Estimating the association parameter for copula models under dependent censoring

Summary. Many biomedical studies involve the analysis of multiple events. The dependence between the times to these end points is often of scientific interest. We investigate a situation when one end point is subject to censoring by the other. The model assumptions of Day and co-workers and Fine and co-workers are extended to more general structures where the level of association may vary with time. Two types of estimating function are proposed. Asymptotic properties of the proposed estimators are derived. Their finite sample performance is studied via simulations. The inference procedures are applied to two real data sets for illustration.

[1]  R. Day,et al.  Adaptation of bivariate frailty models for prediction, with application to biological markers as prognostic indicators , 1997 .

[2]  J. Shih,et al.  A goodness-of-fit test for association in a bivariate survival model , 1998 .

[3]  J. Klein,et al.  Survival Analysis: Techniques for Censored and Truncated Data , 1997 .

[4]  D. Harrington,et al.  Counting Processes and Survival Analysis , 1991 .

[5]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[6]  S W Lagakos,et al.  Using auxiliary variables for improved estimates of survival time. , 1977, Biometrics.

[7]  R. Prentice,et al.  A generalisation of the Mantel—Haenszel test to bivariate failure time data , 1996 .

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

[9]  Martin T. Wells,et al.  Nonparametric estimators of the bivariate survival function under simplified censoring conditions , 1997 .

[10]  A. Adam Ding,et al.  On assessing the association for bivariate current status data , 2000 .

[11]  S W Lagakos,et al.  A stochastic model for censored-survival data in the presence of an auxiliary variable. , 1976, Biometrics.

[12]  J. Crowley,et al.  Covariance Analysis of Heart Transplant Survival Data , 1977 .

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

[14]  James M. Robins,et al.  Comparing two failure time distributions in the presence of dependent censoring , 1996 .

[15]  Martin T. Wells,et al.  Model Selection and Semiparametric Inference for Bivariate Failure-Time Data , 2000 .

[16]  J O'Quigley,et al.  A two-stage procedure for survival studies with surrogate endpoints. , 1995, Biometrics.

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

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

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

[20]  Jason P. Fine,et al.  On semi-competing risks data , 2001 .

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

[22]  T. Louis,et al.  Inferences on the association parameter in copula models for bivariate survival data. , 1995, Biometrics.

[23]  V T Farewell,et al.  The analysis of failure times in the presence of competing risks. , 1978, Biometrics.

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

[25]  Shu-Hui Chang.  A Two‐Sample Comparison for Multiple Ordered Event Data , 2000, Biometrics.