Abstract: In many medical studies some markers, such as the medical costs incurred during each hospitalisation, are only measured when an event, such as a hospitalisation, occurs. In addition, there may exist an informative terminal event that stops the follow-up. In this article, we propose an additive-multiplicative mean model for marker data contingent on recurrent event with an informative terminal event via latent variables. Estimation procedures are developed for parameter estimation, and asymptotic properties of the proposed estimators are derived. In addition, some numerical procedures are provided for model checking. The finite sample properties of the proposed estimators are examined through simulation studies. An application to a medical cost study of chronic heart failure patients from the University of Virginia Health System is illustrated.

Key words and phrases: Estimating equations, joint modeling, latent variables, marker data, recurrent event, terminal event.