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NetMix: A Network-Structured Mixture Model for Reduced-Bias Estimation of Altered Subnetworks

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Research in Computational Molecular Biology (RECOMB 2020)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 12074))

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Abstract

A classic problem in computational biology is the identification of altered subnetworks: subnetworks of an interaction network that contain genes/proteins that are differentially 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 often unknown. For example, some widely-used methods are reported to output very large subnetworks that are difficult to interpret biologically. In this work, we formulate the identification 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 identification of differentially expressed genes from both microarray and RNA-seq experiments and the identification of cancer driver genes in somatic mutation data.

M. A. Reyna and U. Chitra—These authors contributed equally.

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Notes

  1. 1.

    jActiveModules actually maximizes a normalized scan statistic \(\varGamma _{\text {norm}}(S)\). We show in the full paper [65] that maximizing \(\varGamma _{\text {norm}}(S)\) is equivalent to maximizing the unnormalized scan statistic \(\varGamma (S)\) when the data is generated from normal distributions.

  2. 2.

    The scan statistic (2) is the maximization of a non-linear objective function, but for fixed subnetwork size |S| the objective function is linear. We computed the scan statistic by modifying the ILP in heinz [24] to find a subnetwork of a fixed size, and running this ILP over all possible subnetwork sizes.

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Acknowledgments

We thank Mohammed El-Kebir for assistance with implementing jActiveModules* by modifying the ILP in heinz. We thank David Tse for directing us to the network anomaly literature. M.A.R. was supported in part by the National Cancer Institute of the NIH (Cancer Target Discovery and Development Network grant U01CA217875). B.J.R. was supported by US National Institutes of Health (NIH) grants R01HG007069 and U24CA211000.

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Authors and Affiliations

  1. Department of Computer Science, Princeton University, Princeton, NJ, 08544, USA

    Matthew A. Reyna, Uthsav Chitra, Rebecca Elyanow & Benjamin J. Raphael

  2. Department of Biomedical Informatics, Emory University, Atlanta, GA, 30306, USA

    Matthew A. Reyna

  3. Department of Computer Science, Brown University, Providence, RI, 02912, USA

    Rebecca Elyanow

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  1. Carnegie Mellon University, Pittsburgh, PA, USA

    Russell Schwartz

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Reyna, M.A., Chitra, U., Elyanow, R., Raphael, B.J. (2020). NetMix: A Network-Structured Mixture Model for Reduced-Bias Estimation of Altered Subnetworks. In: Schwartz, R. (eds) Research in Computational Molecular Biology. RECOMB 2020. Lecture Notes in Computer Science(), vol 12074. Springer, Cham. https://doi.org/10.1007/978-3-030-45257-5_11

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