Longitudinal perspectives on event history analysis

We discuss event histories from the point of view of longitudinal data analysis, comparing several possible inferential objectives. We show that the Nelson-Aalen estimate of a cumulative intensity may be derived as a limiting solution to a sequence of generalized estimating equations for intermittently observed longitudinal count data. We outline a potential use for the theory in interval-censored recurrent-event models, and demonstrate its applicability using data from a Toronto arthritis clinic. We also discuss connections with rate models, along with some implications for the longitudinal analyst.