A Regression Model for Dependent Gap Times

A natural choice of time scale for analyzing recurrent event data is the ``gap" (or soujourn) time between successive events. In many situations it is reasonable to assume correlation exists between the successive events experienced by a given subject. This paper looks at the problem of extending the accelerated failure time (AFT) model to the case of dependent recurrent event data via intensity modeling. Specifically, the accelerated gap times model of Strawderman (2005), a semiparametric intensity model for independent gap time data, is extended to the case of multiplicative gamma frailty. As argued in Aalen & Husebye (1991), incorporating frailty captures the heterogeneity between subjects and the ``hazard" portion of the intensity model captures gap time variation within a subject. Estimators are motivated using semiparametric efficiency theory and lead to useful generalizations of the rank statistics considered in Strawderman (2005). Several interesting distinctions arise in comparison to the Cox-Andersen-Gill frailty model (e.g., Nielsen et al, 1992; Klein, 1992). The proposed methodology is illustrated by simulation and data analysis.