{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T09:03:08Z","timestamp":1789376588499,"version":"build-2803163510"},"reference-count":43,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T00:00:00Z","timestamp":1789344000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Pharmacol."],"abstract":"<jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>Parametric time-to-event (TTE) modeling is widely used in clinical trials to evaluate treatment response, patient prognosis, and drug-related adverse events (AEs). As follow-up assessments increasingly capture recurrent AEs, there is a growing need for analytical approaches that extend beyond traditional single-event frameworks. However, commonly used TTE models often assume independence between recurrent events, limiting their ability to represent inter-event dependence observed in real-world clinical data.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>We mathematically examined and reconstructed the existing NONMEM\u00ae (version 7.5) control code used for parametric repeated-event analyses and evaluated the statistical foundations of commonly applied parametric and nonparametric approaches, including Kaplan\u2013Meier\u2013based methods. Based on these analyses, we identified methodological gaps and proposed an improved probabilistic framework that more rigorously represents recurrent event dynamics while allowing for multiple dependent event occurrences. The proposed and existing methods were compared through simulation studies under diverse event-generation scenarios, and practical guidance for model selection was developed.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>Three approaches were evaluated: two conventional parametric methods (methods 1, 2) and a newly proposed method (method 3). Overall, when the hazard function remained constant, all three methods produced similar results; however, clear differences in performance emerged depending on hazard dynamics and event density. When the hazard decreased gradually and events were relatively evenly distributed, method 2 demonstrated the closest alignment with nonparametric estimates, whereas when the hazard declined rapidly and events were concentrated in the early phase, method 3 showed a relatively better fit. In addition, because nonparametric estimators inherently involve uncertainty, discrepancies between parametric and nonparametric approaches do not necessarily indicate model misspecification, underscoring the need for careful interpretation in light of data characteristics and underlying hazard structures.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusion<\/jats:title>\n                    <jats:p>These findings highlight the importance of selecting analytical methods according to data characteristics and suggest that complementary use of both widely used and newly proposed methods can improve the accuracy of recurrent event modeling. The proposed guidelines are expected to facilitate more systematic and reliable interpretation of recurrent AE data frequently encountered in clinical trials and real-world clinical settings, ultimately contributing to more robust evaluations of drug efficacy and safety as well as optimization of dosing strategies.<\/jats:p>\n                  <\/jats:sec>","DOI":"10.3389\/fphar.2026.1791423","type":"journal-article","created":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T08:12:17Z","timestamp":1789373537000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["The refinement of repeated exact time-to-event modeling: methodological refinements and implementation in NONMEM\u00ae \u2014part I"],"prefix":"10.3389","volume":"17","author":[{"given":"Jiyoung","family":"Seo","sequence":"first","affiliation":[{"name":"Asan Medical Center, Department of Clinical Pharmacology and Therapeutics, University of Ulsan College of Medicine","place":["Seoul, Republic of Korea"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hyeong-Seok","family":"Lim","sequence":"additional","affiliation":[{"name":"Asan Medical Center, Department of Clinical Pharmacology and Therapeutics, University of Ulsan College of Medicine","place":["Seoul, Republic of Korea"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1965","published-online":{"date-parts":[[2026,9,14]]},"reference":[{"key":"B1","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-68560-1","volume-title":"Survival and event history analysis: a process point of view","author":"Aalen","year":"2008"},{"key":"B2","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1093\/ije\/dyu222","article-title":"Modelling recurrent events: a tutorial for analysis in epidemiology","volume":"44","author":"Amorim","year":"2015","journal-title":"Int. J. Epidemiol."},{"key":"B3","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-4348-9","volume-title":"Statistical models based on counting processes","author":"Andersen","year":"1993"},{"key":"B4","volume-title":"Mathematical analysis","author":"Apostol","year":"1974"},{"key":"B5","unstructured":"On norm sub-additivity and super-additivity inequalities for concave and convex functions\n          \n          \n            \n              Audenaert\n              K. M. R.\n            \n            \n              Aujla\n              J. S.\n            \n          \n          \n          2011"},{"key":"B6","volume-title":"NONMEM user\u2019s guides: introduction to NONMEM 7","author":"Bauer","year":"2022"},{"key":"B7","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-9485-1","volume-title":"Pharmacokinetic\u2013pharmacodynamic modeling and simulation","author":"Bonate","year":"2011"},{"key":"B8","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511804441","volume-title":"Convex optimization","author":"Boyd","year":"2004"},{"key":"B9","doi-asserted-by":"crossref","DOI":"10.1201\/b18041","volume-title":"Modelling survival data in medical research","author":"Collett","year":"2015"},{"key":"B10","volume-title":"The remainder in taylor series","author":"Conrad","year":"2010"},{"key":"B11","volume-title":"The statistical analysis of recurrent events","author":"Cook","year":"2007"},{"key":"B12","unstructured":"Weibull distribution: how to model time-to-event data\n          \n          \n          2026"},{"key":"B13","doi-asserted-by":"publisher","first-page":"2290120","DOI":"10.1155\/2021\/2290120","article-title":"Methods to analyse time-to-event data: the kaplan\u2013meier survival curve","volume":"2021","author":"D\u2019Arrigo","year":"2021","journal-title":"Oxid. Med. Cell Longev."