Rank Product analysis

Rank products: a simple, yet powerful, new method to detect differentially regulated genes in replicated microarray experiments

Rainer Breitling, Patrick Armengaud, Anna Amtmanna, Pawel Herzykb

Overview

Rank Product is a non parametric statistical method of analysing microarray data. It assumes that under the null hypothesis, the order of all items is random, and the probability of findng a specific item among the top r of n items in a list is p = r/n.

Multiplying theses probabilities over i replicates leads to the rank product definition;

[math]RP = \prod_i \frac{r_i}{n_i}[/math]

where r_i is the rank of the item in the i-th list and n_i is the total number of items in the i-th list. The smaller the RP value, the smaller the probability that the observed rank of the item in the list is due to chance. The BioConductor RankProd package produces a list of up and down regulated genes with a probability measure analogous to false discovery rate control.

Usage

This statistical method can analyse single channel and two channel cDNA microarray data. If one class data is provided as input it is assumed to be a matrix of expression ratios (M values). If two class data is provided it is assumed to be a matrix of single channels. e.g.

cl <- rep(1,5) cl <- rep(0:1, c(4,5))

The origin of the data can be specified, single origin is from the same laboratory source, multiple origin is from several different laboratories. e.g.

origin <- c(1,5) origin <- c(1,1,1,2,2)

This is analogous to the inputs into SAM.

Alternative input data for RankProd can be any numeric information, such as M values standardized by each genes standard deviation, or moderated-t statistics after limma analysis.

Example

library(RankProd) data(arab) # Single origin analysis arab.sub <- arab[, which(arab.origin == 1)] arab.cl.sub <- arab.cl[which(arab.origin == 1)] arab.origin.sub <- arab.origin[which(arab.origin == 1)] RP.out <- RP(arab.sub, arab.cl.sub, num.perm = 100, logged = TRUE, na.rm = FALSE, plot = FALSE, rand = 123)

The list elements of RP.out are;

pfp = estimated percentage of false positive predictions pval = raw p-values RPs = Rank Products RPrank = Rank of the rank Products Orirank = list of up/down ranks ("class1 < class2" "class1 > class 2") AveFC = Average fold change

Note

RankSum and RankProd2 are very similar functions

See also

• Publication
• rankProd BioC package
• rankProd documentation
• RankProduct.R
• RankProductVignette.R