fdr.spatial: Assessment of the significance of spatial 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 spatial bias by a one-sided random permutation test. This is achieved by comparing the observed average values of logged fold-changes within a spot's spatial neighbourhood with an empirical distribution generated by random permutation. The significance of spatial bias is given by the false discovery rate.

1	fdr.spatial(X,delta=2,N=100,av="median",edgeNA=FALSE)

`X`	matrix of logged fold changes. For alternative input format, see `fdr.spatial2`.
`delta`	integer determining the size of spot neighbourhoods (`(2delta+1)x(2delta+1)`).
`N`	number of random permutations performed for generation of empirical background distribution
`av`	averaging of `M` within neighbourhood by mean or median (default)
`edgeNA`	treatment of edges of array: For `edgeNA=TRUE`, the significance of a neighbourhood (defined by a sliding window) is set to NA, if the neighbourhood extends over the edges of the matrix.

The function fdr.spatial assesses the significance of spatial bias using a one-sided random permutation test. The null hypothesis states random spotting i.e. the independence of log ratio M and spot location. First, a neighbourhood of a spot is defined by a two dimensional square window of chosen size ((2*delta+1)x(2*delta+1)). Next, a test statistic is defined by calculating the median or mean of M within a symmetrical spot's neighbourhood. An empirical distribution of median/mean of \code{M} is generated based N random permutations of the spot locations on the array. The randomisation and calculation of median/mean of \code{M} is repeated N times. 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 spot location can be assessed. If M is independent of spot's location, the empirical distribution can be expected to be distributed around its mean value. To assess the significance of observing positive deviations of median/mean of \code{M}, the false discovery rate (FDR) is used. It indicates the expected proportion of false discoveries 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 on the array. FDRs equal zero are set to FDR=1/T*N. Varying threshold c determines the FDR for each spot neighbourhood. Correspondingly, the significance of observing negative deviations of median/mean of \code{M} can be determined.

A list of matrices 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.spatial

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

p.spatial, fdr.int, sigxy.plot, fdr.spatial2

# To run these examples, delete the comment signs before the commands.
#
# LOADING DATA
# data(sw)
# M <- v2m(maM(sw)[,1],Ngc=maNgc(sw),Ngr=maNgr(sw),
#                Nsc=maNsc(sw),Nsr=maNsr(sw),main="MXY plot of SW-array 1")
#
# CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS
# For this illustration, N was chosen rather small. For "real" analysis, it should be larger.
# FDR <- fdr.spatial(M,delta=2,N=10,av="median",edgeNA=TRUE)
# sigxy.plot(FDR$FDRp,FDR$FDRn,color.lim=c(-5,5),main="FDR")
#
# LOADING NORMALISED DATA
# data(sw.olin)
# M<- v2m(maM(sw.olin)[,1],Ngc=maNgc(sw.olin),Ngr=maNgr(sw.olin),
#                Nsc=maNsc(sw.olin),Nsr=maNsr(sw.olin),main="MXY plot of SW-array 1")
#
# CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS
# FDR <- fdr.spatial(M,delta=2,N=10,av="median",edgeNA=TRUE)
# VISUALISATION OF RESULTS
# sigxy.plot(FDR$FDRp,FDR$FDRn,color.lim=c(-5,5),main="FDR")