Documentation

Illustrated user guide

Data sources

Biological categories

Database	Version	Retrieval data
Gene Ontology	-	June 2019
KEGG	-	June 2019
miRBase	22	June 2019
miRCarta	1.1	June 2019
Reactome	-	June 2019
WikiPathways	-	June 2019

miRNA targets

Database	Version	Retrieval data
MiRanda	3.3a	June 2019
miRTarBase	7	June 2019
TargetScan	7.1	June 2019

Statistical analysis

All compute intensive tasks have been performed using the GeneTrail2 C++ library [1] and GNU Parallel [2]. Results of the enrichment analysis were evaluated using the freely available statistical programming environment R, version 3.5.

Parameter overview

Statistical test	Over-representation analysis
P-value adjustment	Benjamini-Hochberg
$\alpha$-level	0.05
Minimal category size	2
Maximal category size	1000

Over-representation analysis

In order to judge if a certain biological category is significantly enriched for a certain miRNA, we use a test called over-representation analysis (ORA). This approach has been employed by many authors, e.g. [3], [4], [5], [6], [7]. Here we use the version of ORA that was presented by Backes et al. [3]. This approach is based on the hypergeometric distribution and can be used to test if a set of selected biological entities is significantly more or less present in a biological category than expected by chance.

We use ORA to judge if a biological pathway contains more targets of a certain miRNA than expected by chance. In order to calculate this chance, ORA relies on a reference set R (background). In our case this is a list of all miRNA targets for the corresponding confidence.

Assume a biological category C has k entries in list $T = (t_{1},t_{2},\ldots,t_{n})$ and l entries in reference set $R=(r_{1},r_{2},\ldots,r_{m})$. Based on this information we expect to find $k'=\frac{n*l}{m}$ elements of test set T in category C on average.

If T is a subset of R, the hypergeometric test is applied to compute a p-value for C:

$$P_C(k)=\sum\limits_{i=k}^{n} \frac{\binom{l}{i}\binom{m-l}{n-i}}{\binom{m}{n}}$$

Benjamini Hochberg adjustment

The Benjamini-Hochberg method [8], [9] is a step-up approach to control the false discovery rate. It assumes all p-values to be independent. Given $n$ increasingly sorted p-values $\{p_1,...,p_n\}$, we can can compute the adjusted p-values using the following formula:

$$\tilde p_{i}\ =\ \begin{cases} p_{i} & \text{for } i=n\\ \min \left( \tilde p_{(i-1)}, \frac{n}{i}p_{i} \right) & \text{for }i=n-1 ,...,1 \end{cases}$$

Bibliography