Semiparametric regression for the mean and rate functions of recurrent events
D. Y. Lin, L. J. Wei, I. Yang, Z. Ying
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2000 · Volume 62 · Issue 4
Abstract
The counting process with the Cox-type intensity function has been commonly used to analyse recurrent event data. This model essentially assumes that the underlying counting process is a time-transformed Poisson process and that the covariates have multiplicative effects on the mean and rate function of the counting process. Recently, Pepe and Cai, and Lawless and co-workers have proposed semiparametric procedures for making inferences about the mean and rate function of the counting process without the Poisson-type assumption. In this paper, we provide a rigorous justification of such robust procedures through modern empirical process theory. Furthermore, we present an approach to constructing simultaneous confidence bands for the mean function and describe a class of graphical and numerical techniques for checking the adequacy of the fitted mean–rate model. The advantages of the robust procedures are demonstrated through simulation studies. An illustration with multiple-infection data taken from a clinical study on chronic granulomatous disease is also provided.
Keywords
Counting process, Empirical process, Intensity function, Martingale, Partial likelihood, Poisson process
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