Nonparametric estimators of the bivariate survival function under simplified censoring conditions

SUMMARY New bivariate survival function estimators are proposed in the case where the dependence relationship between the censoring variables are modelled. Specific examples include the cases when censoring variables are univariate, mutually independent or specified by a marginal model. Large sample properties of the proposed estimators are discussed. The finite sample performance of the proposed estimators compared with other fully nonparametric estimators is studied via simulations. A real data example is given.

[1]  Dorota M. Dabrowska,et al.  Kaplan-Meier Estimate on the Plane , 1988 .

[2]  Ramesh M. Korwar,et al.  Nonparametric Tests of Independence for Censored Data. , 1980 .

[3]  Jianwen Cai,et al.  Covariance and survivor function estimation using censored multivariate failure time data , 1992 .

[4]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[5]  C. Genest,et al.  A semiparametric estimation procedure of dependence parameters in multivariate families of distributions , 1995 .

[6]  J. Wellner,et al.  Empirical Processes with Applications to Statistics , 2009 .

[7]  O. Pons,et al.  A test of independence between two censored survival times , 1986 .

[8]  J A Hanley,et al.  Nonparametric estimation of a multivariate distribution in the presence of censoring. , 1983, Biometrics.

[9]  M. Laan.  Efficient estimation in the bivariate censoring model and repairing NPMLE , 1996 .

[10]  D. Oakes,et al.  Bivariate survival models induced by frailties , 1989 .

[11]  Richard D. Gill.  Multivariate Survival Analysis , 1993 .

[12]  Dorota M. Dabrowska,et al.  Rank Tests for Independence for Bivariate Censored Data , 1986 .

[13]  C. Genest.  Frank's family of bivariate distributions , 1987 .

[14]  P. Billingsley,et al.  Convergence of Probability Measures , 1969 .

[15]  D. Clayton.  A model for association in bivariate life tables and its application in epidemiological studies of familial tendency in chronic disease incidence , 1978 .

[16]  Ronald C. Pruitt.  Identifiability of Bivariate Survival Curves from Censored Data , 1993 .

[17]  Ross L. Prentice,et al.  On assessing the strength of dependency between failure time variates , 1996 .

[18]  Sue Leurgans,et al.  Nonparametric Estimation of a Bivariate Survival Function in the Presence of Censoring , 1986 .

[19]  C. Genest,et al.  The Joy of Copulas: Bivariate Distributions with Uniform Marginals , 1986 .

[20]  D. Oakes,et al.  A concordance test for independence in the presence of censoring. , 1982, Biometrics.

[21]  G. Maguluri.  Semiparametric Estimation of Association in a Bivariate Survival Function , 1993 .

[22]  Zhiliang Ying,et al.  A simple nonparametric estimator of the bivariate survival function under univariate censoring , 1993 .

[23]  C. Genest,et al.  Statistical Inference Procedures for Bivariate Archimedean Copulas , 1993 .