Bateson W. Facts limiting the theory of heredity. Science. 1907;26(672):649–60.

Article
CAS
PubMed
Google Scholar

Fisher RA. The correlation between relatives on the supposition of mendelian inheritance. Earth Environ Sci Trans R Soc Edinb. 1919;52(2):399–433.

Article
Google Scholar

Wang X, Elston RC, Zhu X. The meaning of interaction. Hum Heredity. 2010;70(4):269–77.

Article
PubMed
PubMed Central
Google Scholar

Van Steen K, Moore J. How to increase our belief in discovered statistical interactions via large-scale association studies? Hum Genet. 2019;138(4):293–305.

Article
PubMed
PubMed Central
Google Scholar

Moore JH, Williams SM. Traversing the conceptual divide between biological and statistical epistasis: systems biology and a more modern synthesis. Bioessays. 2005;27(6):637–46.

Article
CAS
PubMed
Google Scholar

Cordell HJ. Epistasis: what it means, what it doesn’t mean, and statistical methods to detect it in humans. Hum Mol Genet. 2002;11(20):2463–8.

Article
CAS
PubMed
Google Scholar

Phillips PC. Epistasis-the essential role of gene interactions in the structure and evolution of genetic systems. Nat Rev Genet. 2008;9(11):855–67.

Article
CAS
PubMed
PubMed Central
Google Scholar

Van Steen K. Travelling the world of gene–gene interactions. Brief Bioinform. 2012;13(1):1–19.

Article
PubMed
Google Scholar

Wang J, Joshi T, Valliyodan B, Shi H, Liang Y, Nguyen HT, Zhang J, Xu D. A Bayesian model for detection of high-order interactions among genetic variants in genome-wide association studies. BMC Genom. 2015;16(1):1011.

Article
Google Scholar

Hemani G, Shakhbazov K, Westra H-J, Esko T, Henders AK, McRae AF, Yang J, Gibson G, Martin NG, Metspalu A, et al. Detection and replication of epistasis influencing transcription in humans. Nature. 2014;508(7495):249–53.

Article
CAS
PubMed
PubMed Central
Google Scholar

Pecanka J, Jonker MA, Bochdanovits Z, Van Der Vaart AW. A powerful and efficient two-stage method for detecting gene-to-gene interactions in GWAS. Biostatistics. 2017;18(3):477–94.

Article
PubMed
Google Scholar

Calle ML, Urrea Gales V, Malats i Riera N, Van Steen K et al. Mb-mdr: model-based multifactor dimensionality reduction for detecting interactions in high-dimensional genomic data. 2008.

Bessonov K, Gusareva ES, Van Steen K. A cautionary note on the impact of protocol changes for genome-wide association snp × snp interaction studies: an example on ankylosing spondylitis. Hum Genet. 2015;134(7):761–73.

Article
PubMed
Google Scholar

Chang Y-C, Wu J-T, Hong M-Y, Tung Y-A, Hsieh P-H, Yee SW, Giacomini KM, Oyang Y-J, Chen C-Y. Genepi: gene-based epistasis discovery using machine learning. BMC Bioinform. 2020;21(1):1–13.

Article
Google Scholar

Ellinghaus D, Jostins L, Spain SL, Cortes A, Bethune J, Han B, Park YR, Raychaudhuri S, Pouget JG, Hübenthal M, et al. Analysis of five chronic inflammatory diseases identifies 27 new associations and highlights disease-specific patterns at shared loci. Nat Genet. 2016;48(5):510–8.

Article
CAS
PubMed
PubMed Central
Google Scholar

Watanabe K, Taskesen E, Van Bochoven A, Posthuma D. Functional mapping and annotation of genetic associations with FUMA. Nat Commun. 2017;8(1):1–11.

Article
CAS
Google Scholar

Duroux D, Climente-González H, Wienbrandt L, Van Steen K. Network aggregation to enhance results derived from multiple analytics. In: IFIP international conference on artificial intelligence applications and innovations, 2020. Springer. p. 128–140.

Gusareva ES, Van Steen K. Practical aspects of genome-wide association interaction analysis. Hum Genet. 2014;133(11):1343–58.

