Details on multivariable and univariable methods

The topology-based pathway analysis methods test one of the two types of null hypotheses as proposed in [6] for gene set enrichment analysis. The first hypothesis expects the genes in a pathway to be at most as often differentially expressed as the genes outside the pathway (the remaining genes measured in the experiment). Methods testing this hypothesis typically use gene randomization in the assessment of statistical significance and cannot be applied in an experiment that only measured expression of genes in a particular pathway. The second group of methods tests the hypothesis that no gene from a pathway is differentially expressed. These methods can be used for both genome-wide as well as pathway-specific experiments but require sufficient sample size for sample randomization. Independently on the hypothesis tested, we can further distinguish multivariable and univariable methods. Known multivariable methods either use Gaussian Graphical Models [9] or Fourier analysis on graphs [8]. Univariable methods, typically increase the weight of the differentially expressed genes as function of their topological properties (position in the graph, proximity of other differentially expressed genes etc.) [7, 1, 12] or transform the expression profile of each sample separately from gene-level to pathway-level [5]. As a consequence, a change in the topological structure influences the result of the analysis in any of the topology-based methods.