p.spatial: Assessment of the significance of spatial bias based on...
In OLIN: Optimized local intensity-dependent normalisation of two-color microarrays

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

This function assesses the significance of spatial bias. 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 permutation tests. The significance is given by (adjusted) p-values derived in one-sided permutation test.

1	p.spatial(X,delta=2,N=-1,av="median",p.adjust.method="none")

`X`	matrix of logged fold changes
`delta`	integer determining the size of spot neighbourhoods (`(2delta+1)x(2delta+1)`).
`N`	number of samples for generation of empirical background distribution
`av`	averaging of `M` within neighbourhood by mean or median (default)
`p.adjust.method`	method for adjusting p-values due to multiple testing regime. The available methods are “none”, “bonferroni”, “holm”, “hochberg”, “hommel” and “fdr”. See also `p.adjust`.

The function p.spatial assesses the significance of spatial bias using an 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 for N random samples of size ((2*delta+1)x(2*delta+1)). Note that this scheme defines a sampling with replacement procedure whereas sampling without replacement is used for fdr.spatial. Comparing the 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}, p-values are calculated using Fisher's method. The p-value equals the fraction of values in the empirical distribution which are larger than the observed value . The minimal p-value is set to 1/N. Correspondingly, the significance of observing negative deviations of median/mean of \code{M} can be determined.

A list of vectors containing the p-values for positive (Pp) and negative (Pn) deviations of median/mean of \code{M} of the spot's neighbourhood is produced.

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

fdr.int, sigxy.plot, p.adjust

# To run these examples, "un-comment" them!
#
# 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.
# P <- p.spatial(M,delta=2,N=10000,av="median")
# sigxy.plot(P$Pp,P$Pn,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
# P <- p.spatial(M,delta=2,N=10000,av="median")
# VISUALISATION OF RESULTS
# sigxy.plot(P$Pp,P$Pn,color.lim=c(-5,5),main="FDR")