# A general modular framework for gene set enrichment analysis

## Contents

### 1 Citation

M Ackermann and K Strimmer, A general modular framework for gene set enrichment analysis, 2009, BMC Bioinformatics, 10:47, pages etc in any possible citation style.

### 2 Summary

Gene set analyses have a modular structure, i.e. they consist of

- gene level statistics
- gene level significance assessment
- gene set statistics
- gene set significance assessment
- statistical conclusion

Alternatively, steps 1.-3. might be replaced by a single global test.

In this paper, 261 different variants of gene set enrichment procedures were evaluated based on simulated and experimental data.

### 3 Study outcomes

#### 3.1 Outcome O1: Gene level statistics

- The choice of the gene-level statistics (t, moderated t, or correlation) does NOT have a great impact
- t statistic, moderated t, and correlation fail to find gene sets that contain up- and downregulated genes

Outcomes O1 and O2 are presented as Table 2 in the original publication.

#### 3.2 Outcome O2: Transformation of the gene level statistics

- The transformation of the gene level statistic has a substantial impact
- Transformations help to find gene sets that contain up- and downregulated genes
- Combination of square transformation and rank transformation shows the best overall performance
- Binary transformation (i.e. using a cutpoint) and FDRs decrease the performance

Outcomes O1 and O2 are presented as Table 2 in the original publication.

#### 3.3 Outcome O3: Gene set statistics

- "mean and the maxmean statistic produce ... overall very good results"
- "median and the Wilcoxon test are primarily advantageous if the competitive null hypothesis is tested, or if there are many outliers in the data"
- "conditional FDR ... vary strongly with the choice of the gene-level statistic, transformation and permutation approach.
- The ES score showed a rather weak performance

Outcomes O3 are presented as Table 3 in the original publication.

#### 3.4 Outcome O4: Significance assessment

- The parametric approach has the best power but is overoptimistic if the assumption of statistical indpendence is violated
- Permutation seems to slightly outperform resampling
- "restandardization procedure performs very similar to resampling"

Outcomes O4 are presented as Table 4 in the original publication.

#### 3.5 Outcome O5: Global approaches

- The performance of the globaltest procedure "is not better than that of the less sophisticated univariate methods" but "is computationally a little bit faster".
- For Hotellings T2-test:
- an "overall poor" performance was obtained
- "the uncorrelated sets are found with the same reliability as with univariate approaches. However, ... the sets with correlation ... are hardly detected."
- shows "improved performance with sample label permutation as opposed to gene sampling."

Outcomes O5 are presented as Table 5 for the global test and in Table 6 for Hotellings T2 in the original publication.

#### 3.6 Further outcomes

### 4 Study design and evidence level

#### 4.1 General aspects

- 100 data sets were simulated
- The simulated data sets have 600 features (genes) and 20 samples (10 vs. 10)
- The data was simulated with normally distributed noise with variance equals to one
- 520 genes were consided as uninformative (delta=0, rho=0)
- Altogether, nine different simulation data sets were generated that consist of the following combinations:
- Gene sets with different levels of differential expression (delta \in {0, 0.75, 1, -1}) were simulated
- Gene sets with varying levels of intra-group correlation (rho \in {0, 0.6, -0.6}) were simulated
- Gene sets that contain regulated and unregulated genes (half/half) were generated as well as gene set that contain up- and downregulated genes.

- "The gene set statistic ES was not combined with a binary transformation since the latter does not allow a sensible ranking of the genes."
- In total
- 3 gene level statistics ×
- 5 transformations ×
- 6 gene set statistics ×
- 3 significance assessments
- minus 9 insensible combinations
- = 261 (in total) variants of gene set analyses were considered

- The authors count how frequently the p-values that assess significance at the gene-set level are below a significance level 0.05

#### 4.2 Design for Outcome O1: Gene level statistics

- The authors consider the impact of the selected approach at for module 1 (see summary above)
- Three approaches were considered: t, moderated t and correlation
- These approaches were evaluated for five different transformations (see O2)

- Multiple other approaches
- The authors already provide the important hint that the dependency on the gene level test statistic might be more relevant for smaller sample size (e.g. 3 vs 3)

#### 4.3 Design for Outcome O2: Transformation of the gene level statistics

- The outcome was generated for five different transformations (and three gene level statistics)

#### 4.4 Design for Outcome O3: Gene set statistics

- Three gene set statistics were investigated:
- mean
- maxmean
- median
- ES
- conditional FDR
- Wilcoxon

- This analyses were performed for the moderated t statistic (gene level) and by using the quadratic transformation. For significance assessment, resampling was applied.

#### 4.5 Design for Outcome O4: Significance assessment

- Four different approaches for assessing significance at the gene set level were evaluated:
- parametric
- resampling
- permutation
- restandardization

- This analysis was performed by using the moderated t as the gene level statistic in combination with a quadratic transformation and the mean as the gene set statistic

#### 4.6 Design for Outcome O5: Global approaches

- globaltest andHotelling's T2-test with a shrinkage covariance matrix was considered

### 5 Further comments and aspects

- Simulation is NOT based on characteristics or gene sets derived from real data
- The paper provides very comprehensive outcomes in terms of combinations of approaches
- After the paper was published another type of gene set statistics appeared that is based on Kolmogorov-Smirnov test. This approach is applied e.g. for GSEA.