Estimation of dynamic models of recurrent events with censored data

In this paper, we consider estimation of dynamic models of recurrent events (event histories) in continuous time using censored data. We develop maximum simulated likelihood estimators where missing data are integrated out using Monte Carlo and importance sampling methods. We allow for random effects and integrate out this unobserved heterogeneity using a quadrature rule. In Monte Carlo experiments, we find that maximum simulated likelihood estimation is practically feasible and performs better than both listwise deletion and auxiliary modelling of initial conditions. In an empirical application, we study ischaemic heart disease events for male Maoris in New Zealand.