iterativeRUV: Remove unwanted variation from a gene expression matrix using...

In RUVnormalize: RUV for normalization of expression array data

Description

The function takes as input a gene expression matrix as well as the index of negative control genes and replicate samples. It estimates and remove unwanted variation from the gene expression. The major difference with naiveRandRUV and naiveReplicateRUV is that iterativeRUV jointly estimates the factor of interest and the unwanted variation term. It does so iteratively, by estimating each term using the current estimate of the other one.

Usage

iterativeRUV(Y, cIdx, scIdx=NULL, paramXb, k, nu.coeff=0, cEps=1e-08, maxIter=30,
  Wmethod="svd", Winit=NULL, wUpdate=maxIter + 1, tol=1e-6)

Arguments

Y	Expression matrix where the rows are the samples and the columns are the genes.
cIdx	Column index of the negative control genes in Y, for estimation of unwanted variation.
scIdx	Matrix giving the set of replicates. Each row is a set of arrays corresponding to replicates of the same sample. The number of columns is the size of the largest set of replicates, and the smaller sets are padded with -1 values. For example if the sets of replicates are (1,11,21), (2,3), (4,5), (6,7,8), the scIdx should be 1 11 21 2 3 -1 4 5 -1 6 7 8
paramXb	A list containing parameters for the estimation of the term of interest: K corresponds to the rank of X. lambda is the regularization parameter. Large values of lambda lead to sparser, more shrunk estimates of beta. D, batch, iter and mode should not be modified unless you are familiar with sparse dictionary learning algorithms.
k	Desired rank for the estimated unwanted variation term. The returned rank may be lower if the replicate arrays and control genes did not contain a signal of rank k.
nu.coeff	Regularization parameter for the unwanted variation.
cEps	tolerance for relative changes of Wa and Xb estimators at each step. When both get smaller than cEps, the iterations stop.
maxIter	Maximum number of iterations.
Wmethod	'svd' or 'rep', depending whether W is estimated from control genes or replicate samples.
Winit	Optionally provides an initial value for W.
wUpdate	Number of iterations between two updates of W. By default, W is never updated. Make sure that enough iterations are done after the last update of W. E.g, setting W to maxIter will only allow for one iteration of estimating alpha given (Xb, W) and no re-estimation of Xb.
tol	Smallest ratio allowed between a squared singular value of Y[, cIdx] and the largest of these squared singular values. All smaller singular values are discarded.

Details

In terms of model, the rank k can be thought of as the number of independent sources of unwanted variation in the data (i.e., if one source is a linear combination of other sources, it does not increase the rank). The ridge nu.coeff should be inversely proportional to the (expected) magnitude of the unwanted variation.

In practice, even if the real number of independent sources of unwanted variation (resp. their magnitude) is known, using a smaller k (resp., larger ridge) could yield better corrections because one may not have enough samples to effectively estimate all the effects.

More intuition and guidance on the practical choice of these parameters are available in the paper (http://biostatistics.oxfordjournals.org/content/17/1/16.full) and its supplement (http://biostatistics.oxfordjournals.org/content/suppl/2015/08/17/kxv026.DC1/kxv026supp.pdf). In particular: - Equation 2.3 in the manuscript gives an interpretation of the ridge parameter in terms of a probabilistic model. - Section 5.1 of the manuscript provides guidelines to select both parameters on real data. - Section 3 of the supplement compares the effect of reducing the rank and increasing the ridge. - Section 4 of the supplement gives a detailed discussion of how to select the ridge parameter on a real example.

Value

A list containing the following terms:

X, b	if p is not NULL, contains an estimate of the factor of interest (X) and its effect (beta) obtained using rank-p restriction of the SVD of Y - W alpha.
W, a	Estimates of the unwanted variation factors (W) and their effect (alpha).
cY	The corrected expression matrix Y - W alpha.

Examples

if(require('RUVnormalizeData') && require('spams')){
    ## Load the spams library
    library(spams)
    
    ## Load the data
    data('gender', package='RUVnormalizeData')
    
    Y <- t(exprs(gender))
    X <- as.numeric(phenoData(gender)$gender == 'M')
    X <- X - mean(X)
    X <- cbind(X/(sqrt(sum(X^2))))
    chip <- annotation(gender)
    
    ## Extract regions and labs for plotting purposes
    lregions <- sapply(rownames(Y),FUN=function(s) strsplit(s,'_')[[1]][2])
    llabs <- sapply(rownames(Y),FUN=function(s) strsplit(s,'_')[[1]][3])
    
    ## Dimension of the factors
    m <- nrow(Y)
    n <- ncol(Y)
    p <- ncol(X)
    
    Y <- scale(Y, scale=FALSE) # Center gene expressions
    
    cIdx <- which(featureData(gender)$isNegativeControl) # Negative control genes
    
    ## Prepare plots
    annot <- cbind(as.character(sign(X)))
    colnames(annot) <- 'gender'
    plAnnots <- list('gender'='categorical')
    lab.and.region <- apply(rbind(lregions, llabs),2,FUN=function(v) paste(v,collapse='_'))
    gender.col <- c('-1' = "deeppink3", '1' = "blue")
    