Article
PubMed
Google Scholar

Abegaz F, Van Lishout F, Mahachie John JM, Chiachoompu K, Bhardwaj A, Gusareva ES, Wei Z, Hakonarson H, Van Steen K, Consortium, I.I.G. Epistasis detection in genome-wide screening for complex human diseases in structured populations. Syst Med. 2019;2(1):19–27.

Franzin A, Sambo F, Di Camillo B. bnstruct: an r package for Bayesian network structure learning in the presence of missing data. Bioinformatics. 2017;33(8):1250–2.

CAS
PubMed
Google Scholar

R Core Team: R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2019). R Foundation for Statistical Computing. https://www.R-project.org/

Meyer PE, Meyer MPE. Package ‘infotheo’. R Packag. version 2009; 1.

Dougherty J, Kohavi R, Sahami M. Supervised and unsupervised discretization of continuous features. In: Machine learning proceedings 1995. Elsevier; 1995. p. 194–202.

Ignac TM, Skupin A, Sakhanenko NA, Galas DJ. Discovering pair-wise genetic interactions: an information theory-based approach. PLoS ONE. 2014;9(3):92310.

Article
Google Scholar

Varadan V, Miller DM III, Anastassiou D. Computational inference of the molecular logic for synaptic connectivity in *C. elegans*. Bioinformatics. 2006;22(14):497–506.

Article
Google Scholar

Hu T, Sinnott-Armstrong NA, Kiralis JW, Andrew AS, Karagas MR, Moore JH. Characterizing genetic interactions in human disease association studies using statistical epistasis networks. BMC Bioinform. 2011;12(1):1–13.

Article
CAS
Google Scholar

Meyer PE, Lafitte F, Bontempi G. minet: Ar/bioconductor package for inferring large transcriptional networks using mutual information. BMC Bioinform. 2008;9(1):461.

Article
Google Scholar

Peng H, Long F, Ding C. Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy. IEEE Trans Pattern Anal Mach Intell. 2005;27(8):1226–38.

Article
PubMed
Google Scholar

Csardi G, Nepusz T, et al. The igraph software package for complex network research. InterJournal Complex Syst. 2006;1695(5):1–9.

Google Scholar

Csardi MG. Package ‘igraph’. Last accessed. 2013;3(09):2013.

Kondor RI, Lafferty J. Diffusion kernels on graphs and other discrete structures. In: Proceedings of the 19th international conference on machine learning, vol 2002; 2002. p. 315–22.

Smola AJ, Kondor R. Kernels and regularization on graphs. In: Learning theory and kernel machines. Springer; 2003. p. 144–158.

Qiu Y, Mei J, Guennebaud G, Niesen J. Rspectra: solvers for large scale eigenvalue and svd problems. R package version 0.12-0. 2016;405.

Antonelli J, Mazumdar M, Bellinger D, Christiani D, Wright R, Coull B, et al. Estimating the health effects of environmental mixtures using Bayesian semiparametric regression and sparsity inducing priors. Ann Appl Stat. 2020;14(1):257–75.

Article
Google Scholar

Lesaffre E, Lawson AB. Bayesian biostatistics. Hoboken: Wiley; 2012. p. 358.

Book
Google Scholar

van den Berg I, Fritz S, Boichard D. Qtl fine mapping with bayes c (π): a simulation study. Genet Sel Evol. 2013;45(1):1–11.

Google Scholar

Barbieri MM, Berger JO, et al. Optimal predictive model selection. Ann Stat. 2004;32(3):870–97.

Article
Google Scholar

Ly V, Fokoué E. Frequentist approximation of the bayesian posterior inclusion probability by stochastic subsampling. J Adv Math Comput Sci. 2016;1–22.

Warde-Farley D, Donaldson SL, Comes O, Zuberi K, Badrawi R, Chao P, Franz M, Grouios C, Kazi F, Lopes CT, et al. The genemania prediction server: biological network integration for gene prioritization and predicting gene function. Nucleic Acids Res. 2010;38(suppl-2):214–20.

Article
Google Scholar

Li T, Wernersson R, Hansen RB, Horn H, Mercer J, Slodkowicz G, Workman CT, Rigina O, Rapacki K, Stærfeldt HH, et al. A scored human protein-protein interaction network to catalyze genomic interpretation. Nat Methods. 2017;14(1):61.

