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The analysis of such data using nonparametric multistate models was not possible until recently but is very desirable as it allows for more flexibility than its parametric counterparts. The single available result to date has some unique drawbacks. We propose a nonparametric estimator of the transition intensities for interval\u2010censored multistate data using an Expectation Maximization algorithm. The method allows for a mix of interval\u2010censored and right\u2010censored (exactly observed) transitions. A condition to check for the convergence of the algorithm is given. A simulation study comparing the proposed estimator to a consistent estimator is performed and shown to yield near identical estimates at smaller computational cost. A data set on the emergence of teeth in children is analyzed. Software to perform the analyses is publicly available.<\/jats:p>","DOI":"10.1002\/sim.70225","type":"journal-article","created":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T11:04:23Z","timestamp":1755255863000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Nonparametric Estimation of Transition Intensities in Interval\u2010Censored Markov Multistate Models Without Loops"],"prefix":"10.1002","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9011-3743","authenticated-orcid":false,"given":"Daniel","family":"Gomon","sequence":"first","affiliation":[{"name":"Mathematical Institute Leiden University  Leiden the Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5395-1422","authenticated-orcid":false,"given":"Hein","family":"Putter","sequence":"additional","affiliation":[{"name":"Mathematical Institute Leiden University  Leiden the Netherlands"},{"name":"Department of Biomedical Data Sciences Leiden University Medical Centre  Leiden the Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2025,8,15]]},"reference":[{"key":"e_1_2_10_2_1","volume-title":"Survival Analysis With Interval\u2010Censored Data","author":"Bogaerts K.","year":"2020"},{"key":"e_1_2_10_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1976.tb01597.x"},{"key":"e_1_2_10_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0258(19980130)17:2<219::AID-SIM735>3.0.CO;2-O"},{"key":"e_1_2_10_5_1","doi-asserted-by":"publisher","DOI":"10.1191\/0962280202sm279ra"},{"issue":"3","key":"e_1_2_10_6_1","first-page":"141","article-title":"An Empirical Transition Matrix for Non\u2010Homogeneous Markov Chains Based on Censored Observations","volume":"5","author":"Aalen O. 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