NetMix: A network-structured mixture model for reduced-bias estimation of altered subnetworks

Abstract

A classic problem in computational biology is the identi cation of altered subnetworks: subnetworks of an interaction network that contain genes/proteins that are di erentially expressed, highly mutated, or otherwise aberrant compared to other genes/proteins. Numerous methods have been developed to solve this problem under various assumptions, but the statistical properties of these methods are o en unknown. For example, some widely-used methods are reported to output very large subnetworks that are di cult to interpret biologically. In this work, we formulate the identi cation of altered subnetworks as the problem of estimating the parameters of a class of probability distributions which we call the Altered Subset Distribution (ASD). We derive a connection between a popular method, jActiveModules, and the maximum likelihood estimator (MLE) of the ASD. We show that the MLE is statistically biased, explaining the large subnetworks output by jActiveModules. We introduce NetMix, an algorithm that uses Gaussian mixture models to obtain less biased estimates of the parameters of the ASD. We demonstrate that NetMix outperforms existing methods in identifying altered subnetworks on both simulated and real data, including the identi cation of di erentially expressed genes from both microarray and RNA-seq experiments and the identi cation of cancer driver genes in somatic mutation data. Availability: NetMix is available online at h ps://github.com/raphael-group/netmix.

NetMix2: Unifying network propagation and altered subnetworks

“…The ASP describes a broad class of problems that are studied in many fields including computational biology [8, 6, 60], statistics [72, 54, 57, 73] and machine learning [55, 61, 74], with different problems making different choices for (1) the distributions 𝒟 a , 𝒟 b and (2) the subnetwork family 𝒮. Two prominent examples of distributions 𝒟 a , 𝒟 b that have been previously studied in the biological literature are the following.…”

“…A major challenge with altered subnetwork approaches is to choose an appropriate subnetwork family. For example, connectivity is often too weak of an assumption for biological networks, e.g., some methods that use connectivity identify large subnetworks [59] because of a statistical bias in a commonly used test statistic [60, 61].…”

“…Because of these heuristics, network propagation approaches typically do not have provable guarantees for altered subnetwork identification. In contrast, methods that explicitly rely on a well-defined subnetwork family often have statistical or theoretical guarantees, e.g., jActiveModules [49] computes a maximum likelihood estimator while our recent estimator NetMix is asymptotically unbiased [60, 61].…”

“…NetMix2 generalizes NetMix [60] to a wide range of subnetwork families and vertex score distributions. Specifically, NetMix2 takes as input a wide variety of subnetwork families, including not only the “connected family” used in existing altered subnetwork methods [6, 8, 60] but also any subnetwork family defined by linear or quadratic constraints, such as subnetworks with high edge density or subnetworks with small cut-size. We use this flexibility to investigate the topology of subnetworks identified by network propagation methods.…”

“…Instead, we derive the propagation family , a subnetwork family that we show “approximates” the subnetworks identified by network propagation approaches and thereby unifies the two major network approaches in the literature: network propagation and altered subnetwork identification. NetMix2 also uses local false discovery rate (local FDR) methods [69, 70, 71] to flexibly model vertex score distributions, in contrast to the strict parametric assumptions made by existing methods [8, 60].…”