R/ebayes.R

In limma: Linear Models for Microarray Data

#  EMPIRICAL BAYES FUNCTIONS

eBayes <- function(fit,proportion=0.01,stdev.coef.lim=c(0.1,4),trend=FALSE,robust=FALSE,winsor.tail.p=c(0.05,0.1))
#	Empirical Bayes statistics to select differentially expressed genes.
#	Accepts and returns an MArrayLM object.
#	Gordon Smyth
#	4 August 2003.  Last modified 18 Feb 2018.
{
	if(trend) if(is.null(fit$Amean)) stop("Need Amean component in fit to estimate trend")
	eb <- .ebayes(fit=fit,proportion=proportion,stdev.coef.lim=stdev.coef.lim,trend=trend,robust=robust,winsor.tail.p=winsor.tail.p)
	fit$df.prior <- eb$df.prior
	fit$s2.prior <- eb$s2.prior
	fit$var.prior <- eb$var.prior
	fit$proportion <- proportion
	fit$s2.post <- eb$s2.post
	fit$t <- eb$t
	fit$df.total <- eb$df.total
	fit$p.value <- eb$p.value
	fit$lods <- eb$lods
	if(!is.null(fit$design) && is.fullrank(fit$design)) {
		F.stat <- classifyTestsF(fit,fstat.only=TRUE)
		fit$F <- as.vector(F.stat)
		df1 <- attr(F.stat,"df1")
		df2 <- attr(F.stat,"df2")
		if(df2[1] > 1e6) # Work around bug in R 2.1
			fit$F.p.value <- pchisq(df1*fit$F,df1,lower.tail=FALSE)
		else
			fit$F.p.value <- pf(fit$F,df1,df2,lower.tail=FALSE)
	}
	fit
}

.ebayes <- function(fit,proportion=0.01,stdev.coef.lim=c(0.1,4),trend=FALSE,robust=FALSE,winsor.tail.p=c(0.05,0.1))
#	Empirical Bayes statistics to select differentially expressed genes
#	Gordon Smyth
#	Created 8 Sept 2002.  Last revised 12 Apr 2020.
#	Made a non-exported function 18 Feb 2018.
{
	coefficients <- fit$coefficients
	stdev.unscaled <- fit$stdev.unscaled
	sigma <- fit$sigma
	df.residual <- fit$df.residual
	if(is.null(coefficients) || is.null(stdev.unscaled) || is.null(sigma) || is.null(df.residual)) stop("No data, or argument is not a valid lmFit object")
	if(max(df.residual)==0) stop("No residual degrees of freedom in linear model fits")
	if(!any(is.finite(sigma))) stop("No finite residual standard deviations")
	if(trend) {
		covariate <- fit$Amean
		if(is.null(covariate)) stop("Need Amean component in fit to estimate trend")
	} else {
		covariate <- NULL
	}

#	Moderated t-statistic
	out <- squeezeVar(sigma^2, df.residual, covariate=covariate, robust=robust, winsor.tail.p=winsor.tail.p)
	out$s2.prior <- out$var.prior
	out$s2.post <- out$var.post
	out$var.prior <- out$var.post <- NULL
	out$t <- coefficients / stdev.unscaled / sqrt(out$s2.post)
	df.total <- df.residual + out$df.prior
	df.pooled <- sum(df.residual,na.rm=TRUE)
	df.total <- pmin(df.total,df.pooled)
	out$df.total <- df.total
	out$p.value <- 2*pt(-abs(out$t),df=df.total)

