The analysis of recurrent failure times: The time-dependent Yule process approach

Analysis of recurrent events has been widely discussed in medical, health services, insurance, and engineering areas in recent years. This paper proposes to use a non-homogeneous Yule process with the proportional intensity assumption to model the hazard function on recurrent events data and the associated risk factors. The assumption is that repeated events occur (for each individual) as a non-homogeneous Yule process with intensity function lambda(t) = lambda(0)(t) (.) exp(Z beta) is made. The baseline intensity function, lambda(0)(t), is assumed to follow a Weibull distribution. The major advantage of using the Yule process is that the hazard function will be proportional to the number of events occurring up to time t. Maximum likelihood estimation is used to provide estimates of the parameters in the model, and a generalized scoring iterative procedure is applied in numerical computation. Model comparisons between the proposed method and other existing recurrent models are addressed using simulated data.