Estimating the survival function under a generalized Koziol-Green model with partially informative censoring

Metrika

Volumn 48, Issue 3, 1998, Pages 189-207

  Gather, Ursula ^a   Pawlitschko, Jörg ^a  

^a TU DORTMUND UNIVERSITY   (Germany)

Author keywords

ACL estimator; Asymptotic representation of estimators; Informative random censoring; Kaplan Meier estimator; Koziol Green model

Indexed keywords

EID: 0033422018     PISSN: 00261335     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (29)

1. Abdushukurov AA (1984) On some estimates of the distribution function under random censorship. In: Conference of Young Scientists. Math. Inst. Acad. Sci. Uzbek. SSR, Taschkent. VINITI No. 8756-V (in Russian)
2. Andersen PK, Borgan Ø, Gill RD, Keiding N (1993) Statistical models based on counting processes. Springer, New York
3. Armitage, P (1959) The comparison of survival curves. J. Roy. Statist. Soc. Ser. A 122:279-300
4. Beirlant J, Carbonez A, van der Meulen E (1992) Long run proportional hazards models of random censorship. J. Statist. Plann. Inference 32:25-44
5. Billingsley P (1968) Convergence of probability measures. Wiley, New York
6. Breslow NE, Crowley J (1974) A large sample study of the life table and product limit estimates under random censorship. Ann. Statist. 2:437-453
7. Burke MD, Csörgo S, Horváth L (1981) Strong approximations of some biometric estimates under random censorship. Z. Wahrscheinlichkeitstheorie verw. Gebiete 56:87-112
8. Cheng PE, Lin GD (1984) Maximum likelihood estimation of survival function under the Koziol-Green proportional hazards model. Technical report B-84-5, Institute of Statistics, Academica Sinica, Taipei, Taiwan
9. Cheng PE, Lin GD (1987) Maximum likelihood estimation of a survival function under the Koziol-Green proportional hazards model. Statist. Probab. Lett. 5:75-80
10. Cox DR (1959) The analysis of exponentially distributed life-times with two types of failure. J. Roy. Statist. Soc. Ser. B 21:411-421
11. Csörgo S (1988) Estimation in the proportional hazards model of random censorship. Statistics 19:437-463
12. Csörgo S (1989) Testing for the proportional hazards model of random censorship. In: Mandl P, Hušková M (eds.) Proceedings of the Fourth Prague Symposium on Asymptotic Statistics. Charles University Press, Prague, pp. 41-53
13. Csörgo S (1998) Testing for the partial proportional hazards model of random censorship. In: Hušková M, Lachout P, Víšek JA (eds.) Prague Stochastics' 98 Proceedings. Union of Czech Mathematicians and Physicists, Prague, pp. 87-92
14. Csörgo S, Horváth L (1981) On the Koziol-Green model for random censorship. Biometrika 68:391-401
15. Csörgo S, Horváth L (1983) The rate of strong uniform consistency for the product-limit estimator. Z. Wahrscheinlichkeitstheorie verw. Gebiete 62:411-426
16. Földes A, Rejto L (1981) A LIL type result for the product limit estimator. Z. Wahrscheinlichkeitstheorie verw. Gebiete 56:75-86
17. Gill RD (1980) Censoring and stochastic integrals. Mathematical Centre Tracts 124, Amsterdam
18. Gill RD, van der Vaart AW (1993) Non- and semiparametric maximum likelihood estimators and the von Mises method - II. Scand. J. Statist. 20:271-288
19. Hollander M, Peña E (1989) Families of confidence bands for the survival function under the general random censorship model and the Koziol-Green model. Can. J. Statist. 17:59-74
20. Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53:457-481
21. Klein JP, Moeschberger ML (1997) Survival analysis: Techniques for censored and truncated data. Springer, New York
22. Koziol JA, Green SB (1976) A Cramér-von Mises statistic for randomly censored data. Biometrika 63:465-474
23. Lo S-H, Singh K (1986) The product-limit estimator and the bootstrap: Some asymptotic representations. Probab. Th. Rel. Fields 71:455-465
24. Lo S-H, Mack YP, Wang JL (1989) Density and hazard rate estimation for censored data via strong representations of the Kaplan-Meier estimator. Probab. Th. Rel. Fields 80:461-473
25. Major P, Rejto L (1988) Strong embedding of the estimator of the distribution function under random censorship. Ann. Statist. 16:1113-1132
26. Peña EA, Rohatgi VK (1989) Survival function estimation for a generalized proportional hazards model of random censorship. J. Statist. Plann. Inference 22:371-389
27. Peterson AV (1977) Expressing the Kaplan-Meier estimator as a function of empirical subsurvival functions. J. Amer. Statist. Assoc. 72:854-858
28. State W, Wang J-L (1993) The strong law under random censorship. Ann. Statist. 21:1591-1607
29. Winter BB, Földes A, Rejto L (1978) Glivenko-Cantelli theorems for the product-limit estimate. Probab. Contr. Inf. Th. 7:213-225