)) set.stats.ped(x, verbose = getOption("gaston.verbose",TRUE))
x |
|
set.p |
If |
set.mu_sigma |
If |
verbose |
If |
set.stats is called by default by all functions that create a bed.matrix, unless
the global option gaston.auto.set.stats is FALSE (cf example below).
set.stats and set.stats.ped update x@ped, adding the following variables:
N0, N1, N2 and NAs give for each individual the number of
autosomal SNPs with a genotype equal to 0, 1, 2 and missing, respectively
N0.x, N1.x, N2.x and NAs.x idem for chromosome X
N0.y, N1.y, N2.y and NAs.y idem for chromosome Y
N0.mt, N1.mt, N2.mt and NAs.mt idem for mitochondrial SNPs
callrate, callrate.x, callrate.y, callrate.mt
is the individual callrate for autosomal, X, Y, mitochondrial SNPs
hz, hz.x, hz.y, hz.mt is the individual heterozygosity
for autosomal, X, Y, mitochondrial SNPs
set.stats and set.stats.snps update x@snps, adding the following variables:
N0, N1, N2 and NAs give for each SNP the number of individuals
with a genotype equal to 0, 1, 2 and missing, respectively
N0.f, N1.f, N2.f and NAs.f give, only for SNPs on chromosome X,
the number of female individuals with a genotype equal to 0, 1, 2 and missing, respectively
callrate is the SNP callrate (for Y linked SNPs, the callrate is computed usin
males only).
maf is the Minor Allele Frequency
hz is the SNP heterozygosity (for X linked SNPs, the heterozygosity is computed
using females only).
If set.p = TRUE, x@p is updated with the alternate allele frequency.
If set.mu_sigma = TRUE, x@mu is updated with the genotype mean (equal to 2*x@p)
and x@sigma with the genotype standard deviation (should be approximately sqrt(2*x@p*(1-x@p))
under Hardy-Weinberg Equilibrium).
A bed.matrix similar to x, with slots updated as described above.
Hervé Perdry and Claire Dandine-Roulland
# Disable auto set stats : options(gaston.auto.set.stats = FALSE) # Load data data(TTN) x <- as.bed.matrix(TTN.gen, TTN.fam, TTN.bim) str(x@ped) str(x@snps) # Compute statistics x <- set.stats(x) str(x@ped) str(x@snps) # restore default behavior options(gaston.auto.set.stats = TRUE)# Disable auto set stats : options(gaston.auto.set.stats = FALSE) # Load data data(TTN) x <- as.bed.matrix(TTN.gen, TTN.fam, TTN.bim) str(x@ped) str(x@snps) # Compute statistics x <- set.stats(x) str(x@ped) str(x@snps) # restore default behavior options(gaston.auto.set.stats = TRUE)
Determines which SNPs are duplicates of previous SNPs and returns their indices.
SNP.duplicated(x, by = "chr:pos")SNP.duplicated(x, by = "chr:pos")
x |
A bed.matrix or a data.frame |
by |
The criterium used to determined if SNP is duplicated. |
When x is a bed.matrix, the data.frame x@bed will be used.
The columns that will be taken in consideration
Are id, chr, pos, A1, and A2. Not all columns
are mandatory, depending on the value of by.
The possible values for by are "chr:pos", "chr:pos:alleles", "id",
"id:chr:pos" and "id:chr:pos:alleles".
The default is by = "chr:pos", which means that two SNPs are considered as duplicated if they have
same chr and pos values.
Currently, when using a criterium involving alleles, this function does not consider the possibility of alleles swaps or reference strand flips.
An integer vector of indices of SNPs which are duplicates of previously seen SNPs.
Returns a vector of the positions of (first) SNP matching of its first argument in its second.
SNP.match(x, table, by = "chr:pos:alleles")SNP.match(x, table, by = "chr:pos:alleles")
x |
A bed.matrix or a data.frame |
table |
A bed.matrix or a data.frame |
by |
The criterium used to matchSNPs |
When x is a bed.matrix, the data.frame x@bed will be used; the
same holds for table. The columns that will be taken in consideration
are id, chr, pos, A1, and A2. Not all columns
are mandatory (see below).
The matching criterium is specified by parameter by.
