Penalized survival models for the analysis of alternating recurrent event data

Recurrent event data are widely encountered in clinical and observational studies. Most methods for recurrent events treat the outcome as a point process and, as such, neglect any associated event duration. This generally leads to a less informative and potentially biased analysis. We propose a joint model for the recurrent event rate (of incidence) and duration. The two processes are linked through a bivariate normal frailty. For example, when the event is hospitalization, we can treat the time to admission and length‐of‐stay as two alternating recurrent events. In our method, the regression parameters are estimated through a penalized partial likelihood, and the variance‐covariance matrix of the frailty is estimated through a recursive estimating formula. Moreover, we develop a likelihood ratio test to assess the dependence between the incidence and duration processes. Simulation results demonstrate that our method provides accurate parameter estimation, with a relatively fast computation time. We illustrate the methods through an analysis of hospitalizations among end‐stage renal disease patients.