Abstract
This article mainly considers the recurrent event process with independent censoring mechanism through a more flexible varying-coefficient model. The smoothing estimators for the varying-coefficient functions are also proposed via maximizing the kernel weight version of the log-partial likelihood function with respect to the coefficients at each time point. For the selection of appropriate bandwidths and the construction of confidence intervals, the consistent empirical smoothing estimators for the covariance functions of the estimators and a bias correction method are considered. As for the baseline effect function of recurrent events in the population, two different smoothing estimation methods are suggested and investigated. In this study, the asymptotic properties of the proposed smoothing estimators are derived. The finite sample properties of our methods are examined through a Monte Carlo simulation. Moreover, the procedures are applied to a recurrent sample of AIDS link to intravenous experiences (ALIVE) cohort study.
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References
Andersen P.K., Borgan O., Gill R.D., Keiding N. (1993). Statistical models based on counting processes. 76. New York, Springer
Cai Z., Sun Y. (2003). Local linear estimation for time-dependent coefficients in Cox’s regression models. Scandinavian Journal of Statistics 30: 93–111
Gasser Th., Müller H.-G. (1978). Kernel estimation of regression functions. smoothing techniques for curve estimation. In: Gasser Th., Rosenblatt M. (eds) Spring Lecture Notes in Mathematics 757. Berlin, Springer, pp 23–68
Gray R.J. (1992). Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis. Journal of the American Statistical Association 87: 942–951
Lancaster T., Intrator O. (1998). Panel data with survival: hospitalization of HIV-positive patients. Journal of the American Statistical Association 93: 46–53
Lawless J.F., Nadeau C. (1995). Some simple robust method for the analysis of recurrent events. Technometrics 37: 158–168
Lin D.Y., Wei L.J., Yang I., Ying Z. (2000). Semiparametric regression for the mean and rate functions of recurrent events. Journal of the Royal Statistical Society B62: 711–730
Martinussen T., Scheike T.H. (2002). A flexible additive multiplicative hazard model. Biometrika 89: 283–298
Murphy S., Sen P. (1991). Time-dependent coefficients in a Cox-type regression model. Stochastic Processes an Their Applications 39: 153–180
Nelson W.B. (1995). Confidence limits for recurrence data-applied to cost or number of product repairs. Technometrics 37: 147–157
Pepe M.S., Cai J. (1993). Some graphical displays and marginal regression analyses for recurrent failure times and time dependent covariates. Journal of the American Statistical Association 88: 811–820
Schucany W.R. (1995). Adaptive bandwidth choice for kernel regression. Journal of the American Statistical Association 90: 535–540
Tian L., Zucker D., Wei L.J. (2005). On the Cox model with time-varying regression coefficients. Journal of the American Statistical Association 100: 172–183
Wang M.-C., Qin J., Chiang C.-T. (2001). Analyzing recurrent event data with informative censoring. Journal of the American Statistical Association 96: 1057–1065
Vlahov D., Anthony J.C., Muñov A., Margolick J., Nelson K.E., Celentano D.D., Solomon L., 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
Winnett A., Sasieni P. (2003). Iterated residuals and time-varying covariate effect in Cox regression. Journal of the Royal Statistical Society, B65: 473–488
Zuuker D.M., Karr A.F. (1990). Nonparametric survival analysis with time-dependent covariates: a penalized partial likelihood approach. The Annals of Statistics 18: 329–353
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Chiang, CT., Wang, MC. Varying-coefficient model for the occurrence rate function of recurrent events. Ann Inst Stat Math 61, 197–213 (2009). https://doi.org/10.1007/s10463-007-0129-1
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DOI: https://doi.org/10.1007/s10463-007-0129-1