Robust and accurate data enrichment statistics via distribution function of sum of weights

Motivation: Term-enrichment analysis facilitates biological interpretation by assigning to experimentally/computationally obtained data annotation associated with terms from controlled vocabularies. This process usually involves obtaining statistical significance for each vocabulary term and using the most significant terms to describe a given set of biological entities, often associated with weights. Many existing enrichment methods require selections of (arbitrary number of) the most significant entities and/or do not account for weights of entities. Others either mandate extensive simulations to obtain statistics or assume normal weight distribution. In addition, most methods have difficulty assigning correct statistical significance to terms with few entities. Results: Implementing the well-known Lugananni-Rice formula, we have developed a novel approach, called SaddleSum, that is free from all the aforementioned constraints and evaluated it against several existing methods. With entity weights properly taken into account, SaddleSum is internally consistent and stable with respect to the choice of number of most significant entities selected. Making few assumptions on the input data, the proposed method is universal and can thus be applied to areas beyond analysis of microarrays. Employing asymptotic approximation, SaddleSum provides a term-size-dependent score distribution function that gives rise to accurate statistical significance even for terms with few entities. As a consequence, SaddleSum enables researchers to place confidence in its significance assignments to small terms that are often biologically most specific.