Abstract
This paper proposes kernel estimation of the occurrence rate function for recurrent event data with informative censoring. An informative censoring model is considered with assumptions made on the joint distribution of the recurrent event process and the censoring time without modeling the censoring distribution. Under the validity of the informative censoring model, we also show that an estimator based on the assumption of independent censoring becomes inappropriate and is generally asymptotically biased. To investigate the asymptotic properties of the proposed estimator, the explicit form of its asymptotic mean squared risk and the asymptotic normality are derived. Meanwhile, the empirical consistent smoothing estimator for the variance function of the estimator is suggested. The performance of the estimators are also studied through Monte Carlo simulations. An epidemiological example of intravenous drug user data is used to show the influence of informative censoring in the estimation of the occurrence rate functions for inpatient cares over time.
Similar content being viewed by others
References
Andersen, P. K., Borgan, O., Gill, R. D. and Keiding, N. (1993).Statistical Models Based on Counting Processes, Springer, New York.
Bartoszyński, R., Brown, B. W., McBride, C. M. and Thompson, J. R. (1981). Some nonparametric techniques for estimating the intensity function of a cancer related nonstationary poisson process,Ann. Statist.,9, 1050–1060.
Gasser, Th. and Müller H.-G. (1978). Kernel estimation of regression functions,Smoothing Techniques for Curve Estimation (eds. Th. Gasser and M. Rosenblatt), Lecture Notes in Mathematics, No. 757, 23–68, Springer, Berlin.
Lancaster, T. and Intrator, O. (1998). Panel data with survival: Hospitalization of HIV-positive patients,J. Amer. Statist. Assoc.,93, 46–53.
Lawless, J. F. and Nadeau, C. (1995). Some simple robust method for the analysis of recurrent events,Technometrics,37, 158–168.
Lawless, J. F., Nadeau, C. and Cook, R. J. (1997). Analysis of mean and rate functions for recurrent events,Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis (eds. D. Y. Lin and T. R. Fleming), 37–49, Springer, New York.
Lin, D. Y., Wei, L. J., Yang, I. and Ying, Z. (2000). Semiparametric regression for the mean and rate functions of recurrent events,J. Roy. Statist. Soc. Ser. B,62, 711–730.
Nelson, W. B. (1988). Graphical analysis of system repair data,Journal of Quality Technology,20, 24–35.
Pepe, M. S. and Cai, J. (1993). Some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates,J. Amer. Statist. Assoc.,88, 811–820.
Robins, J. M., Rotnitzky, A. and Zhao, L. P. (1995). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data,J. Amer. Statists. Assoc.,90, 106–121.
Scharfstein, D. O., Rotnitzky, A. and Robins, J. M. (1999). Adjusting for nonignorable drop-out using semiparametric nonresponse models,J. Amer. Statist. Assoc.,94, 1096–1120.
Sun, J. and Wei, L. J. (2000). Regression analysis of panel count data with covariate-dependent observation and censoring times,J. Roy. Statist. Soc. Ser. B,62, 293–302.
Vlahov, D., Anthony, J. C., Muñov, A., Margolick, J., Nelson, K.E., Celentano, D. D., Solomon, L. and Polk, B. F. (1991). The ALIVE study: A longitudinal study of HIV-1 infection in intravenous drug users: Description of methods,The Journal of Drug Issues,21, 759–776.
Wang, M. C., Qin, J. and Chiang, C. T. (2001). Analyzing recurrent event data with informative censoring,J. Amer. Statist. Assoc.,96, 1057–1065.
Author information
Authors and Affiliations
About this article
Cite this article
Chiang, CT., Wang, MC. Smoothing estimation of rate function for recurrent event data with informative censoring. Ann Inst Stat Math 56, 87–100 (2004). https://doi.org/10.1007/BF02530526
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02530526