fdr.int {OLIN} | R Documentation

## Assessment of the significance of intensity-dependent bias

### Description

This function assesses the significance of intensity-dependent bias by an one-sided random permutation test. The observed average values of logged fold-changes within an intensity neighbourhood are compared to an empirical distribution generated by random permutation. The significance is given by the false discovery rate.

### Usage

    fdr.int(A,M,delta=50,N=100,av="median")

### Arguments

`A` | vector of average logged spot intensity
`M` | vector of logged fold changes
`delta` | integer determining the size of the neighbourhood. The actual window size is (`2 * delta+1`).
`N` | number of random permutations performed for generation of empirical distribution
`av` | averaging of `M` within neighbourhood by mean or median (default)

### Details

The function `fdr.int` assesses significance of intensity-dependent bias using a one-sided random permutation test. The null hypothesis states the independence of A and M. To test if `M` depends on `A`, spots are ordered with respect to A. This defines a neighbourhood of spots with similar A for each spot. Next, a test statistic is defined by calculating the median or mean of `M` within a symmetrical spot's intensity neighbourhood of chosen size (`2 *delta+1`). An empirical distribution of the test statistic is produced by calculating for `N` random intensity orders of spots. Comparing this empirical distribution of median/mean of `M` with the observed distribution of median/mean of `M`, the independence of `M` and `A` is assessed. If `M` is independent of `A`, the empirical distribution of median/mean of `M` can be expected to be distributed around its mean value. The false discovery rate (FDR) is used to assess the significance of observing positive deviations of median/mean of `M`. It indicates the expected proportion of false positives among rejected null hypotheses. It is defined as FDR=q*T/s, where q is the fraction of median/mean of `M` larger than chosen threshold c for the empirical distribution, `s` is the number of neighbourhoods with (median/mean of `M`)> c for the distribution derived from the original data and `T` is the total number of neighbourhoods in the original data. Varying threshold c determines the FDR for each spot neighbourhood. FDRs equal zero are set to FDR=1/T*N for computational reasons, as `log10(FDR)` is plotted by `sigint.plot`. Correspondingly, the significance of observing negative deviations of median/mean of `M` can be determined. If the neighbourhood window extends over the limits of the intensity scale, the significance is set to `NA`.

### Value

A list of vector containing the false discovery rates for positive (`FDRp`) and negative (`FDRn`) deviations of median/mean of `M` (of the spot's neighbourhood) is produced.

### Note

The same functionality but with our input and output formats is offered by `fdr.int`

### Author(s)

Matthias E. Futschik (http://itb.biologie.hu-berlin.de/~futschik)

### See Also

`fdr.int2`,`p.int`, `fdr.spatial`, `sigint.plot`

### Examples

    # To run these examples, delete the comment signs (#) in front of the commands.
    #
    # LOADING DATA NOT-NORMALISED
    # data(sw)
    # CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS
    # For this example, N was chosen rather small. For "real" analysis, it should be larger.
    # FDR <- fdr.int(maA(sw)[,1],maM(sw)[,1],delta=50,N=10,av="median")
    # VISUALISATION OF RESULTS
    # sigint.plot(maA(sw)[,1],maM(sw)[,1],FDR$FDRp,FDR$FDRn,c(-5,-5))

    # LOADING NORMALISED DATA
    # data(sw.olin)
    # CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS
    # FDR <- fdr.int(maA(sw.olin)[,1],maM(sw.olin)[,1],delta=50,N=10,av="median")
    # VISUALISATION OF RESULTS
    # sigint.plot(maA(sw.olin)[,1],maM(sw.olin)[,1],FDR$FDRp,FDR$FDRn,c(-5,-5))

[Package OLIN version 1.10.0 Index]