- 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 inexpression profiling , it can be used to combine ranked lists in various application domains, includingproteomics ,metabolomics , statisticalmeta-analysis , and generalfeature selection .**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 is used to determine how likely a given RP value or better is observed in a random experiment.

1. step: generate "p"permutation s 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 $pfp(g)=E\_\{RP\}(g)/r\_\{g,i\}$**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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