fdr.spatial {OLIN} | R Documentation

## Assessment of the significance of spatial bias

### 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

    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)

### See Also

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

### Examples

    # 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")

[Package OLIN version 1.70.0 Index]