Table 1 Formulation of summary statistics mean, absmean, median, and maxmean for both self-contained and competitive testing
From: Roastgsa: a comparison of rotation-based scores for gene set enrichment analysis
Self-contained score | Competitive score | |
|---|---|---|
Mean | \(T_{mean}^{SC} = \frac{1}{m_o}\sum \limits _{i\in S}\delta _i\) | \(T_{mean}^{CO} = \frac{1}{m_o}\sum \limits _{i\in S} \frac{\delta _i - \bar{\delta }}{\hbox {sd}(\delta )}\) |
Absmean | \(T_{absmean}^{SC} = \frac{1}{m_o}\sum \limits _{i\in S} |\delta _i|\) | \(T_{absmean}^{CO} =\frac{1}{m_o}\sum \limits _{i\in S} \frac{|\delta _i| - \bar{|\delta |}}{\hbox {sd}(|\delta |)}\) |
Median | \(T_{median}^{SC}=\hbox {med}_{i \in S}\delta _i\) | \(T_{median}^{CO}=\hbox {med}_{i \in S} \frac{\delta _i - \hbox {med}{\delta }}{\hbox {mad}(\delta )}\) |
Maxmean | \(T_{maxmean}^{SC}=\frac{1}{m_o}\sum \limits _{i\in S}\delta _i^*\) | \(T_{maxmean}^{CO}=\frac{1}{m_o}\sum \limits _{i\in S} \frac{\delta _i^* - \bar{\delta ^*}}{\hbox {sd}(\delta ^*)}\) |
\(\delta _i^* = \delta _i \hbox {I}[sgn(\delta _i) = sgn(T_{mean}^{SC})]\) | \(\delta _i^* = \delta _i \hbox {I}[sgn(\delta _i) = sgn(T_{mean}^{CO})]\) | |
\([\delta _i] \equiv \hbox {modt-statistics, } i\in \Omega = [1,\ldots ,q]\) | ||
Notation | \(S \equiv \hbox {Testing gene set,} S\subset \Omega , \,\,\, m_0 = |S|,\,\, C = \Omega \setminus S\) | |
\(\bar{\delta } = q^{-1}\sum _{i\in \Omega } \delta _i, \,\,\, \bar{|\delta |} = q^{-1}\sum _{i\in \Omega } |\delta _i|, \,\,\, \hbox {med}\delta = \hbox {med}_{i \in \Omega }\delta _i\) | ||
\(\hbox {mad} \equiv \hbox {median absolute deviation from the median}\) | ||