# Multiple event times in the presence of informative censoring: modeling and analysis by copulas

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## Abstract

Motivated by a breast cancer research program, this paper is concerned with the joint survivor function of multiple event times when their observations are subject to informative censoring caused by a terminating event. We formulate the correlation of the multiple event times together with the time to the terminating event by an Archimedean copula to account for the informative censoring. Adapting the widely used two-stage procedure under a copula model, we propose an easy-to-implement pseudo-likelihood based procedure for estimating the model parameters. The approach yields a new estimator for the marginal distribution of a single event time with semicompeting-risks data. We conduct both asymptotics and simulation studies to examine the proposed approach in consistency, efficiency, and robustness. Data from the breast cancer program are employed to illustrate this research.

## Keywords

Efficiency and robustness Marginal distribution Pseudo-likelihood estimation Variable correlation Variance estimation## Notes

### Acknowledgements

The statistical research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), the Canadian Statistical Sciences Institute (CANSSI), and the National Institute of Allergy and Infectious Disease (NIAID). The breast cancer research was funded by the Canadian Institutes of Health Research (TT7-128272). The authors thank the AE and two referees for their helpful comments and suggestions.

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