A frailty model for recurrent events during alternating restraint and non-restraint time periods.

We consider recurrent events of the same type that occur during alternating restraint and non-restraint time periods. This research is motivated by a study on juvenile recidivism, where the probationers were followed for re-offenses during alternating placement periods and free-time periods. During the placement periods, the probationers were under a restricted environment with direct supervision of the probation officers. During the free-time periods, the probationers were released to home and not under direct supervision. Although re-offenses can occur during both types of time periods, the intensities of the re-offenses are very different. Thus, these two types of time periods should be modeled differently. The same data structure also arises in many biomedical settings, as exemplified by tumor metastases during chemotherapy and chemo-free periods. In this paper, we propose a joint modeling framework that explicitly accounts for the different types of time periods, as well as the within-subject dependence during the same type and between different types of time periods. The estimation procedure is implemented in SAS and is easily accessible to practical investigators. We evaluate the proposed method through simulation studies under several realistic scenarios and demonstrate the feasibility of the proposed method by applying it to the juvenile recidivism dataset.