Published 2003 in Lifetime Data Analysis 9(3), pp. 293-303.


Recurrent event data typically exhibit the phenomenon of intra-individual correlation, owing to not only observed covariates but also random effects. In many applications, the population can be reasonably postulated as a heterogeneous mixture of individual renewal processes, and the inference of interest is the effect of individual-level covariates. In this article, we suggest and investigate a marginal proportional hazards model for gaps between recurrent events. A connection is established between observed gap times and clustered survival data, however, with informative cluster size. We then derive a novel and general inference procedure for the latter, based on a functional formulation of standard Cox regression. Large-sample theory is established for the proposed estimators of the regression coefficients and the baseline cumulative hazard function. Numerical studies demonstrate that the procedure performs well under practical sample sizes. Application to the well-known bladder tumor data is given as illustration


Statistical Methodology | Statistical Models | Statistical Theory | Survival Analysis