OLIN (version 1.50.0)

p.spatial: Assessment of the significance of spatial bias based on p-values

Description

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.

Usage

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

Arguments

X

matrix of logged fold changes

delta

integer determining the size of spot neighbourhoods ((2*delta+1)x(2*delta+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.

Value

Pp) and negative (Pn) deviations of $median/mean of \code{M}$ of the spot's neighbourhood is produced.

Details

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.

See Also

fdr.int, sigxy.plot, p.adjust

Examples

# 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")