Evaluating Whether a Module is Preserved in Another Network

Abstract

In network applications, one is often interested in studying whether modules are preserved across multiple networks. For example, to determine whether a pathway of genes is perturbed in a certain condition, one can study whether its connectivity pattern is no longer preserved. Non-preserved modules can be either biologically uninteresting (e.g., reflecting data outliers) or interesting (e.g., reflecting species-specific modules). An intuitive approach for studying module preservation is to cross-tabulate module membership. But this approach often cannot address questions about the preservation of connectivity patterns between nodes. Thus, cross-tabulation-based approaches often fail to recognize that important aspects of a network module are preserved. Cross-tabulation methods make it difficult to argue that a module is not preserved. The weak statement (“the reference module does not overlap with any of the identified test set modules”) is less relevant in practice than the strong statement (“the module cannot be found in the test network irrespective of the parameter settings of the module detection procedure”). Network concepts allow one to determine whether a module is preserved and reproducible in another network. Module preservation statistics have important applications, e.g., the wiring of apoptosis genes in a human cortical network differs from that in chimpanzees. It is advantageous to aggregate multiple preservation statistics into summary preservation statistics, e.g., Zsummary and medianRank. Our applications show that the correlation structure underlying correlation networks facilitates the definition of particularly powerful module preservation statistics. Evaluating module preservation is in general different from evaluating cluster preservation. However, when modules are defined as clusters, then close relationships exist with cluster preservation statistics. This chapter describes results from a collaboration with Peter Langfelder et al. (Plos Comput Biol 7(1):e1001057, 2011).