ebayes {limma} | R Documentation

## Empirical Bayes Statistics for Differential Expression

### Description

Given a series of related parameter estimates and standard errors, compute moderated t-statistics, moderated F-statistic, and log-odds of differential expression by empirical Bayes shrinkage of the standard errors towards a common value.

### Usage

    ebayes(fit, proportion=0.01, stdev.coef.lim=c(0.1,4))
    eBayes(fit, proportion=0.01, stdev.coef.lim=c(0.1,4))
    treat(fit, lfc=0)

### Arguments

`fit` | an `MArrayLM` fitted model object produced by `lmFit` or `contrasts.fit`, or an unclassed list produced by `lm.series`, `gls.series` or `mrlm` containing components `coefficients`, `stdev.unscaled`, `sigma` and `df.residual`
`proportion` | numeric value between 0 and 1, assumed proportion of genes which are differentially expressed
`stdev.coef.lim` | numeric vector of length 2, assumed lower and upper limits for the standard deviation of log2-fold-changes for differentially expressed genes
`lfc` | the minimum log2-fold-change which is considered material

### Details

These functions is used to rank genes in order of evidence for differential expression. They use an empirical Bayes method to shrink the probe-wise sample variances towards a common value and to augmenting the degrees of freedom for the individual variances (Smyth, 2004). The functions accept as input argument `fit` a fitted model object from the functions `lmFit`, `lm.series`, `mrlm` or `gls.series`. The fitted model object may have been processed by `contrasts.fit` before being passed to `eBayes` to convert the coefficients of the design matrix into an arbitrary number of contrasts which are to be tested equal to zero. The columns of `fit` define a set of contrasts which are to be tested equal to zero.

The empirical Bayes moderated t-statistics test each individual contrast equal to zero. For each probe (row), the moderated F-statistic tests whether all the contrasts are zero. The F-statistic is an overall test computed from the set of t-statistics for that probe. This is exactly analogous the relationship between t-tests and F-statistics in conventional anova, except that the residual mean squares and residual degrees of freedom have been moderated between probes.

The estimates `s2.prior` and `df.prior` are computed by `fitFDist`. `s2.post` is the weighted average of `s2.prior` and `sigma^2` with weights proportional to `df.prior` and `df.residual` respectively. The `lods` is sometimes known as the B-statistic. The F-statistics `F` are computed by `classifyTestsF` with `fstat.only=TRUE`.

`eBayes` doesn't compute ordinary (unmoderated) t-statistics by default, but these can be easily extracted from the linear model output, see the example below.

`ebayes` is the earlier and leaner function. `eBayes` is intended to have a more object-orientated flavor as it produces objects containing all the necessary components for downstream analysis.

`treat` computes empirical Bayes moderated-t p-values relative to a minimum required fold-change threshold. Instead of testing for genes which have log-fold-changes different from zero, it tests whether the log2-fold-change is greater than `lfc` in absolute value (McCarthy and Smyth, 2009). `treat` is concerned with p-values rather than posterior odds, so it does not compute the B-statistic `lods`. The idea of thresholding doesn't apply to F-statistics in a straightforward way, so moderated F-statistics are also not computed.

### Value

`eBayes` produces an object of class `MArrayLM` with the following components, see `MArrayLM-class`. `ebayes` produces an ordinary list without `F` or `F.p.value`. `treat` produces an `MArrayLM` object, but without `lods`, `var.prior`, `F` or `F.p.value`.

`t` | numeric vector or matrix of moderated t-statistics
`p.value` | numeric vector of p-values corresponding to the t-statistics
`s2.prior` | estimated prior value for `sigma^2`
`df.prior` | degrees of freedom associated with `s2.prior`
`s2.post` | vector giving the posterior values for `sigma^2`
`lods` | numeric vector or matrix giving the log-odds of differential expression
`var.prior` | estimated prior value for the variance of the log2-fold-change for differentially expressed gene
`F` | numeric vector of moderated F-statistics for testing all contrasts defined by the columns of `fit` simultaneously equal to zero
`F.p.value` | numeric vector giving p-values corresponding to `F`

### Author(s)

Gordon Smyth

### References

McCarthy, D. J., and Smyth, G. K. (2009). Testing significance relative to a fold-change threshold is a TREAT. Bioinformatics. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/btp053

Loennstedt, I., and Speed, T. P. (2002). Replicated microarray data. Statistica Sinica 12, 31-46.

Smyth, G. K. (2004). Linear models and empirical Bayes methods for assessing differential expression in microarray experiments. Statistical Applications in Genetics and Molecular Biology, Volume 3, Article 3. http://www.bepress.com/sagmb/vol3/iss1/art3

### See Also

`squeezeVar`, `fitFDist`, `tmixture.matrix`.

An overview of linear model functions in limma is given by 06.LinearModels.

### Examples

    #  See also lmFit examples

    #  Simulate gene expression data,
    #  6 microarrays and 100 genes with one gene differentially expressed
    set.seed(2004); invisible(runif(100))
    M <- matrix(rnorm(100*6,sd=0.3),100,6)
    M[1,] <- M[1,] + 1
    fit <- lmFit(M)

    #  Ordinary t-statistic
    par(mfrow=c(1,2))
    ordinary.t <- fit$coef / fit$stdev.unscaled / fit$sigma
    qqt(ordinary.t,df=fit$df.residual,main="Ordinary t")
    abline(0,1)

    #  Moderated t-statistic
    eb <- eBayes(fit)
    qqt(eb$t,df=eb$df.prior+eb$df.residual,main="Moderated t")
    abline(0,1)
    #  Points off the line may be differentially expressed
    par(mfrow=c(1,1))

[Package limma version 2.16.5 Index]