R/permutationMultipleLmMatrix.R

In GIGSEA: Genotype Imputed Gene Set Enrichment Analysis

#' permutationMultipleLmMatrix
#'
#' permutationMultipleLmMatrix is a permutation test to calculate the empirical
#' p values for weighted multiple linear regression
#'
#' @param fc a vector of numeric values representing gene expression fold 
#' change
#' @param net a matrix of numeric values in the size of gene number x gene set 
#' number, representing the connectivity between genes and gene sets
#' @param weights a vector of numeric values representing the weights of 
#' permuated genes
#' @param num an integer value representing the number of permutations
#' @param step an integer value representing the number of permutations in 
#' each step 
#' @param verbose an boolean value indicating whether or not to print output to 
#' the screen 
#'
#' @return a data frame comprising following columns:
#' \itemize{
#' \item {term} a vector of character values incidating the names of gene sets.
#' \item {usedGenes} a vector of numeric values indicating the number of genes 
#' used in the model.
#' \item {observedTstats} a vector of numeric values indicating the observed 
#' t-statistics for the weighted multiple regression coefficients.
#' \item {empiricalPval} a vector of numeric values [0,1] indicating the 
#' permutation-based empirical p values.
#' \item {BayesFactor} a vector of numeric values indicating the Bayes Factor 
#' for the multiple test correction.
#' }
#'
#' @export
#'
#' @importFrom stats lm pt qnorm
#' @importFrom utils read.table write.table
#' @importFrom Matrix sparseMatrix
#' @importFrom locfdr locfdr
#' @import MASS
#' 
#' @examples
#' 
#' # load data
#' data(heart.metaXcan)
#' gene <- heart.metaXcan$gene_name
#'
#' # extract the imputed Z-score of differential gene expression, which 
#' # follows the normal distribution
#' fc <- heart.metaXcan$zscore
#'
#' # use as weights the prediction R^2 and the fraction of imputation-used SNPs 
#' usedFrac <- heart.metaXcan$n_snps_used / heart.metaXcan$n_snps_in_cov
#' r2 <- heart.metaXcan$pred_perf_r2
#' weights <- usedFrac*r2
#'
#' # build a new data frame for the following weighted linear regression-based 
#' # enrichment analysis
#' data <- data.frame(gene,fc,weights)
#' head(data)
#'
#' net <- MSigDB.KEGG.Pathway$net
#'
#' # intersect the imputed genes with the gene sets of interest
#' data2 <- orderedIntersect( x=data, by.x=data$gene, by.y=rownames(net))
#' net2 <- orderedIntersect( x=net, by.x=rownames(net), by.y=data$gene)
#' all( rownames(net2) == as.character(data2$gene) )
#'
#' # the MGSEA.res1 uses the weighted multiple linear regression to do 
#' # permutation test, 
#' # while MGSEA.res2 used the solution of weighted matrix operation. The 
#' # latter one takes substantially less time.
#' # system.time( MGSEA.res1<-permutationMultipleLm(fc=data2$fc, net=net2, 
#' # weights=data2$weights, num=1000))
#' system.time( MGSEA.res2<-permutationMultipleLmMatrix(fc=data2$fc, net=net2, 
#' weights=data2$weights, num=1000))
#' head(MGSEA.res2)
#'
#' @author Shijia Zhu, \email{shijia.zhu@@mssm.edu}
#'
#' @seealso \code{\link{orderedIntersect}}; 
#' \code{\link{permutationMultipleLm}};
#'
permutationMultipleLmMatrix <- function( fc , net , weights=rep(1,nrow(net)) , 
                                        num=100 , step=1000 , verbose=TRUE )
{
    fc[is.na(fc)] <- 0
    weights[is.na(weights)]<-0
    net <- as.matrix(net)
    net[is.na(net)] <- 0
    net <- net[,colSums(net)>0]
    
    x <- net
    w <- weights
    y <- fc
    
    X <- cbind(1,x)
    W <- diag(w)
    A0 <- t(X) %*% W
    A <- ginv(A0 %*% X)
    B <- A0 %*% y
    coefs <- A %*% B
    predicts <- X %*% coefs
    residuals <- y - predicts
    delta <- colSums( w * residuals^2 )/( sum(w>0,na.rm=TRUE)-qr(X)$rank )
    se <- vapply( delta , function(d) sqrt( d * diag(A) ) , numeric(nrow(A)) )
    t <- coefs/se
    observedTstats <- as.matrix(t[-1,1])
    observedPval <- 2 * pt(abs(observedTstats), 
                           df=sum(weights>0, na.rm=TRUE)-2, lower.tail=FALSE)
    
    empiricalSum <- rep(0,ncol(net))
    if( num%%step==0 )
    {
        steps <- rep(step,num%/%step)
    } else {
        steps <- c( rep(step,num%/%step) , num%%step )
    }
    cs_steps <- c( 1, cumsum(steps) )
    
    for( i in seq_along(steps) )
    {
        stepi <- steps[i]
        shuffledFC <- vapply( seq_len(stepi) , 
                          function(s) sample(fc) , numeric(length(fc)) )
         
        B <- A0 %*% shuffledFC
        coefs <- A %*% B
        predicts <- X %*% coefs
        residuals <- shuffledFC - predicts
        delta <- colSums( w * residuals^2 )/( sum(w>0,na.rm=TRUE)-qr(X)$rank )
        se <- vapply( delta , function(d) sqrt( d*diag(A) ), numeric(nrow(A)) )
        t <- coefs/se
        shuffledTstats <- as.matrix(t[-1,])
        
        for(j in seq_len(nrow(shuffledTstats)) )
        {
            if(observedTstats[j]>0) 
            {
                empiricalSum[j] <- empiricalSum[j] + 
                    sum( shuffledTstats > observedTstats[j] )
            } else {
                empiricalSum[j] <- empiricalSum[j] + 
                    sum( shuffledTstats < observedTstats[j] )
            }
        }
        
        for(j in cs_steps[i]:cs_steps[i+1]  ) 
        {
            if(verbose) reportProgress(j,num,10)
        }
    }
    
    term <- colnames(net)
    usedGenes <- apply(as.matrix(net), 2, function(x) sum(x!=0,na.rm=TRUE) )
    empiricalPval <- (empiricalSum+0.1)/(num*ncol(net))
    
    #lc = locfdr( sign(observedTstats) * qnorm(empiricalPval) , plot=0 )
    #lc = locfdr( observedTstats , plot=0 )
    zscore <- qnorm(empiricalPval)
    lc <- locfdr( c(zscore,-zscore) , plot=0 )
    localFdr <- lc$fdr[seq_along(zscore)]
    
    p0 <- lc$fp0[3,3]
    # p0 <- lc$fp0[3,3] - 1.96*lc$fp0[4,3]
  
    BayesFactor <- (1-localFdr)/localFdr *  p0/abs(1-p0)
    
    pval <- data.frame(term,usedGenes,observedTstats,empiricalPval,BayesFactor)
    rownames(pval) <- NULL
    #pval <- pval[order(pval$BayesFactor,decreasing=TRUE),]
    pval <- pval[order(pval$empiricalPval),]
    pval
    
}