Pathway analysis through mutual information.

MOTIVATION: In pathway analysis, we aim to establish a connection between the activity of a particular biological pathway and a difference in phenotype. There are many available methods to perform pathway analysis, many of them rely on an upstream differential expression analysis, and many model the relations between the abundances of the analytes in a pathway as linear relationships. RESULTS: Here, we propose a new method for pathway analysis, MIPath, that relies on information theoretical principles and, therefore, does not model the association between pathway activity and phenotype, resulting in relatively few assumptions. For this, we construct a graph of the data points for each pathway using a nearest-neighbor approach and score the association between the structure of this graph and the phenotype of these same samples using Mutual Information while adjusting for the effects of random chance in each score. The initial nearest neighbor approach evades individual gene-level comparisons, hence making the method scalable and less vulnerable to missing values. These properties make our method particularly useful for single-cell data. We benchmarked our method on several single-cell datasets, comparing it to established and new methods, and found that it produces robust, reproducible, and meaningful scores. AVAILABILITY AND IMPLEMENTATION: Source code is available at https://github.com/statisticalbiotechnology/mipath, or through Python Package Index as "mipathway."

Survival analysis of pathway activity as a prognostic determinant in breast cancer.

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 number 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.

A simple null model for inferences from network enrichment analysis.

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.