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Equating the nested sequence to a filtration and the appearance and disappearance of features to events, we show that simple event history methods can be used for the analysis of topological data. We propose a version of the well-known Nelson\u2013Aalen cumulative hazard estimator for the comparison of topological features of random fields and for testing parametric assumptions. We suggest a Cox proportional hazards approach for the analysis of embedded metric trees. The Nelson\u2013Aalen method is illustrated on globally distributed climate data and on neutral hydrogen distribution in the Milky Way. The Cox method is used to compare vascular patterns in fundus images of the eyes of healthy and diabetic retinopathy patients.<\/jats:p>","DOI":"10.1093\/biomet\/asaa097","type":"journal-article","created":{"date-parts":[[2020,11,5]],"date-time":"2020-11-05T12:36:50Z","timestamp":1604579810000},"page":"757-773","source":"Crossref","is-referenced-by-count":5,"title":["Event history and topological data analysis"],"prefix":"10.1093","volume":"108","author":[{"given":"K","family":"Garside","sequence":"first","affiliation":[{"name":"School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. K.A.Garside2@newcastle.ac.uk\u2003 A.Gjoka2@newcastle.ac.uk\u2003 Robin.Henderson@newcastle.ac.uk\u2003 H.A.Johnson@newcastle.ac.uk\u2003 Irina.Makarenko@newcastle.ac.uk"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A","family":"Gjoka","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. K.A.Garside2@newcastle.ac.uk\u2003 A.Gjoka2@newcastle.ac.uk\u2003 Robin.Henderson@newcastle.ac.uk\u2003 H.A.Johnson@newcastle.ac.uk\u2003 Irina.Makarenko@newcastle.ac.uk"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R","family":"Henderson","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. K.A.Garside2@newcastle.ac.uk\u2003 A.Gjoka2@newcastle.ac.uk\u2003 Robin.Henderson@newcastle.ac.uk\u2003 H.A.Johnson@newcastle.ac.uk\u2003 Irina.Makarenko@newcastle.ac.uk"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H","family":"Johnson","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. K.A.Garside2@newcastle.ac.uk\u2003 A.Gjoka2@newcastle.ac.uk\u2003 Robin.Henderson@newcastle.ac.uk\u2003 H.A.Johnson@newcastle.ac.uk\u2003 Irina.Makarenko@newcastle.ac.uk"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I","family":"Makarenko","sequence":"additional","affiliation":[{"name":"School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. K.A.Garside2@newcastle.ac.uk\u2003 A.Gjoka2@newcastle.ac.uk\u2003 Robin.Henderson@newcastle.ac.uk\u2003 H.A.Johnson@newcastle.ac.uk\u2003 Irina.Makarenko@newcastle.ac.uk"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,11,16]]},"reference":[{"key":"2021111803494576400_B1","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-68560-1","volume-title":"Survival and Event History Analysis","author":"Aalen","year":"2008"},{"key":"2021111803494576400_B2","article-title":"Persistence images: a stable vector representation of persistent homology","author":"Adams","year":"2016"},{"key":"2021111803494576400_B3","doi-asserted-by":"crossref","first-page":"11878","DOI":"10.1073\/pnas.1706885114","article-title":"Modeling and replicating statistical topology and evidence for CMB nonhomogeneity","volume":"114","author":"Adler","year":"2017","journal-title":"Proc. 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