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Biometrika 1998 85(3):605-618; doi:10.1093/biomet/85.3.605
© 1998 by Biometrika Trust
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Accelerated failure time models for counting processes

D. Y. LIN, L. J. WEI and ZHILIANG YING

Department of Biostatistics, Box 357232, University of Washington Seattle, Washington 98195, U.S.A.danyu{at}biostat.washington.edu
Department of Biostatistics, Harvard University 677 Huntington Avenue, Boston, Massachusetts 02115, U.S.A.wei{at}biostat.harvard.edu
Department of Statistics, Hill Center, Busch Campus, Rutgers University, Piscataway New Jersey 08855, U.S.A.zying{at}stat.rutgers.edu

We present a natural extension of the conventional accelerated failure time model for survival data to formulate the effects of covariates on the mean function of the counting process for recurrent events. A class of consistent and asymptotically normal rank estimators is developed for estimating the regression parameters of the proposed model. In addition, a Nelson-Aalen-type estimator for the mean function of the counting process is constructed, which is consistent and, properly normalised, converges weakly to a zeromean Gaussian process. We assess the finite-sample properties of the proposed estimators and the associated inference procedures through Monte Carlo simulation and provide an application to a well-known bladder cancer study.

Key Words: Accelerated life model • Censoring • Cox regression • Log-rank statistic • Multiple events • Poisson process • Proportional hazards • Rank regression • Recurrent events • Survival data


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