fdr.int {OLIN}R Documentation

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)

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 (bar{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 M with the observed distribution of median/mean of M, the independence of M and A is assessed. If M is independent of A, the empirical distribution of median/mean of 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 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 M larger than chosen threshold c for the empirical distribution, s is the number of neighbourhoods with (median/mean of 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 M can be determined. If the neighbourhood window extends over the limits of the intensity scale, the significance is set to NA.

Value

A list of vector containing the false discovery rates for positive (FDRp) and negative (FDRn) deviations of median/mean of M (of the spot's neighbourhood) is produced.

Author(s)

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

See Also

p.int, fdr.spatial, sigint.plot

Examples


# To run these examples, "un-comment" them!
#
# LOADING DATA NOT-NORMALISED
# data(sw)
# CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS
# For this  illustration, 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))


[Package OLIN version 1.3.2 Index]