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

## Description

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.

## Usage

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

## Arguments

 `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`

## Details

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.

## Value

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`.

## Note

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

## Author(s)

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

`p.int2`,`fdr.int`, `sigint.plot`, `p.adjust`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```# 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)) ```