EOC {OCplus} | R Documentation

## Estimated or empirical FDR, sensitivity, etc as a function of cutoff level

### Description

`EOC` computes and optionally plots the estimated operating characteristics for data from a microarray experiment with two groups of subjects. The false discovery rate (FDR) is estimated based on random permutations of the data and plotted against the cutoff level on the t-statistic; a curve for the classical sensitivity can be added. Different curves for different proportions of non-differentially expressed genes can be compared in the same plot, and the sample size per group can be varied between plots.

`FDRp` is the function that does the underlying hard work and requires package `multtest`.

### Usage

    EOC(xdat, grp, p0, paired = FALSE, nperm = 25, seed = NULL, plot = TRUE, ...)

    FDRp(xdat, grp, test = "t.equalvar", p0, nperm, seed)

### Arguments

`xdat` | the matrix of expression values, with genes as rows and samples as columns
`grp` | a grouping variable giving the class membership of each sample, i.e. each column in `xdat`; for `EOC`, this can be any type of variable, as long as it has exactly two distinct values, whereas `FDRp` expects to see only 0s and 1s, see Details.
`p0` | if supplied, an estimate for the proportion of non-differentially expressed genes; if not supplied, the routine will estimate it, see Details.
`paired` | logical value indicating whether this is independent sample situation (default) or a paired sample situation. Note that paired samples need to follow each other in the data matrix (as in 010101...

when `paired=TRUE`.

`nperm` | number of permutations for establishing the null distribution of the t-statistic
`test` | the type of test to use, see `mt.teststat`; when called from `EOC`, this is always the default.
`seed` | the random seed from which the permutations are started
`plot` | logical value indicating whether to do the plot
`...` | graphical parameters, passed to `plot.FDR.result`

### Details

`EOC` is the empirical counterpart of the function `TOC`. It estimates the FDR and sensitivity for a given data set of expression values measured on subjects in two groups. The FDR is estimated locally based on the empirical Bayes approach outlined by Efron et al., see References. `FDRp` implements the details of this method; this requires among other things the permutation distribution of the t-statistic, which is calculated via a call to function `mt.teststat` of package `multtest`. This explains why both functions barf at missing values in the expression data.

Note that `p0` is by default estimated from the data, as originally suggested by Efron et al. so as to make ratio between the densities of the observed distribution of t-statistics and the permutation distribution smaller than 1; alternatively, the user can supply his own guesstimate of the proportion of non-differentially expressed genes in the data.

Note also that `FDRp` keeps all permuations in the memory during compuations. For a large number of genes, this will limit the number of possible permuations.

### Value

For `EOC`, an object of class `FDR.result`, which inherits from class `data.frame`. The three columns list for each gene its t-statistic, the estimated FDR (two-sided), and the estimated sensitivity. Additionally, the object carries an attribute `param`, which is a list with four entries: `p0`, the assumed proportion of non-differentially expressed genes used in calculating the FDR; `p0.est`, a logical value indicating whether `p0` was estimated or user-supplied; `statistic` indicates how the t-statistic was computed, i.e. how its sign should be interpreted in terms of relative over- or under expression, and a logical flag `paired` to indicate whether a paired t-statistic was used.

`FDRp` returns a list with essentially the same elements, plus additionally the values of the observed and permuted distribution of the t-statistics for each gene.

### Note

Both the curve labels and the legend may be squashed if the plotting device is too small. Increasing the size of the device and re-plotting should improve readability.

### Author(s)

Y. Pawitan and A. Ploner

### References

Pawitan Y, Michiels S, Koscielny S, Gusnanto A, Ploner A (2005) False Discovery Rate, Sensitivity and Sample Size for Microarray Studies. Bioinformatics, 21, 3017-3024.

Efron B, Tibshirani R, Storey JD, Tusher V. (2001) Empirical Bayes Analysis of a Microarray Experiment. JASA, 96(456), p. 1151-60.

### See Also

`plot.FDR.result`, `OCshow`, `mt.teststat`

### Examples

    # We simulate a small example with 5 percent regulated genes and
    # a rather large effect size
    set.seed(2003)
    xdat = matrix(rnorm(50000), nrow=1000)
    xdat[1:25, 1:25] = xdat[1:25, 1:25] - 2
    xdat[26:50, 1:25] = xdat[26:50, 1:25] + 2
    grp = rep(c("Sample A","Sample B"), c(25,25))

    # The default, with legend
    ret = EOC(xdat, grp, legend=TRUE)
    # Look at the results: yes
    ret[1:10,]
    which(ret$FDR<0.05)
    # Extra information
    attr(ret,"param")

    # Run the same data with different permutations: fairly stable, but with
    # different p0
    ret = EOC(xdat, grp, seed=2000)
    which(ret$FDR<0.07)

    # Misspecify the p0: not too bad here
    ret = EOC(xdat, grp, p0=0.99)
    which(ret$FDR<0.01)

    # We simulate data in a paired setting
    # Note the arrangement of the columns
    set.seed(2004)
    xdat = matrix(rnorm(50000), nrow=1000)
    ndx1 = seq(1,50, by=2)
    xdat[1:25, ndx1] = xdat[1:25, ndx1] - 2
    xdat[26:50, ndx1] = xdat[26:50, ndx1] + 2
    grp = rep(c("Sample A","Sample B"), 25)

    ret = EOC(xdat, grp, paired=TRUE)
    which(ret$FDR<0.05)

[Package OCplus version 1.64.0 Index]