p.int: Calculates significance of intensity-dependent bias
In OLIN: Optimized local intensity-dependent normalisation of two-color microarrays

Description Usage Arguments Details Value Note Author(s) See Also Examples

This function assesses the significance of intensity-dependent bias. This is achieved by comparing the observed average values of logged fold-changes within an intensity neighbourhood with an empirical distribution generated by permutation tests. The significance is given by (adjusted) p-values.

1	p.int(A,M,delta=50,N=-1,av="median",p.adjust.method="none")

`A`	vector of average logged spot intensity
`M`	vector of logged fold changes
`delta`	integer determining the size of the neighbourhood (`2 * delta+1`).
`N`	number of random samples (of size `2 * delta+1`) used for the generation of empirical distribution. If N is negative, the number of samples 100 times the length of `A`.
`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`

The function p.int assesses the significance of intensity-dependent bias using a 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, the test statistic is the median or mean of M within a spot's intensity neighbourhood of chosen size (2 *delta+1). The empirical distribution of the this statistic is then generated based on N random samples (with replacement). (Note that sampling without replacement is used for fdr.int. Also note, that different meaning of argument N in p.int and fdr.int. The argument N in p.int is the number fo independent samples (of size 2 *delta+1) derived from the original distribution. The argument N in fdr.int states how many times the original distribution is randomised and the permutated distribution is used for generating the empirical distribution.) 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 symmetrically distributed around its mean value. To assess the significance of observing positive deviations of the p-values are used. It indicates the expected proportion of neighbourhoods with larger median/mean of \code{M} than the actual one based on the empirical distribution of median/mean of \code{M}. 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. Since this assessment of significance involves multiple testing, an adjustment of the p-values might be advisable.

A list of vector containing the p-values for positive (Pp) and negative (Pn) deviations of median/mean of \code{M} of the spot's neighbourhood is produced. Values corresponding to spots within an interval of delta at the lower or upper end of the A-scale are set to NA.

The same functionality but with our input and output formats is offered by p.int2

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

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

# 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.
# P <- p.int(maA(sw)[,1],maM(sw)[,1],delta=50,N=10000,av="median",p.adjust.method="none")
# VISUALISATION OF RESULTS
# sigint.plot(maA(sw)[,1],maM(sw)[,1],Sp=P$Pp,Sn=P$Pn,c(-5,-5))

# LOADING NORMALISED DATA
# data(sw.olin)
# CALCULATION OF SIGNIFICANCE OF SPOT NEIGHBOURHOODS 
# P <- p.int(maA(sw.olin)[,1],maM(sw.olin)[,1],delta=50,N=10000,av="median",p.adjust.method="none")
# VISUALISATION OF RESULTS
# sigint.plot(maA(sw.olin)[,1],maM(sw.olin)[,1],Sp=P$Pp,Sn=P$Pn,c(-5,-5))