# Rank product

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Rank product

The rank product is a biologically motivated test for the detection of differentially expressed genes in replicated microarray experiments.It is a simple non-parametric statistical method based on ranks of fold changes. In addition to its use in expression profiling, it can be used to combine ranked lists in various application domains, including proteomics, metabolomics, statistical meta-analysis, and general feature selection.

Calculation of the rank product

Given "n" genes and "k" replicates, let $e_\left\{g,i\right\}$ be the fold change and $r_\left\{g,i\right\}$ the rank of gene "g" in the "i"-th replicate.

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

Determination of significance levels

Simple permutation-based estimation is 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 $E_\left\{RP\right\}\left(g\right)=c/p$
5. step: calculate the percentage of false positives as $pfp\left(g\right)=E_\left\{RP\right\}\left(g\right)/r_\left\{g,i\right\}$

References

* Breitling, R., Armengaud, P., Amtmann, A., and Herzyk, P.(2004) Rank Products: A simple, yet powerful, new method to detect differentially regulated genes in replicated microarray experiments, FEBS Letters, 573:83–-92

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