There are 5 possible criteria : (i) matching by chromosome and position
with by = "chr:pos", (ii) matching by chromosome, position, and alleles
with by = "chr:pos:alleles", (iii) matching by id with by = "id",
(iv) matching by id, chromosome and position with by = "id:chr:pos",
and (v) matching by id, chromosome, position and alleles with by = "id:chr:pos:alleles".
For each SNP in x, the function looks for the position of the first
matching SNP in table. If alleles are included in the matching criterium
(ie if allele columns A1 and A2 are present in x), the function
also checks for SNP matching with swapped alleles (a SNP A/C would match a
SNP C/A), or with reference strand flipped (i.e. a SNP A/C would match a SNP T/G)
or both (a SNP A/C would match a SNP G/T).
This function should prove useful for data set merging.
A named list with one or three members, depending on whether alleles are included in the matching criterium.
index |
An integer vector giving the position of first match in |
swap |
A logical vector indicating whether the match is with swapped alleles |
flip |
A logical vector indicating whether the match is with flipped strand |
Remove duplicated SNPs, taking into account possible genotype mismatches
SNP.rm.duplicates(x, by = "chr:pos", na.keep = TRUE, incomp.rm = TRUE)SNP.rm.duplicates(x, by = "chr:pos", na.keep = TRUE, incomp.rm = TRUE)
x |
A bed.matrix |
by |
The criterium used to determine duplicates |
na.keep |
If |
incomp.rm |
If |
Positions of duplicated SNPs are determined using SNP.duplicated
using parameter by (we recommend to use "chr:pos", the default).
Then the function considers the possibility of alleles swaps or reference strand flips.
In case of allele incompatibility, the SNPs can be removed or not (according to incomp.rm
parameter).
When alleles can be matched, only one of the two SNPs is conserved. If there are
genotype incompatibilities between the duplicates for some individuals, these genotypes are set
to NA. The parameter na.keep settles the case of genotypes missing in one
of the SNPs.
Moreover the function takes special care of SNP with possible alleles "0".
This case occurs for monomorphic SNPs, when data are read from a .ped file; for
example, a whole column of A A's will result in a SNP with alleles "A" and
"0". If there's a duplicate of the SNP with a few, says, A C's in it,
it will have alleles "A" and "C". In that case, SNP.duplicated
with by = "chr:pos:alleles" will not consider these SNPs as duplicates.
A bed.matrix without duplicated SNPs.
SNP.match, SNP.duplicated, dupli
# Use example data of 10 individuals with 7 duplicated SNPs data(dupli) x <- as.bed.matrix(dupli.gen, fam = dupli.ped, bim = dupli.bim) # There are any duplicated positions: dupli.bim x1 <- SNP.rm.duplicates(x) # By default (na.keep = TRUE), as soon as the genotype is missing # in one of the SNPs it is set to missing # (here looking at duplicated SNPs 2a and 2b) as.matrix(x[,2:3]) as.matrix(x1[,2]) # With na.keep = FALSE x2 <- SNP.rm.duplicates(x, na.keep = FALSE) as.matrix(x2[,2]) # Let's examinate SNP 3.a and 3.b (swapped alleles) as.matrix(x[,4:5]) as.matrix(x1[,3]) as.matrix(x2[,3]) # and so on... (see also ?dupli)# Use example data of 10 individuals with 7 duplicated SNPs data(dupli) x <- as.bed.matrix(dupli.gen, fam = dupli.ped, bim = dupli.bim) # There are any duplicated positions: dupli.bim x1 <- SNP.rm.duplicates(x) # By default (na.keep = TRUE), as soon as the genotype is missing # in one of the SNPs it is set to missing # (here looking at duplicated SNPs 2a and 2b) as.matrix(x[,2:3]) as.matrix(x1[,2]) # With na.keep = FALSE x2 <- SNP.rm.duplicates(x, na.keep = FALSE) as.matrix(x2[,2]) # Let's examinate SNP 3.a and 3.b (swapped alleles) as.matrix(x[,4:5]) as.matrix(x1[,3]) as.matrix(x2[,3]) # and so on... (see also ?dupli)
bed.matrix Evaluate a condition and return logical vector or indices
test.snps(x, condition, na.to.false = TRUE) test.inds(x, condition, na.to.false = TRUE) which.snps(x, condition) which.inds(x, condition)test.snps(x, condition, na.to.false = TRUE) test.inds(x, condition, na.to.false = TRUE) which.snps(x, condition) which.inds(x, condition)
x |
|
condition |
Condition used to select SNPs |
na.to.false |
If |
The conditions can involve global variables and all variables defined
in the data frame x@snps, in particular for test.snps and which.snps
chr, id, dist, pos, A1, A2
If basic stats have been computed (see set.stats), N0, N1, N2, NAs, callrate, maf, hz, etc.
