{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T18:43:41Z","timestamp":1786128221765,"version":"build-2736575974"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1014570","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T00:00:00Z","timestamp":1786060800000}}],"reference-count":44,"publisher":"Public Library of Science (PLoS)","issue":"7","license":[{"start":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T00:00:00Z","timestamp":1785456000000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100009053","name":"The Wellcome Trust DBT India Alliance","doi-asserted-by":"publisher","award":["IA\/I\/17\/2\/503323"],"award-info":[{"award-number":["IA\/I\/17\/2\/503323"]}],"id":[{"id":"10.13039\/501100009053","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"\n Distinguishing correlation from causation is a fundamental challenge in many scientific fields, including biology, especially when interventions like randomized controlled trials are infeasible and only observational data are available. Methods based on statistical tests of conditional independence within the Mendelian Randomization framework can detect causality between two observed variables that are each associated with a third instrumental variable. However, these methods for detecting causal relationships between traits (e.g., two gene expression or clinical traits associated with a genetic variant, all observed in the same population) often assume a linear relationship, thereby hindering the discovery of causal gene networks from genomics data. We have developed NLCD, a method for NonLinear Causal Discovery from genomics data based on nonlinear regression modeling and conditional feature importance scoring. NLCD uses these techniques to extend the statistical tests in an existing linear causal discovery method called the Causal Inference Test (CIT). We benchmarked NLCD against current state-of-the-art methods: CIT, Findr, and MRPC. On simulated datasets, NLCD performs comparably to most methods in detecting linear relations (Average AUPRC (Area Under the Precision-Recall Curve) of NLCD\u2009=\u20090.94, CIT\u2009=\u20090.94, Findr\u2009=\u20090.94, and MRPC\u2009=\u20090.99), and outperforms them in detecting nonlinear (sine and sawtooth type) relations between two genes (Average AUPRC of NLCD\u2009=\u20090.76, CIT\u2009=\u20090.60, Findr\u2009=\u20090.56, and MRPC\u2009=\u20090.73). When tested on a nonlinear subset of a yeast genomic dataset to recover known causal relations involving transcription factors, NLCD and CIT performed comparable to each other and slightly better than Findr and MRPC (Average AUPRC of NLCD\u2009=\u20090.82, CIT\u2009=\u20090.81, Findr\u2009=\u20090.71, and MRPC\u2009=\u20090.54). On application to a human genomic dataset, NLCD revealed active causal gene pairs (\n IRF1<\/jats:italic>\n \n \n \n \n \n \u2192<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n PSME1<\/jats:italic>\n and\n HLA-C<\/jats:italic>\n \n \n \n \n \n \u2192<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n HLA-T<\/jats:italic>\n ) in the muscle tissue, and clarified the promises and challenges in discovering causal gene networks in tissues under\n in vivo<\/jats:italic>\n human settings.\n <\/jats:p>","DOI":"10.1371\/journal.pcbi.1014570","type":"journal-article","created":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T17:40:08Z","timestamp":1785519608000},"page":"e1014570","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["NLCD: A method to discover nonlinear causal relations among genes"],"prefix":"10.1371","volume":"22","author":[{"given":"Aravind","family":"Easwar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8490-4087","authenticated-orcid":true,"given":"Manikandan","family":"Narayanan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,7,31]]},"reference":[{"key":"pcbi.1014570.ref001","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511803161","volume-title":"Causality: Models, Reasoning, and Inference","author":"J Pearl","year":"2009","edition":"2"},{"issue":"12","key":"pcbi.1014570.ref002","doi-asserted-by":"crossref","first-page":"1223","DOI":"10.1016\/j.jclinepi.2004.03.011","article-title":"Methods to assess intended effects of drug treatment in observational studies are reviewed","volume":"57","author":"OH Klungel","year":"2004","journal-title":"J Clin Epidemiol"},{"key":"pcbi.1014570.ref003","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1186\/1471-2156-10-23","article-title":"Disentangling molecular relationships with a causal inference test","volume":"10","author":"J Millstein","year":"2009","journal-title":"BMC Genet"},{"issue":"7","key":"pcbi.1014570.ref004","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1038\/ng1589","article-title":"An integrative genomics approach to infer causal associations between gene expression and disease","volume":"37","author":"EE Schadt","year":"2005","journal-title":"Nat Genet"},{"issue":"8","key":"pcbi.1014570.ref005","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1005703","article-title":"Efficient and accurate causal inference with hidden confounders from genome-transcriptome variation data","volume":"13","author":"L Wang","year":"2017","journal-title":"PLoS Comput Biol"},{"issue":"10","key":"pcbi.1014570.ref006","article-title":"Harnessing