A prevailing technique to infer function from lists of identifications, from molecular biological high-throughput experiments, is over-representation analysis, where the identifications are compared to predefined sets of related genes often referred to as pathways. As at least some pathways are known to be incomplete in their annotation, algorithmic efforts have been made to complement them with information from functional association networks. While the terminology varies in the literature, we will here refer to such methods as Network Enrichment Analysis (NEA). Traditionally, the significance of inferences from NEA has been assigned using a null model constructed from randomizations of the network. Here we instead argue for a null model that more directly relates to the set of genes being studied, and have designed one dynamic programming algorithm that calculates the score distribution of NEA scores that makes it possible to assign unbiased mid p values to inferences. We also implemented a random sampling method, carrying out the same task. We demonstrate that our method obtains a superior statistical calibration as compared to the popular NEA inference engine, BinoX, while also providing statistics that are easier to interpret.

High throughput biology enables the measurements of relative concentrations of thousands of biomolecules from e.g. tissue samples. The process leaves the investigator with the problem of how to best interpret the potentially large numbers of differences between samples. Many activities in a cell depend on ordered reactions involving multiple biomolecules, often referred to as pathways. It hence makes sense to study differences between samples in terms of altered pathway activity, using so-called pathway analysis. Traditional pathway analysis gives significance to differences in the pathway components' concentrations between sample groups, however, less frequently used methods for estimating individual samples' pathway activities have been suggested. Here we demonstrate that such a method can be used for pathway-based survival analysis. Specifically, we investigate the pathway activities' association with patients' survival time based on the transcription profiles of the METABRIC dataset. Our implementation shows that pathway activities are better prognostic markers for survival time in METABRIC than the individual transcripts. We also demonstrate that we can regress out the effect of individual pathways on other pathways, which allows us to estimate the other pathways' residual pathway activity on survival. Furthermore, we illustrate how one can visualize the often interdependent measures over hierarchical pathway databases using sunburst plots.

Pathway analysis comes in many forms. Most are seeking to establish a connection between the activity of a certain biological pathway and a difference in phenotype, often relying on an upstream differential expression analysis to establish the difference between case and control. This process usually models this relationship using many assumptions, often of a linear nature, and may also involve statistical tests where the calculation of false discovery rates is not trivial.

Here, we propose a new method for pathway analysis, MIPath, that relies on information theoretical principles, and therefore is absent of a model for the nature of the association between pathway activity and phenotype, resulting on a very minimal set of assumptions. For this, we construct a different graph of samples for each pathway and score the association between the structure of this graph and any phenotype variable using Mutual Information, while adjusting for the effects of random chance in each score.

Our experiments show that this method produces robust and reproducible scores that successfully result in a high rank for target pathways on single cell datasets, outperforming established methods for pathway analysis on these same conditions.