Modeling gap times between recurrent events by marginal rate function

Gap times between recurrent events are often encountered in longitudinal follow-up studies related to medical science, biostatistics, econometrics, reliability, criminology, demography, and other areas. There have been many models to fit such data, such as proportional hazards (PH) model and additive hazards (AH) model, among others. Standard partial likelihood can be employed to draw their statistical inference. The inference from a direct PH or AH assumption on the gap times, however, is less intuitive and straightforward than marginal rate models–which are often preferred by practitioners due to their more direct interpretations for identifying risk factors. In addition, the existing models have not adequately considered zero-recurrence subjects often encountered in recurrent event data. To overcome these shortcomings, we propose an alternative gap time model using an additive marginal rate function that accounts for zero-recurrence subjects. Local profile-likelihood is applied to estimate the model attributes, and the asymptotic properties of the estimators are established as well. The performance of the proposed estimators is evaluated by a simulation study. The proposed model is applied to analyze a set of data on pulmonary exacerbations and rhDNase treatment.