Article
CAS
PubMed
Google Scholar

Sherman BT, Lempicki RA, et al. Systematic and integrative analysis of large gene lists using DAVID bioinformatics resources. Nat Protoc. 2009;4(1):44.

Article
PubMed
Google Scholar

Huang DW, Sherman BT, Lempicki RA. Bioinformatics enrichment tools: paths toward the comprehensive functional analysis of large gene lists. Nucleic Acids Res. 2009;37(1):1–13.

Article
Google Scholar

Piñero J, Bravo À, Queralt-Rosinach N, Gutiérrez-Sacristán A, Deu-Pons J, Centeno E, García-García J, Sanz F, Furlong LI. Disgenet: a comprehensive platform integrating information on human disease-associated genes and variants. Nucleic Acids Rese. 2016;943.

Piñero J, Queralt-Rosinach N, Bravo A, Deu-Pons J, Bauer-Mehren A, Baron M, Sanz F, Furlong LI. Disgenet: a discovery platform for the dynamical exploration of human diseases and their genes. Database. 2015;2015.

Yoshioka A, Miyata H, Doki Y, Yamasaki M, Sohma I, Gotoh K, Takiguchi S, Fujiwara Y, Uchiyama Y, Monden M. Lc3, an autophagosome marker, is highly expressed in gastrointestinal cancers. Int J Oncol. 2008;33(3):461–8.

CAS
PubMed
Google Scholar

Giatromanolaki A, Koukourakis MI, Georgiou I, Kouroupi M, Sivridis E. Lc3a, lc3b and beclin-1 expression in gastric cancer. Anticancer Res. 2018;38(12):6827–33.

Article
CAS
PubMed
Google Scholar

Gregersen PK, Amos CI, Lee AT, Lu Y, Remmers EF, Kastner DL, Seldin MF, Criswell LA, Plenge RM, Holers VM, et al. Rel, encoding a member of the nf-κb family of transcription factors, is a newly defined risk locus for rheumatoid arthritis. Nat Genet. 2009;41(7):820–3.

Article
CAS
PubMed
PubMed Central
Google Scholar

Sakai H, Ohuchida K, Mizumoto K, Cui L, Nakata K, Toma H, Nagai E, Tanaka M. Inhibition of p600 expression suppresses both invasiveness and anoikis resistance of gastric cancer. Ann Surg Oncol. 2011;18(7):2057–65.

Article
PubMed
PubMed Central
Google Scholar

Kalim AS, Liana E, Fauzi AR, Sirait DN, Afandy D, Kencana SMS, Purnomo E, Iskandar K, Makhmudi A, et al. Aberrant ubr4 expressions in hirschsprung disease patients. BMC Pediatr. 2019;19(1):493.

Article
PubMed
PubMed Central
Google Scholar

Ng SC, Shi HY, Hamidi N, Underwood FE, Tang W, Benchimol EI, Panaccione R, Ghosh S, Wu JC, Chan FK, et al. Worldwide incidence and prevalence of inflammatory bowel disease in the 21st century: a systematic review of population-based studies. Lancet. 2017;390(10114):2769–78.

Article
PubMed
Google Scholar

Niel C, Sinoquet C, Dina C, Rocheleau G. A survey about methods dedicated to epistasis detection. Front Genet. 2015;6:285.

Article
PubMed
PubMed Central
Google Scholar

Wright MN, Ziegler A, König IR. Do little interactions get lost in dark random forests? BMC Bioinform. 2016;17(1):145.

Article
Google Scholar

Duroux D, Climente-Gonzáles H, Azencott C-A, Van Steen K. Interpretable network-guided epistasis detection. bioRxiv 2020.

Behr M, Kumbier K, Cordova-Palomera A, Aguirre M, Ashley E, Butte A, Arnaout R, Brown JB, Preist J, Yu B. Learning epistatic polygenic phenotypes with Boolean interactions. bioRxiv 2020.

Oh S, Lee J, Kwon M-S, Weir B, Ha K, Park T. A novel method to identify high order gene-gene interactions in genome-wide association studies: gene-based MDR. BMC Bioinform. 2012;13:1–9 (**BioMed Central**).

Article
Google Scholar

Fouladi R. From statistical to biological interactions towards an omics-integrated MB-MDR framework. Ph.D. thesis, Université de Liège, Liège, Belgique 2018.

