Robust estimation for longitudinal data with informative observation times

In this paper we focus on regression analysis of irregularly observed longitudinal data that often occur in medical follow-up studies and observational investigations. The analysis of these data involves two processes. One is the underlying longitudinal response process of interest and the other is the observation process that controls observation times. Most of the existing methods, however, rely on some restrictive models or assumptions such as the Poisson assumption. For this we propose a class of more flexible joint models and a robust estimation approach for regression analysis of longitudinal data with related observation times. The asymptotic properties of the proposed estimators are established and a model checking procedure is also presented. The numerical studies indicate that the proposed methods work well for practical situations.