{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T14:26:23Z","timestamp":1783347983183,"version":"3.54.6"},"reference-count":30,"publisher":"Oxford University Press (OUP)","issue":"4","license":[{"start":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T00:00:00Z","timestamp":1763683200000},"content-version":"vor","delay-in-days":44,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["R37 AI054165"],"award-info":[{"award-number":["R37 AI054165"]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1915829"],"award-info":[{"award-number":["DMS-1915829"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,8]]},"abstract":"<jats:title>ABSTRACT<\/jats:title>\n                  <jats:p>Motivated by a malaria vaccine efficacy trial, this paper investigates generalized nonparametric temporal models of intensity processes with multiple time scales. Through the choice of link functions, the proposed models encompass a wide range of models such as the multiplicative temporal intensity model and the additive temporal intensity model. A maximum likelihood estimation procedure is developed to estimate the effects of two time-scales via the local linear smoothing with double kernels. Computational algorithms are developed to facilitate applications of the proposed method. An adaptive algorithm is developed to overcome the challenges of overlapping covariates. A cross-validation bandwidth selection procedure based on the logarithm of likelihood criteria is discussed. The asymptotic properties of the proposed estimators are investigated. Our simulation study shows that the proposed methods have satisfactory finite sample performance for both the multiplicative temporal intensity model and additive temporal intensity model. The proposed methods are applied to analyze the MAL-094\/MAL-095 malaria vaccine efficacy trial data to investigate how the new malaria infection risk changes over time and how a prior infection or vaccination changes the future infection risk. The proposed method provides new insight into the protective effects of the malaria vaccine against new malaria infections and how the vaccine efficacy is modified by the history of prior malaria infection over time.<\/jats:p>","DOI":"10.1093\/biomtc\/ujaf146","type":"journal-article","created":{"date-parts":[[2025,11,21]],"date-time":"2025-11-21T08:36:37Z","timestamp":1763714197000},"source":"Crossref","is-referenced-by-count":0,"title":["Generalized nonparametric temporal modeling of recurrent events with application to a malaria vaccine trial"],"prefix":"10.1093","volume":"81","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6701-7873","authenticated-orcid":false,"given":"Fei","family":"Heng","sequence":"first","affiliation":[{"name":"University of North Florida Department of Mathematics and Statistics, , Jacksonville, FL 32224 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3140-4572","authenticated-orcid":false,"given":"Yanqing","family":"Sun","sequence":"additional","affiliation":[{"name":"University of North Carolina at Charlotte Department of Mathematics and Statistics, , Charlotte, NC 28223 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jing","family":"Xu","sequence":"additional","affiliation":[{"name":"Vaccine and Infectious Disease, Fred Hutchinson Cancer Center , Seattle, WA 98109 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2662-9427","authenticated-orcid":false,"given":"Peter B","family":"Gilbert","sequence":"additional","affiliation":[{"name":"Vaccine and Infectious Disease, Fred Hutchinson Cancer Center , Seattle, WA 98109 ,","place":["United States"]},{"name":"University of Washington Department of Biostatistics, , Seattle, WA 98109 ,","place":["United States"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,11,21]]},"reference":[{"key":"2026070610021334200_bib1","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1214\/aos\/1176344247","article-title":"Nonparametric inference for a family of counting processes","volume":"6","author":"Aalen","year":"1978","journal-title":"Annals of Statistics"},{"key":"2026070610021334200_bib2","first-page":"1","volume-title":"Statistical Models Based on Counting Processes. 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