De Andrade M, Wang X. Entropy based genetic association tests and gene–gene interaction tests. Stat Appl Genet Mol Biol. 2011;10(1):38.

Article
PubMed Central
Google Scholar

Ferrario PG, König IR. Transferring entropy to the realm of GxG interactions. Brief Bioinform. 2018;19(1):136–47.

PubMed
Google Scholar

Calle ML, Urrea V, Vellalta G, Malats N, Steen K. Improving strategies for detecting genetic patterns of disease susceptibility in association studies. Stat Med. 2008;27(30):6532–46.

Article
CAS
PubMed
Google Scholar

Fan R, Zhong M, Wang S, Zhang Y, Andrew A, Karagas M, Chen H, Amos C, Xiong M, Moore J. Entropy-based information gain approaches to detect and to characterize gene–gene and gene–environment interactions/correlations of complex diseases. Genet Epidemiol. 2011;35(7):706–21.

Article
CAS
PubMed
PubMed Central
Google Scholar

Kwon M-S, Park M, Park T. Igent: efficient entropy based algorithm for genome-wide gene–gene interaction analysis. BMC Med Genom. 2014;7(S1):6.

Article
Google Scholar

Malten J, König IR. Modified entropy-based procedure detects gene–gene-interactions in unconventional genetic models. BMC Med Genom. 2020;13:1–12.

Article
Google Scholar

Fouladi R, Bessonov K, Van Lishout F, Van Steen K. Model-based multifactor dimensionality reduction for rare variant association analysis. Hum Heredity. 2015;79(3–4):157–67.

Article
CAS
PubMed
Google Scholar

Wang T, Ho G, Ye K, Strickler H, Elston RC. A partial least-square approach for modeling gene–gene and gene–environment interactions when multiple markers are genotyped. Genet Epidemiol Off Publ Int Genet Epidemiol Soc. 2009;33(1):6–15.

CAS
Google Scholar

Li J, Tang R, Biernacka JM, De Andrade M. Identification of gene–gene interaction using principal components. BMC Proc. 2009;3:1–6 (**BioMed Central**).

Article
CAS
Google Scholar

Stanislas V, Dalmasso C, Ambroise C. Eigen-epistasis for detecting gene–gene interactions. BMC Bioinform. 2017;18(1):1–14.

Article
Google Scholar

Cattaert T, Calle ML, Dudek SM, John JMM, van Lishout F, Urrea V, Ritchie MD, van Steen K. A detailed view on model-based multifactor dimensionality reduction for detecting gene–gene interactions in case–control data in the absence and presence of noise. Ann Hum Genet. 2011;75(1):78.

Article
PubMed
Google Scholar

Zhang Y, Jiang B, Zhu J, Liu JS. Bayesian models for detecting epistatic interactions from genetic data. Ann Hum Genet. 2011;75(1):183–93.

Article
PubMed
Google Scholar

Pineda S, Sirota M. Determining significance in the new era for p values. J Pediatr Gastroenterol Nutr. 2018;67(5):547–8.

Article
PubMed
PubMed Central
Google Scholar

Sjölander A, Vansteelandt S. Frequentist versus Bayesian approaches to multiple testing. Eur J Epidemiol. 2019;34(9):809–21.

Article
PubMed
PubMed Central
Google Scholar

Huang JK, Carlin DE, Yu MK, Zhang W, Kreisberg JF, Tamayo P, Ideker T. Systematic evaluation of molecular networks for discovery of disease genes. Cell Syst. 2018;6(4):484–95.

Article
CAS
PubMed
PubMed Central
Google Scholar

Ritchie MD, Van Steen K. The search for gene–gene interactions in genome-wide association studies: challenges in abundance of methods, practical considerations, and biological interpretation. Ann Transl Med. 2018;6(8):157.

Article
PubMed
PubMed Central
Google Scholar

Jostins L, Ripke S, Weersma RK, Duerr RH, McGovern DP, Hui KY, Lee JC, Schumm LP, Sharma Y, Anderson CA, et al. Host-microbe interactions have shaped the genetic architecture of inflammatory bowel disease. Nature. 2012;491(7422):119–24.

Article
CAS
PubMed
PubMed Central
Google Scholar