    ## Remove platform effect by centering.
    
    Y[chip=='hgu95a.db',] <- scale(Y[chip=='hgu95a.db',], scale=FALSE)
    Y[chip=='hgu95av2.db',] <- scale(Y[chip=='hgu95av2.db',], scale=FALSE)
    
    ## Number of genes kept for clustering, based on their variance
    nKeep <- 1260
    
    ## Prepare control samples
    
    scIdx <- matrix(-1,84,3)
    rny <- rownames(Y)
    added <- c()
    c <- 0
    
    ## Replicates by lab
    for(r in 1:(length(rny) - 1)){
        if(r %in% added)
            next
        c <- c+1
        scIdx[c,1] <- r
        cc <- 2
        for(rr in seq(along=rny[(r+1):length(rny)])){
            if(all(strsplit(rny[r],'_')[[1]][-3] ==  strsplit(rny[r+rr],'_')[[1]][-3])){
                scIdx[c,cc] <- r+rr
                cc <- cc+1
                added <- c(added,r+rr)
            }
        }   
    }
    scIdxLab <- scIdx
    
    scIdx <- matrix(-1,84,3)
    rny <- rownames(Y)
    added <- c()
    c <- 0
    
    ## Replicates by region
    for(r in 1:(length(rny) - 1)){
        if(r %in% added)
            next
        c <- c+1
        scIdx[c,1] <- r
        cc <- 2
        for(rr in seq(along=rny[(r+1):length(rny)])){
            if(all(strsplit(rny[r],'_')[[1]][-2] ==  strsplit(rny[r+rr],'_')[[1]][-2])){
                scIdx[c,cc] <- r+rr
                cc <- cc+1
                added <- c(added,r+rr)
            }
        }
    }
    scIdx <- rbind(scIdxLab,scIdx)
    
    ## Number of genes kept for clustering, based on their variance
    nKeep <- 1260
    
    ## Prepare plots
    annot <- cbind(as.character(sign(X)))
    colnames(annot) <- 'gender'
    plAnnots <- list('gender'='categorical')
    lab.and.region <- apply(rbind(lregions, llabs),2,FUN=function(v) paste(v,collapse='_'))
    gender.col <- c('-1' = "deeppink3", '1' = "blue")
    
    ##---------------------------
    ## Iterative replicate-based
    ##---------------------------
    
    cEps <- 1e-6
    maxIter <- 30
    p <- 20
    
    paramXb <- list()
    paramXb$K <- p
    paramXb$D <- matrix(c(0.),nrow = 0,ncol=0)
    paramXb$batch <- TRUE
    paramXb$iter <- 1
    paramXb$mode <- 'PENALTY'
    paramXb$lambda <- 0.25
    
    ## Correction
    iRes <- iterativeRUV(Y, cIdx, scIdx, paramXb, k=20, nu.coeff=0,
                         cEps, maxIter,
                         Wmethod='rep', wUpdate=11)
    
    ucY <- iRes$cY
    
    ## Cluster the corrected data
    sdY <- apply(ucY, 2, sd)
    ssd <- sort(sdY,decreasing=TRUE,index.return=TRUE)$ix
    kmresIter <- kmeans(ucY[,ssd[1:nKeep]],centers=2,nstart=200)
    vclustIter <- kmresIter$cluster
    IterScore <- clScore(vclustIter,X)
    
    ## Plot the corrected data
    svdResIter <- NULL
    svdResIter <- svdPlot(ucY[, ssd[1:nKeep], drop=FALSE],
                          annot=annot,
                          labels=lab.and.region,
                          svdRes=svdResIter,
                          plAnnots=plAnnots,                    
                          kColors=gender.col, file=NULL)   
    
    ##--------------------------
    ## Iterated ridge
    ##--------------------------
    
    paramXb <- list()
    paramXb$K <- p
    paramXb$D <- matrix(c(0.),nrow = 0,ncol=0)
    paramXb$batch <- TRUE
    paramXb$iter <- 1
    paramXb$mode <- 'PENALTY' #2
    paramXb$lambda <- 1
    paramXb$lambda2 <- 0
    
    ## Correction
    iRes <- iterativeRUV(Y, cIdx, scIdx=NULL, paramXb, k=nrow(Y), nu.coeff=1e-2/2,
                         cEps, maxIter,
                         Wmethod='svd', wUpdate=11)
    
    nrcY <- iRes$cY
    
    ## Cluster the corrected data
    sdY <- apply(nrcY, 2, sd)
    ssd <- sort(sdY,decreasing=TRUE,index.return=TRUE)$ix
    kmresIter <- kmeans(nrcY[,ssd[1:nKeep]],centers=2,nstart=200)
    vclustIter <- kmresIter$cluster
    IterRandScore <- clScore(vclustIter,X)
    
    ## Plot the corrected data
    svdResIterRand <- NULL
    svdResIterRand <- svdPlot(nrcY[, ssd[1:nKeep], drop=FALSE],
                              annot=annot,
                              labels=lab.and.region,
                              svdRes=svdResIterRand,
                              plAnnots=plAnnots,                    
                              kColors=gender.col, file=NULL)   
}

RUVnormalize documentation built on Nov. 8, 2020, 8:01 p.m.