Modeling and Inferential Thoughts for Consecutive Gap Times Observed with Death and Censoring

In the perspective of biomedical applications, consider a recurrent event situation with a relatively low degree of recurrence. In this setting, the focus is placed on successive inter-event gap times which are observed in the presence of both a terminal event like death and independent censoring. The terminal event is potentially related to recurrent events while the censoring process is an independent nuisance that bears on the total observation time i.e. on the sum of the successive gap times. We review different modeling and inferential strategies. We also present a nonparametric estimation method of joint distribution functions and outline the need for future developments.