If Hardy-Weinberg Equilibrium test has been performed (see set.hwe), hwe.
and for test.inds and which.inds
famid, id, father, mother, sex, pheno
If basic stats have been computed (see set.stats),
N0, N1, N2, NAs, callrate, etc.
test.snps and test.inds return a logical vector of length ncol(x) and nrow(x) respectively. which.snps(x, condition) is
equivalent to which(test.snps(x, condition)) and which.inds(x, condition) to which(test.inds(x, condition)).
select.snps, select.inds, set.stats, set.hwe
# Load data data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) # SNPs and individuals with a callrate < 100% w <- test.snps(x, callrate < 1) table(w) which.snps(x, callrate < 1) which.inds(x, callrate < 1)# Load data data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) # SNPs and individuals with a callrate < 100% w <- test.snps(x, callrate < 1) table(w) which.snps(x, callrate < 1) which.inds(x, callrate < 1)
These data have been extracted from the 1000 Genomes data.
The data set contains the genotype matrix TTN.gen, the pedigree matrix TTN.fam and a matrix TTN.bim,
corresponding to 503 individuals of European populations and 733 SNPs on chromosome 2, on a ~600kb segment
containing the Titin gene. There is also a factor TTN.pop, which gives the population from which each
individual is drawn (CEU = Utah residents of Northern Western European ancestry, FIN = Finnish, GBR = England and Scottland,
IBS = Iberian, TSI = Toscani).
data(TTN)data(TTN)
There are three data objects in the dataset:
TTN.genGenotype matrix
TTN.fam Data frame containing all variables corresponding to a .fam file
TTN.bim Data frame containing all variables corresponding to a .bim file
TTN.popFactor giving the population from which each individual is drawn
The data were obtained from the 1000 Genomes project (see https://www.internationalgenome.org/).
McVean et al, 2012, An integrated map of genetic variation from 1,092 human genomes, Nature 491, 56-65 doi:10.1038/nature11632
data(TTN) x <- as.bed.matrix(TTN.gen, TTN.fam, TTN.bim) xdata(TTN) x <- as.bed.matrix(TTN.gen, TTN.fam, TTN.bim) x
bed.matrix Save a bed.matrix in several files
write.bed.matrix(x, basename, bed = paste(basename, ".bed", sep=""), fam = paste(basename, ".fam", sep=""), bim = paste(basename, ".bim", sep=""), rds = paste(basename, ".rds", sep=""))write.bed.matrix(x, basename, bed = paste(basename, ".bed", sep=""), fam = paste(basename, ".fam", sep=""), bim = paste(basename, ".bim", sep=""), rds = paste(basename, ".rds", sep=""))
x |
|
basename |
Basename of all files |
bed |
Name of the |
fam |
Name of the |
bim |
Name of the |
rds |
Name of the |
If any of bed, fam, bim and rds is NULL,
the corresponding file will not be written.
The .fam and .bim files are useful for reading files with other softwares.
The .rds file can be read by read.bed.matrix.
The .bed, .fam and .bim files follow the PLINK specifications
(http://zzz.bwh.harvard.edu/plink/binary.shtml).
Hervé Perdry and Claire Dandine-Roulland
# Load data data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) # Write object in LCT.bed and LCT.RData ## Not run: write.bed.matrix(x, "LCT") ## End(Not run)# Load data data(LCT) x <- as.bed.matrix(LCT.gen, LCT.fam, LCT.bim) # Write object in LCT.bed and LCT.RData ## Not run: write.bed.matrix(x, "LCT") ## End(Not run)