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Nonparametric estimation of an event-free survival distribution under cross-sectional sampling. (English) Zbl 1383.62225
Ferger, Dietmar (ed.) et al., From statistics to mathematical finance. Festschrift in honour of Winfried Stute. Cham: Springer (ISBN 978-3-319-50985-3/hbk; 978-3-319-50986-0/ebook). 57-67 (2017).
Summary: In Survival Analysis and other fields, a target of much interest is the event-free survival, which evaluates along time the probability of surviving without undergoing a certain intermediate event (recurrence, infection, and so on). Under cross-sectional sampling, only individuals in progress (alive) at the cross-section date are recruited, thus the survival times are left-truncated by the recruitment times. In this setting, there exists much literature on nonparametric estimation of the total survival, focused on the product-limit estimator for left-truncated and possibly right-censored data. However, estimation of the event-free survival has not been investigated in much detail. In this work we review this problem and we introduce a new nonparametric estimator for the event-free survival, which overcomes some of the limitations of existing approaches. Asymptotic results are discussed. A comparative numerical study is conducted.
For the entire collection see [Zbl 1383.62010].
MSC:
62N05 Reliability and life testing
62G05 Nonparametric estimation
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