eprintid: 10059558 rev_number: 19 eprint_status: archive userid: 608 dir: disk0/10/05/95/58 datestamp: 2018-10-31 09:01:25 lastmod: 2021-09-24 22:10:38 status_changed: 2018-10-31 09:01:25 type: article metadata_visibility: show creators_name: Li, X creators_name: Xie, S creators_name: McColgan, P creators_name: Tabrizi, SJ creators_name: Scahill, R creators_name: Zeng, D creators_name: Wang, Y title: Learning Subject-Specific Directed Acyclic Graphs With Mixed Effects Structural Equation Models From Observational Data ispublished: pub subjects: UCH divisions: UCL divisions: B02 divisions: C07 divisions: D07 divisions: F86 keywords: graphical models, network analysis, causal structure discovery, heterogeneity, regularization note: © 2018 Li, Xie, McColgan, Tabrizi, Scahill, Zeng and Wang. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) (http://creativecommons.org/licenses/by/4.0/). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. abstract: The identification of causal relationships between random variables from large-scale observational data using directed acyclic graphs (DAG) is highly challenging. We propose a new mixed-effects structural equation model (mSEM) framework to estimate subject-specific DAGs, where we represent joint distribution of random variables in the DAG as a set of structural causal equations with mixed effects. The directed edges between nodes depend on observed exogenous covariates on each of the individual and unobserved latent variables. The strength of the connection is decomposed into a fixed-effect term representing the average causal effect given the covariates and a random effect term representing the latent causal effect due to unobserved pathways. The advantage of such decomposition is to capture essential asymmetric structural information and heterogeneity between DAGs in order to allow for the identification of causal structure with observational data. In addition, by pooling information across subject-specific DAGs, we can identify causal structure with a high probability and estimate subject-specific networks with a high precision. We propose a penalized likelihood-based approach to handle multi-dimensionality of the DAG model. We propose a fast, iterative computational algorithm, DAG-MM, to estimate parameters in mSEM and achieve desirable sparsity by hard-thresholding the edges. We theoretically prove the identifiability of mSEM. Using simulations and an application to protein signaling data, we show substantially improved performances when compared to existing methods and consistent results with a network estimated from interventional data. Lastly, we identify gray matter atrophy networks in regions of brain from patients with Huntington’s disease and corroborate our findings using white matter connectivity data collected from an independent study. date: 2018-10-02 date_type: published publisher: FRONTIERS MEDIA SA official_url: https://doi.org/10.3389/fgene.2018.00430 oa_status: green full_text_type: pub language: eng primo: open primo_central: open_green article_type_text: Article verified: verified_manual elements_id: 1595716 doi: 10.3389/fgene.2018.00430 language_elements: English lyricists_name: McColgan, Peter lyricists_name: Scahill, Rachael lyricists_name: Tabrizi, Sarah lyricists_id: PEMCC11 lyricists_id: RSCAH26 lyricists_id: SJTAB21 actors_name: Cuccu, Clara actors_id: CCCUC40 actors_role: owner full_text_status: public publication: Frontiers in Genetics volume: 9 article_number: 430 pages: 13 issn: 1664-8021 citation: Li, X; Xie, S; McColgan, P; Tabrizi, SJ; Scahill, R; Zeng, D; Wang, Y; (2018) Learning Subject-Specific Directed Acyclic Graphs With Mixed Effects Structural Equation Models From Observational Data. Frontiers in Genetics , 9 , Article 430. 10.3389/fgene.2018.00430 <https://doi.org/10.3389/fgene.2018.00430>. Green open access document_url: https://discovery.ucl.ac.uk/id/eprint/10059558/1/LI_fgene-09-00430.pdf