},{"key":"B14","unstructured":"Event instantaneous hazard based on kaplan\u2013meier survival estimates [R package epiR version 2.0.75]\n          \n          \n          2026"},{"key":"B15","volume-title":"Counting processes and survival analysis","author":"Fleming","year":"2011"},{"key":"B16","doi-asserted-by":"publisher","first-page":"954","DOI":"10.1002\/psp4.70009","article-title":"Population pharmacokinetic\/pharmacodynamic and exposure\u2013response modeling of garadacimab in healthy volunteers and patients with hereditary angioedema","volume":"14","author":"Garcia","year":"2025","journal-title":"CPT Pharmacometrics and Syst. Pharmacol."},{"key":"B17","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1111\/j.0006-341X.2000.00554.x","article-title":"Nonparametric analysis of recurrent events and death","volume":"56","author":"Ghosh","year":"2000","journal-title":"Biometrics"},{"key":"B18","doi-asserted-by":"publisher","first-page":"e70231","DOI":"10.1002\/psp4.70231","article-title":"Impact of event-related treatment modifications in exposure-response analyses of repeated time-to-event data","volume":"15","author":"Goulooze","year":"2026","journal-title":"CPT Pharmacometrics and Syst. Pharmacol."},{"key":"B19","first-page":"1","article-title":"The natural duration of cancer","volume":"33","author":"Greenwood","year":"1926","journal-title":"Rep. Public Health Med. Subj."},{"key":"B20","doi-asserted-by":"crossref","DOI":"10.1002\/9781118032985","volume-title":"The statistical analysis of failure time data","author":"Kalbfleisch","year":"2002"},{"key":"B21","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1080\/01621459.1958.10501452","article-title":"Nonparametric estimation from incomplete observations","volume":"53","author":"Kaplan","year":"1958","journal-title":"J. Am. Stat. Assoc."},{"key":"B22","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4419-6646-9","volume-title":"Survival analysis: a self-learning text","author":"Kleinbaum","year":"2012"},{"key":"B23","volume-title":"Theory and application of infinite series","author":"Knopp","year":"1951"},{"key":"B24","doi-asserted-by":"crossref","DOI":"10.1201\/b17203","volume-title":"Mixed effects models for the population approach","author":"Lavielle","year":"2014"},{"key":"B25","volume-title":"Statistical models and methods for lifetime data","author":"Lawless","year":"2003"},{"key":"B26","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1186\/1471-2288-14-17","article-title":"Estimating time-to-onset of adverse drug reactions from spontaneous reporting databases","volume":"14","author":"Leroy","year":"2014","journal-title":"BMC Med. Res. Methodol."},{"key":"B27","article-title":"Concavity and the second derivative","volume-title":"Calculus","year":"2023"},{"key":"B28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.12793\/tcp.2021.29.e7","article-title":"Brief introduction to parametric time-to-event models","volume":"29","author":"Lim","year":"2021","journal-title":"Transl. Clin. Pharmacol."},{"key":"B29","volume-title":"Intermediate and mean value theorems and taylor series","author":"Miller","year":"2016"},{"key":"B30","volume-title":"Distribution (Weibull) fitting","year":"2026"},{"key":"B31","doi-asserted-by":"crossref","DOI":"10.1002\/0471725234","volume-title":"Applied life data analysis","author":"Nelson","year":"1982"},{"key":"B32","volume-title":"Taylor and Maclaurin Series","year":"2022"},{"key":"B33","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198507659.001.0001","volume-title":"In all likelihood: statistical modelling and inference using likelihood","author":"Pawitan","year":"2001"},{"key":"B34","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1007\/s00392-018-1205-7","article-title":"Time-to-first-event versus recurrent-event analysis: points to consider for selecting a meaningful analysis strategy in clinical trials with composite endpoints","volume":"107","author":"Rauch","year":"2018","journal-title":"Clin. Res. Cardiol."},{"key":"B35","volume-title":"Discrete mathematics and its applications","author":"Rosen","year":"2012"},{"key":"B36","volume-title":"Principles of mathematical analysis","author":"Rudin","year":"1976"},{"key":"B37","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1093\/acprof:oso\/9780195152968.001.0001","volume-title":"Applied longitudinal data analysis: modeling change and event occurrence","author":"Singer","year":"2003"},{"key":"B38","article-title":"A package for survival analysis in R (Version dated August 13, 2023). R package vignette, survival package","author":"Therneau","year":""},{"key":"B39","unstructured":"Survival analysis [R package version 3.5-5]\n          \n          \n            \n              Therneau\n              T. M."},{"key":"B40","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1007\/978-1-4757-3294-8_8","article-title":"Ordered multiple events","volume-title":"Modeling survival data: extending the cox model","author":"Therneau","year":"2000"},{"key":"B41","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/978-0-387-21706-2_13","volume-title":"Modern applied statistics with S","author":"Venables","year":"2002"},{"key":"B42","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1080\/01621459.1999.10473831","article-title":"Nonparametric estimation of a recurrent survival function","volume":"94","author":"Wang","year":"1999","journal-title":"J. Am. Stat. Assoc."},{"key":"B43","doi-asserted-by":"publisher","first-page":"860","DOI":"10.1002\/jcph.70008","article-title":"Efanesoctocog alfa population pharmacokinetics and repeated time-to-event analysis of bleeds in adults, adolescents, and children with severe hemophilia A","volume":"65","author":"Wong","year":"2025","journal-title":"J. Clin. Pharmacol."}],"container-title":["Frontiers in Pharmacology"],"original-title":[],"link":[{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fphar.2026.1791423\/full","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,14]],"date-time":"2026-09-14T08:12:26Z","timestamp":1789373546000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.frontiersin.org\/articles\/10.3389\/fphar.2026.1791423\/full"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,14]]},"references-count":43,"alternative-id":["10.3389\/fphar.2026.1791423"],"URL":"https:\/\/doi.org\/10.3389\/fphar.2026.1791423","relation":{},"ISSN":["1663-9812"],"issn-type":[{"value":"1663-9812","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,14]]},"article-number":"1791423"}}