Algebraic Comparison of Partial Lists in Bioinformatics

The outcome of a functional genomics pipeline is usually a partial list of genomic features, ranked by their relevance in modelling biological phenotype in terms of a classification or regression model. Due to resampling protocols or to a metaanalysis comparison, it is often the case that sets of alternative feature lists (possibly of different lengths) are obtained, instead of just one list. Here we introduce a method, based on permutations, for studying the variability between lists ("list stability") in the case of lists of unequal length. We provide algorithms evaluating stability for lists embedded in the full feature set or just limited to the features occurring in the partial lists. The method is demonstrated by finding and comparing gene profiles on a large prostate cancer dataset, consisting of two cohorts of patients from different countries, for a total of 455 samples.