#	B-statistic
	var.prior.lim <- stdev.coef.lim^2/median(out$s2.prior)
	out$var.prior <- tmixture.matrix(out$t,stdev.unscaled,df.total,proportion,var.prior.lim)
	if(anyNA(out$var.prior)) {
		out$var.prior[ is.na(out$var.prior) ] <- 1/out$s2.prior
		warning("Estimation of var.prior failed - set to default value")
	}
	r <- rep(1,NROW(out$t)) %o% out$var.prior
	r <- (stdev.unscaled^2+r) / stdev.unscaled^2
	t2 <- out$t^2
	Infdf <- out$df.prior > 10^6
	if(any(Infdf)) {
		kernel <- t2*(1-1/r)/2
		if(any(!Infdf)) {
			t2.f <- t2[!Infdf]
			r.f <- r[!Infdf]
			df.total.f <- df.total[!Infdf]
			kernel[!Infdf] <- (1+df.total.f)/2*log((t2.f+df.total.f) / (t2.f/r.f+df.total.f))
		}
	} else
		kernel <- (1+df.total)/2*log((t2+df.total) / (t2/r+df.total))
	out$lods <- log(proportion/(1-proportion))-log(r)/2+kernel
	out
}

tmixture.matrix <- function(tstat,stdev.unscaled,df,proportion,v0.lim=NULL)
#	Estimate the prior variance of the coefficients for DE genes
#	Gordon Smyth
#	18 Nov 2002. Last modified 12 Dec 2003.
{
	tstat <- as.matrix(tstat)
	stdev.unscaled <- as.matrix(stdev.unscaled)
	if(any(dim(tstat) != dim(stdev.unscaled))) stop("Dims of tstat and stdev.unscaled don't match")
	if(!is.null(v0.lim)) if(length(v0.lim) != 2) stop("v0.lim must have length 2")
	ncoef <- ncol(tstat)
	v0 <- rep(0,ncoef)
	for (j in 1:ncoef) v0[j] <- tmixture.vector(tstat[,j],stdev.unscaled[,j],df,proportion,v0.lim)	
	v0
}

tmixture.vector <- function(tstat,stdev.unscaled,df,proportion,v0.lim=NULL)
#	Estimate scale factor in mixture of two t-distributions
#	tstat is assumed to follow sqrt(1+v0/v1)*t(df) with probability proportion and t(df) otherwise
#	v1 is stdev.unscaled^2 and v0 is to be estimated
#	Gordon Smyth
#	18 Nov 2002.  Last modified 9 Jun 2020.
{
#	Remove missing values
	if(anyNA(tstat)) {
		o <- !is.na(tstat)
		tstat <- tstat[o]
		stdev.unscaled <- stdev.unscaled[o]
		df <- df[o]
	}

#	ntarget t-statistics will be used for estimation
	ngenes <- length(tstat)
	ntarget <- ceiling(proportion/2*ngenes)
	if(ntarget < 1) return(NA)

#	If ntarget is v small, ensure p at least matches selected proportion
#	This ensures ptarget < 1
	p <- max(ntarget/ngenes,proportion)

#	Method requires that df be equal
	tstat <- abs(tstat)
	MaxDF <- max(df)
	i <- df < MaxDF
	if(any(i)) {
		TailP <- pt(tstat[i],df=df[i],lower.tail=FALSE,log.p=TRUE)
		tstat[i] <- qt(TailP,df=MaxDF,lower.tail=FALSE,log.p=TRUE)
		df[i] <- MaxDF
	}

#	Select top statistics
	o <- order(tstat,decreasing=TRUE)[1:ntarget]
	tstat <- tstat[o]
	v1 <- stdev.unscaled[o]^2

#	Compare to order statistics
	r <- 1:ntarget
	p0 <- 2*pt(tstat,df=MaxDF,lower.tail=FALSE)
	ptarget <- ( (r-0.5)/ngenes - (1-p)*p0 ) / p
	v0 <- rep_len(0,length.out=ntarget)
	pos <- ptarget > p0
	if(any(pos)) {
		qtarget <- qt(ptarget[pos]/2,df=MaxDF,lower.tail=FALSE)
		v0[pos] <- v1[pos]*((tstat[pos]/qtarget)^2-1)
	}
	if(!is.null(v0.lim)) v0 <- pmin(pmax(v0,v0.lim[1]),v0.lim[2])
	mean(v0)
}