fdr.int: Assessment of the significance of intensity-dependent bias
In OLIN: Optimized local intensity-dependent normalisation of two-color microarrays

Description Usage Arguments Details Value Note Author(s) See Also Examples

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.

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

`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)

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 \code{M} with the observed distribution of median/mean of \code{M}, the independence of M and A is assessed. If M is independent of A, the empirical distribution of median/mean of \code{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 \code{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 \code{M} larger than chosen threshold c for the empirical distribution, s is the number of neighbourhoods with (median/mean of \code{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 \code{M} can be determined. If the neighbourhood window extends over the limits of the intensity scale, the significance is set to NA.

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

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

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

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

# 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))