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Biometrika 2005 92(3):647-666; doi:10.1093/biomet/92.3.647
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© 2005 Biometrika Trust

The accelerated gap times model

Robert L. Strawderman

Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, New York 14853-7801, U.S.A. rls54{at}cornell.edu

This paper develops a new semiparametric model for the effect of covariates on the conditional intensity of a recurrent event counting process. The model is a transparent extension of the accelerated failure time model for univariate survival data. Estimation of the regression parameter is motivated by semiparametric efficiency considerations, extending the class of weighted log-rank estimating functions originally proposed in Prentice (1978) and subsequently studied in detail by Tsiatis (1990) and Ritov (1990). A novel rank-based one-step estimator for the regression parameter is proposed. An Aalen-type estimator for the baseline intensity function is obtained. Asymptotics are handled with empirical process methods, and finite sample properties are studied via simulation. Finally, the new model is applied to the bladder tumour data of Byar (1980).

Key Words: Censoring; Counting process; Cox regression; Log-rank statistic; Martingale; Multiple events; Rank regression; Recurrent events; Survival data

Received September 2003. Revised January 2005.


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