naturally randomized transcription to infer regulatory relationships among genes","volume":"8","author":"LS Chen","year":"2007","journal-title":"Genome Biol"},{"key":"pcbi.1014570.ref007","doi-asserted-by":"crossref","first-page":"460","DOI":"10.3389\/fgene.2019.00460","article-title":"Learning causal biological networks with the principle of Mendelian randomization","volume":"10","author":"MB Badsha","year":"2019","journal-title":"Front Genet"},{"key":"pcbi.1014570.ref008","doi-asserted-by":"crossref","first-page":"651812","DOI":"10.3389\/fgene.2021.651812","article-title":"MRPC: An R Package for Inference of Causal Graphs","volume":"12","author":"MB Badsha","year":"2021","journal-title":"Front Genet"},{"issue":"2","key":"pcbi.1014570.ref009","doi-asserted-by":"crossref","DOI":"10.1093\/genetics\/iyaf064","article-title":"Causal network inference of cis- and trans-gene regulation of expression quantitative trait loci across human tissues","volume":"230","author":"J Kvamme","year":"2025","journal-title":"Genetics"},{"issue":"3","key":"pcbi.1014570.ref010","first-page":"100124","article-title":"Polynomial Mendelian randomization reveals non-linear causal effects for obesity-related traits","volume":"3","author":"J Sulc","year":"2022","journal-title":"HGG Adv"},{"key":"pcbi.1014570.ref011","doi-asserted-by":"crossref","first-page":"904","DOI":"10.1016\/j.addr.2010.05.009","article-title":"Circadian rhythms in gene expression: relationship to physiology, disease, drug disposition and drug action","volume":"62","author":"S Sukumaran","year":"2010","journal-title":"Adv Drug Delivery Rev"},{"issue":"6","key":"pcbi.1014570.ref012","doi-asserted-by":"crossref","first-page":"877","DOI":"10.1097\/EDE.0000000000000161","article-title":"Instrumental variable analysis with a nonlinear exposure-outcome relationship","volume":"25","author":"EPIC-InterAct Consortium","year":"2014","journal-title":"Epidemiology"},{"issue":"9","key":"pcbi.1014570.ref013","doi-asserted-by":"crossref","first-page":"895","DOI":"10.1161\/CIRCULATIONAHA.120.049819","article-title":"Linear and nonlinear mendelian randomization analyses of the association between diastolic blood pressure and cardiovascular events","volume":"143","author":"M Arvanitis","year":"2021","journal-title":"Circulation"},{"key":"pcbi.1014570.ref014","article-title":"DAGs with NO TEARS: Continuous optimization for structure learning","volume":"31","author":"X Zheng","year":"2018","journal-title":"Adv Neural Inform Process Syst"},{"key":"pcbi.1014570.ref015","unstructured":"Zheng X, Dan C, Aragam B, Ravikumar P, Xing EP. Learning sparse nonparametric DAGs. In Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), volume 108 of Proceedings of Machine Learning Research. 2020. pp. 3414\u201325."},{"key":"pcbi.1014570.ref016","article-title":"Gradient-based neural DAG learning","author":"S Lachapelle","year":"2020","journal-title":"In International Conference on Learning Representations (ICLR)"},{"key":"pcbi.1014570.ref017","unstructured":"Yu Y, Chen J, Gao T, Yu M. DAG-GNN: DAG structure learning with graph neural networks. In: Proceedings of the 36th International Conference on Machine Learning (ICML), volume 97 of Proceedings of Machine Learning Research. 2019."},{"key":"pcbi.1014570.ref018","first-page":"804","article-title":"Kernel-based conditional independence test and application in causal discovery.","volume-title":"Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence (UAI)","author":"K Zhang","year":"2011"},{"key":"pcbi.1014570.ref019","first-page":"689","article-title":"Nonlinear causal discovery with additive noise models","volume":"21","author":"PO Hoyer","year":"2008","journal-title":"Adv Neural Inform Process Syst"},{"key":"pcbi.1014570.ref020","unstructured":"Zhang K, Hyv\u00e4rinen A. On the identifiability of the post-nonlinear causal model. In: Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence (UAI). 2009."},{"issue":"546","key":"pcbi.1014570.ref021","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1080\/01621459.2023.2179490","article-title":"Nonlinear causal discovery with confounders","volume":"119","author":"C Li","year":"2024","journal-title":"J Am Stat Assoc"},{"key":"pcbi.1014570.ref022","unstructured":"Gao M, Ding Y, Aragam B. A polynomial-time algorithm for learning nonparametric causal graphs. In: Advances in Neural Information Processing Systems. Vol 33. 2020. pp. 11599\u2013611."},{"key":"pcbi.1014570.ref023","volume-title":"Probabilistic Graphical Models: Principles and Techniques","author":"D Koller","year":"2009"},{"key":"pcbi.1014570.ref024","first-page":"2825","article-title":"Scikit-learn: Machine learning in Python","volume":"12","author":"F Pedregosa","year":"2011","journal-title":"J Mach Learn Res"},{"issue":"8","key":"pcbi.1014570.ref025","doi-asserted-by":"crossref","first-page":"2107","DOI":"10.1007\/s10994-021-06030-6","article-title":"Testing conditional independence in supervised learning algorithms","volume":"110","author":"DS Watson","year":"2021","journal-title":"Mach Learn"},{"key":"pcbi.1014570.ref026","volume-title":"Statistical Inference","author":"G Casella","year":"2002"},{"key":"pcbi.1014570.ref027","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1186\/1471-2105-12-411","article-title":"EPEPT: a