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

Description

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.

Usage

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

Arguments

 X matrix of logged fold changes. For alternative input format, see fdr.spatial2. delta integer determining the size of spot neighbourhoods ((2*delta+1)x(2*delta+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.

Details

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.

Value

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.

Note

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

Author(s)

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