%0 Journal Article
%@ 1664-8021
%A Li, X
%A Xie, S
%A McColgan, P
%A Tabrizi, SJ
%A Scahill, R
%A Zeng, D
%A Wang, Y
%D 2018
%F discovery:10059558
%I FRONTIERS MEDIA SA
%J Frontiers in Genetics
%K graphical models, network analysis, causal structure discovery, heterogeneity, regularization
%T Learning Subject-Specific Directed Acyclic Graphs With Mixed Effects Structural Equation Models From Observational Data
%U https://discovery.ucl.ac.uk/id/eprint/10059558/
%V 9
%X 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.
%Z © 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.