Estimation of cis-eQTL effect sizes using a log of linear model.

The study of expression Quantitative Trait Loci (eQTL) is an important problem in genomics and biomedicine. While detection (testing) of eQTL associations has been widely studied, less work has been devoted to the estimation of eQTL effect size. To reduce false positives, detection methods frequently rely on linear modeling of rank-based normalized or log-transformed gene expression data. Unfortunately, these approaches do not correspond to the simplest model of eQTL action, and thus yield estimates of eQTL association that can be uninterpretable and inaccurate. In this article, we propose a new, log-of-linear model for eQTL action, termed ACME, that captures allelic contributions to cis-acting eQTLs in an additive fashion, yielding effect size estimates that correspond to a biologically coherent model of cis-eQTLs. We describe a non-linear least-squares algorithm to fit the model by maximum likelihood, and obtain corresponding p-values. We perform careful investigation of the model using a combination of simulated data and data from the Genotype Tissue Expression (GTEx) project. Our results reveal little evidence for dominance effects, a parsimonious result that accords with a simple biological model for allele-specific expression and supports use of the ACME model. We show that Type-I error is well-controlled under our approach in a realistic setting, so that rank-based normalizations are unnecessary. Furthermore, we show that such normalizations can be detrimental to power and estimation accuracy under the proposed model. We then show, through effect size analyses of whole-genome cis-eQTLs in the GTEx data, that using standard normalizations instead of ACME noticeably affects the ranking and sign of estimates.

Computing the statistical significance of optimized communities in networks.

In scientific problems involving systems that can be modeled as a network (or "graph"), it is often of interest to find network communities - strongly connected node subsets - for unsupervised learning, feature discovery, anomaly detection, or scientific study. The vast majority of community detection methods proceed via optimization of a quality function, which is possible even on random networks without communities. Therefore there is usually not an easy way to tell if a community is "significant", in this context meaning more internally connected than would be expected under a random graph model without communities. This paper generalizes existing null models and statistical tests for this purpose to bipartite graphs, and introduces a new significance scoring algorithm called Fast Optimized Community Significance (FOCS) that is highly scalable and agnostic to the type of graph. Compared with existing methods on unipartite graphs, FOCS is more numerically stable and better balances the trade-off between detection power and false positives. On a large-scale bipartite graph derived from the Internet Movie Database (IMDB), the significance scores provided by FOCS correlate strongly with meaningful actor/director collaborations on serial cinematic projects.

Significance-based community detection in weighted networks.

Community detection is the process of grouping strongly connected nodes in a network. Many community detection methods for un-weighted networks have a theoretical basis in a null model. Communities discovered by these methods therefore have interpretations in terms of statistical significance. In this paper, we introduce a null for weighted networks called the continuous configuration model. First, we propose a community extraction algorithm for weighted networks which incorporates iterative hypothesis testing under the null. We prove a central limit theorem for edge-weight sums and asymptotic consistency of the algorithm under a weighted stochastic block model. We then incorporate the algorithm in a community detection method called CCME. To benchmark the method, we provide a simulation framework involving the null to plant "background" nodes in weighted networks with communities. We show that the empirical performance of CCME on these simulations is competitive with existing methods, particularly when overlapping communities and background nodes are present. To further validate the method, we present two real-world networks with potential background nodes and analyze them with CCME, yielding results that reveal macro-features of the corresponding systems.

Community Extraction in Multilayer Networks with Heterogeneous Community Structure.

Multilayer networks are a useful way to capture and model multiple, binary or weighted relationships among a fixed group of objects. While community detection has proven to be a useful exploratory technique for the analysis of single-layer networks, the development of community detection methods for multilayer networks is still in its infancy. We propose and investigate a procedure, called Multilayer Extraction, that identifies densely connected vertex-layer sets in multilayer networks. Multilayer Extraction makes use of a significance based score that quantifies the connectivity of an observed vertex-layer set through comparison with a fixed degree random graph model. Multilayer Extraction directly handles networks with heterogeneous layers where community structure may be different from layer to layer. The procedure can capture overlapping communities, as well as background vertex-layer pairs that do not belong to any community. We establish consistency of the vertex-layer set optimizer of our proposed multilayer score under the multilayer stochastic block model. We investigate the performance of Multilayer Extraction on three applications and a test bed of simulations. Our theoretical and numerical evaluations suggest that Multilayer Extraction is an effective exploratory tool for analyzing complex multilayer networks. Publicly available code is available at https://github.com/jdwilson4/MultilayerExtraction.