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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].
62N05 Reliability and life testing
62G05 Nonparametric estimation
Full Text: DOI
[1] Asgharian M, Wolfson DB (2005) Asymptotic behavior of the unconditional NPMLE of the length-biased survivor function from censored prevalent cohort data. Annals of Statistics 33, 2109-2131. · Zbl 1086.62113
[2] Chang SH, Tzeng SJ (2006) Nonparametric estimation of sojourn time distributions for truncated serial event data a weight-adjusted approach. Lifetime Data Analysis 12, 53-67. · Zbl 1117.62107
[3] de Uña-Álvarez J, Veraverbeke N (2017) Copula-graphic estimation with left-truncated and right-censored data. Statistics 51, 387-403. · Zbl 1372.62049
[4] Fluss R, Mandel M, Freedman LS, Weiss IS, Zohar AE, Haklai Z, Gordond ES, Simchena E (2013) Correction of sampling bias in a cross-sectional study of post-surgical complications. Statistics in Medicine, 32, 2467-2478.
[5] Gijbels I, Wang JL (1993) Strong representations of the survival function estimator for truncated and censored data with applications. Journal of Multivariate Analysis 47, 210-229. · Zbl 0809.62027
[6] Sánchez-Sellero C, González-Manteiga W, Van Keilegom I (2005) Uniform representation of product-limit integrals with applications. Scandinavian Journal of Statistics 32, 563-581. · Zbl 1092.62027
[7] Strzalkowska-Kominiak E, Stute W (2010) On the probability of holes in truncated samples. Journal of Statistical Planning and Inference 140, 1519-1528. · Zbl 1185.62171
[8] Stute W (1993) Almost sure representations of the product-limit estimator for truncated data. Annals of Statistics 21, 146-156. · Zbl 0770.62027
[9] Stute W, Wang JL (2008) The central limit theorem under random truncation. Bernoulli 14, 604-622. · Zbl 1157.62017
[10] Tsai WY, Jewell NP, Wang MC (1987) A note on the product-limit estimator under right censoring and left truncation. Biometrika 74, 883-886. · Zbl 0628.62101
[11] Wang MC (1991) Nonparametric estimation from cross-sectional survival data. J. Amer. Statist. Assoc. 86 130-143. · Zbl 0739.62026
[12] Zhou Y, Yip PSF (1999) A strong representation of the product-limit estimator for left truncated and right censored data. Journal of Multivariate Analysis 69, 261-280. · Zbl 1057.62516
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