OLIN (version 1.50.0)

fdr.int: Assessment of the significance of intensity-dependent bias

Description

This function assesses the significance of intensity-dependent bias by an one-sided random permutation test. The observed average values of logged fold-changes within an intensity neighbourhood are compared to an empirical distribution generated by random permutation. The significance is given by the false discovery rate.

Usage

fdr.int(A,M,delta=50,N=100,av="median")

Arguments

A

vector of average logged spot intensity

M

vector of logged fold changes

delta

integer determining the size of the neighbourhood. The actual window size is (2 * delta+1).

N

number of random permutations performed for generation of empirical distribution

av

averaging of M within neighbourhood by mean or median (default)

Value

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

Details

The function fdr.int assesses significance of intensity-dependent bias using a one-sided random permutation test. The null hypothesis states the independence of A and M. To test if M depends on A, spots are ordered with respect to A. This defines a neighbourhood of spots with similar A for each spot. Next, a test statistic is defined by calculating the median or mean of M within a symmetrical spot's intensity neighbourhood of chosen size (2 *delta+1). An empirical distribution of the test statistic is produced by calculating for N random intensity orders of spots. 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 A is assessed. If M is independent of A, the empirical distribution of $median/mean of \code{M}$ can be expected to be distributed around its mean value. The false discovery rate (FDR) is used to assess the significance of observing positive deviations of $median/mean of \code{M}$. It indicates the expected proportion of false positives 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 in the original data. Varying threshold c determines the FDR for each spot neighbourhood. FDRs equal zero are set to $FDR=1/T*N$ for computational reasons, as log10(FDR) is plotted by sigint.plot. Correspondingly, the significance of observing negative deviations of $median/mean of \code{M}$ can be determined. If the neighbourhood window extends over the limits of the intensity scale, the significance is set to NA.

See Also

fdr.int2,p.int, fdr.spatial, sigint.plot

Examples

# To run these examples, delete the comment signs (#) in front of the commands.
#
# LOADING DATA NOT-NORMALISED
# data(sw)
# CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS
# For this example, N was chosen rather small. For "real" analysis, it should be larger.
# FDR <- fdr.int(maA(sw)[,1],maM(sw)[,1],delta=50,N=10,av="median")
# VISUALISATION OF RESULTS
# sigint.plot(maA(sw)[,1],maM(sw)[,1],FDR$FDRp,FDR$FDRn,c(-5,-5))

# LOADING NORMALISED DATA
# data(sw.olin)
# CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS 
# FDR <- fdr.int(maA(sw.olin)[,1],maM(sw.olin)[,1],delta=50,N=10,av="median")
# VISUALISATION OF RESULTS
# sigint.plot(maA(sw.olin)[,1],maM(sw.olin)[,1],FDR$FDRp,FDR$FDRn,c(-5,-5))