{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T18:12:50Z","timestamp":1778782370145,"version":"3.51.4"},"reference-count":16,"publisher":"Public Library of Science (PLoS)","issue":"5","license":[{"start":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:00:00Z","timestamp":1778716800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>We study a functional threshold-crossing setting in which a population-level boundary evolves smoothly over time and crossing events are observed through subject-specific functional trajectories. Motivated by biomedical and environmental applications where brief excursions above a critical level may trigger risk activation, we formulate boundary recovery as a first-passage identification problem and propose a practical estimation strategy based on smoothing observed crossing pairs. The boundary is represented using penalized cubic B-splines with roughness control, and tuning parameters are selected by generalized cross-validation. We further emphasize the distinction between (i) a time-varying benchmark used to define first-passage times and (ii) a reconstructed conditional crossing-level curve summarizing typical values at the moment of transition. A Monte Carlo study demonstrates that the proposed estimator accurately recovers a variety of smooth threshold shapes under different sample sizes and noise levels, with improved performance as crossing information increases. An illustrative application to country-level age-standardized colon cancer incidence trajectories demonstrates how the framework yields stable empirical boundary reconstructions for male and female series, while explicitly accounting for left-censoring induced by the limited observation window.<\/jats:p>","DOI":"10.1371\/journal.pone.0348779","type":"journal-article","created":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T17:32:27Z","timestamp":1778779947000},"page":"e0348779","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["First-passage-based boundary estimation in functional data"],"prefix":"10.1371","volume":"21","author":[{"given":"Ahmet 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