Rank product

The Rank product is a biologically motivated technique for the detection of differentially expressed genes in replicated microarray experiments. It is a simple statistical method based on ranks of fold changes.

Calculation of the Rank product
Given n Genes and k replicates. Let $$e_{g,i}$$ be the fold change and $$r_{g,i}$$ the rank of gene g in the i-th replicate.

Compute the Rank product via the geometric mean: $$RP(g)=(\Pi_{i=1}^kr_{g,i})^{1/k}$$



Determination of significance levels
Simple permutation-based estimation are used to determine how likely a given RP value or better is observed in a random experiment.

1. step: generate p permutations of k rank lists of length n

2. step: calculate the Rank products of the n genes in the p permutations

3. step: count how many times the Rank products of the genes in the permutations are smaller or equal to the observed Rank product. Set c to this value.

4. step: calculate the average expected value for the Rank product by $$E_{RP}(g)=c/p$$

5. step: calculate the percentage of false positives as $$pfp(g)=E_{RP}(g)/RP(g)$$