{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T21:45:49Z","timestamp":1774647949841,"version":"3.50.1"},"reference-count":32,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T00:00:00Z","timestamp":1729123200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"funder":[{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,1,16]]},"abstract":"<jats:title>Summary<\/jats:title>\n               <jats:p>Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serve as important building blocks for forecasting and model building. Decades of research have advanced methods for functional principal component analysis, often assuming independence between the observation times and longitudinal outcomes. Yet such assumptions are fragile in real-world settings where observation times may be driven by outcome-related processes. Rather than ignoring the informative observation time process, we explicitly model the observational times by a general counting process dependent on time-varying prognostic factors. Identification of the mean, covariance function and functional principal components ensues via inverse intensity weighting. We propose using weighted penalized splines for estimation and establish consistency and convergence rates for the weighted estimators. Simulation studies demonstrate that the proposed estimators are substantially more accurate than the existing ones in the presence of a correlation between the observation time process and the longitudinal outcome process. We further examine the finite-sample performance of the proposed method using the Acute Infection and Early Disease Research Program study.<\/jats:p>","DOI":"10.1093\/biomet\/asae055","type":"journal-article","created":{"date-parts":[[2024,10,17]],"date-time":"2024-10-17T12:52:26Z","timestamp":1729169546000},"source":"Crossref","is-referenced-by-count":4,"title":["Functional principal component analysis with informative observation times"],"prefix":"10.1093","volume":"112","author":[{"given":"Peijun","family":"Sang","sequence":"first","affiliation":[{"name":"Department of Statistics and Actuarial Science, University of Waterloo , 200 University Avenue West , Waterloo, Ontario N2L 3G1,","place":["Canada"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dehan","family":"Kong","sequence":"additional","affiliation":[{"name":"Department of Statistical Sciences, University of Toronto , 700 University Avenue , Toronto, Ontario M5G 1X6,","place":["Canada"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7703-707X","authenticated-orcid":false,"given":"Shu","family":"Yang","sequence":"additional","affiliation":[{"name":"Department of Statistics, North Carolina State University , 2311 Stinson Drive , Raleigh, North Carolina 27695,","place":["USA"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2024,10,17]]},"reference":[{"key":"2025101620020454400_asae055-B1","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":"2025101620020454400_asae055-B2","doi-asserted-by":"crossref","DOI":"10.1093\/biomtc\/ujae065","article-title":"Multiply robust estimation of marginal structural models in observational studies subject to covariate-driven observations","volume":"80","author":"Coulombe","year":"2024","journal-title":"Biometrics"},{"key":"2025101620020454400_asae055-B3","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/j.2517-6161.1972.tb00899.x","article-title":"Regression models and life-tables","volume":"34","author":"Cox","year":"1972","journal-title":"J. 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