Competing-triggering effect models for multitype recurrent event data

Multitype recurrent events frequently arise in lifetime data analysis. It is reasonable to assume that previously occurred events can trigger more events to come, either of homogeneous or of heterogeneous categories. Previous work has focused on nonlinear triggering models for the effects of previous events when there is only a single event type. The standard approach is a proportional intensity model, which captures both the magnitude of the triggering effect and its decay over time via a complicated function of time. We propose a general Cox-type structure for modeling the triggering effects among multiple types of events, with separate triggering effects for each event type on events of interest. The nonlinear model formulation permits parameters to be common across models for different event types. We derive partial likelihood estimators and establish the consistency and asymptotic normality of the estimators, as well as provide plug-in variance estimators. We demonstrate a good performance of the methods through a series of simulation experiments. The models are applied to a cohort of patients with Li-Fraumeni syndrome to analyze the triggering effects between breast cancers and non-breast cancers.