| Many longitudinal studies record recurrent event data. Examples of recurrent event data are frequently encountered in biomedical and behavioral sciences, such as relapses of diseases, hospitalizations and violent behaviors. In many studies, the occurrence of subsequent recurrent events may be precluded by a terminal event. Usually, the terminal events or other censoring events are not independent of the recurrent events. Hence, assuming independent censoring like most statistical analyses would be more or less inappropriate.; We propose a semiparametric regression model for informatively censored recurrent event data with time-dependent covariates. In our approach, subject-specific nonstationary Poisson processes are assumed to be the underlying model, which implies a proportional rate model, so that the regression coefficients have the desirable marginal interpretations. Informative censoring is characterized by a latent variable or frailty, which is treated as a nuisance. A profile estimating function is proposed to estimate regression coefficients. Large sample properties of the proposed estimator are established. The estimating procedures are illustrated by simulation studies and a data analysis.; For recurrent event data in the presence of an explicit terminal event, various definitions of the recurrent rate function have been adopted in the proportional rate models. While these rate functions have quite different interpretations, the recognition of the differences has been lacking theoretically and practically. We carefully compare three types of rate functions from both conceptual and quantitative perspectives, and reach the conclusion that careless use of a certain rate function may lead to misleading scientific conclusions. Simulations and a data analysis are conducted for comparisons of the focused models.; A set of one-sample semiparametric estimators of the marginal survival function of the gap times, i.e., times between consecutive recurrent events, is proposed. The inverse weighting technique is used to correct the bias caused by informative censoring, and the techniques of within-cluster averaging and within-cluster resampling are adopted to correct the bias caused by informative cluster size. The performance of the proposed estimators and an existing method are compared by a sequence of simulation studies. |