web service for enhanced P-value estimation in permutation tests","volume":"12","author":"TA Knijnenburg","year":"2011","journal-title":"BMC Bioinformatics"},{"issue":"12","key":"pcbi.1014570.ref028","doi-asserted-by":"crossref","DOI":"10.1093\/bioinformatics\/btp211","article-title":"Fewer permutations, more accurate P-values","volume":"25","author":"TA Knijnenburg","year":"2009","journal-title":"Bioinformatics"},{"key":"pcbi.1014570.ref029","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.35471","article-title":"Genetics of trans-regulatory variation in gene expression","volume":"7","author":"FW Albert","year":"2018","journal-title":"Elife"},{"issue":"2","key":"pcbi.1014570.ref030","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1039\/D0MO00140F","article-title":"Comparison between instrumental variable and mediation-based methods for reconstructing causal gene networks in yeast","volume":"17","author":"A-A Ludl","year":"2021","journal-title":"Mol Omics"},{"key":"pcbi.1014570.ref031","doi-asserted-by":"crossref","DOI":"10.1093\/nar\/gkac1041","article-title":"YEASTRACT+: a portal for the exploitation of global transcription regulation and metabolic model data in yeast biotechnology and pathogenesis","volume":"51","author":"MC Teixeira","year":"2023","journal-title":"Nucleic Acids Res"},{"key":"pcbi.1014570.ref032","volume-title":"Mutual information as an exploratory measure for genomic data with discrete and continuous variables","author":"C Pardy","year":"2013"},{"issue":"1","key":"pcbi.1014570.ref033","doi-asserted-by":"crossref","DOI":"10.1214\/17-AOAS1055","article-title":"Integrative exploration of large high-dimensional datasets","volume":"12","author":"C Pardy","year":"2018","journal-title":"Ann Appl Stat"},{"key":"pcbi.1014570.ref034","first-page":"233","article-title":"The relationship between Precision-Recall and ROC curves.","volume-title":"Proceedings of the 23rd International Conference on Machine Learning, ICML 2006","author":"J Davis","year":"2006"},{"key":"pcbi.1014570.ref035","unstructured":"Flach PA, Kull M. Precision-Recall-Gain curves: PR analysis done right. In Proceedings of the 29th International Conference on Neural Information Processing Systems - Volume 1, NIPS 2015. Cambridge, MA, USA: MIT Press; 2015. pp. 838\u201346,"},{"key":"pcbi.1014570.ref036","first-page":"95","article-title":"Whole-Transcriptome Causal Network Inference with Genomic and Transcriptomic Data.","volume-title":"Gene Regulatory Networks: Methods in Molecular Biology","author":"L Wang","year":"2018"},{"issue":"10","key":"pcbi.1014570.ref037","doi-asserted-by":"crossref","first-page":"1353","DOI":"10.1093\/bioinformatics\/bts163","article-title":"Matrix eQTL: ultra fast eQTL analysis via large matrix operations","volume":"28","author":"AA Shabalin","year":"2012","journal-title":"Bioinformatics"},{"key":"pcbi.1014570.ref038","doi-asserted-by":"crossref","first-page":"1860","DOI":"10.12688\/f1000research.17145.1","article-title":"False positives in trans-eQTL and co-expression analyses arising from RNA-sequencing alignment errors","volume":"7","author":"A Saha","year":"2018","journal-title":"F1000Res"},{"key":"pcbi.1014570.ref039","unstructured":"Saha A, Battle A. Mappability resources for GRCh38 using Gencode v26 annotation. figshare. Dataset. 2018. https:\/\/doi.org\/10.6084\/m9.figshare.7315136.v3"},{"issue":"1","key":"pcbi.1014570.ref040","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.gene.2011.07.004","article-title":"Genome-wide analysis of interferon regulatory factor I binding in primary human monocytes","volume":"487","author":"L Shi","year":"2011","journal-title":"Gene"},{"issue":"1","key":"pcbi.1014570.ref041","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.cell.2013.06.020","article-title":"lincRNAs: genomics, evolution, and mechanisms","volume":"154","author":"I Ulitsky","year":"2013","journal-title":"Cell"},{"issue":"5","key":"pcbi.1014570.ref042","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1261\/rna.2658311","article-title":"Pseudogenes: pseudo-functional or key regulators in health and disease?","volume":"17","author":"RC Pink","year":"2011","journal-title":"RNA"},{"key":"pcbi.1014570.ref043","first-page":"775","article-title":"Fast randomized kernel ridge regression with statistical guarantees.","volume-title":"Proceedings of the 29th International Conference on Neural Information Processing Systems - Volume 1, NIPS 2015","author":"AE Alaoui","year":"2015"},{"issue":"1","key":"pcbi.1014570.ref044","first-page":"193","article-title":"Some remarks about the number of permutations one should consider to perform a permutation test","volume":"64","author":"M Marozzi","year":"2024","journal-title":"Statistica"}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014570","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,7]],"date-time":"2026-08-07T17:54:58Z","timestamp":1786125298000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1014570"}},"subtitle":[],"editor":[{"given":"Yuehua","family":"Cui","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,7,31]]},"references-count":44,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2026,7,31]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1014570","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,31]]}}}