Semiparametric accelerated intensity models for correlated recurrent and terminal events

In clinical and epidemiological studies, recurrent events can arise when a subject repeatedly experiences the event of interest. Often, a terminal event such as death may preclude further occurrence of recurrent events in an informative manner such that the terminal event is strongly correlated with the recurrent event process. In this article, we propose a semiparametric joint analysis of correlated recurrent and terminal events. Specifically, we consider an accelerated intensity model for the recurrent events and an accelerated failure time model for the terminal event. We assess the dependency between the two event processes through a commonly used log-normal or gamma shared frailty. To estimate regression parameters and unspecified baseline intensity functions, we develop an EM algorithm with kernel smoothing adapted for both intensity functions, and perform variance estimation via numerical differentiation of the profile likelihoods. We evaluated the finite sample performance of the proposed method via simulation studies for both gamma and log-normal frailty models, and applied our method to the analysis of tumor recurrences and patient survival times in a soft tissue sarcoma study.