Regression analysis of multivariate panel count data with an informative observation process

Multivariate panel count data arise in event history studies on recurrent events if there exist several related events and study subjects can be examined or observed only at discrete time points instead of over continuous periods. In these situations, a complicated issue that may arise is that the observation time points or process may be related to the underlying recurrent event process of interest. That is, we have informative observation processes. It is obvious that to perform a valid analysis, both the relationship among different types of recurrent events and the informative observation process need to be taken into account. To address these, we propose a robust joint modeling approach. For the estimation of regression parameters, an estimating equation-based inference procedure is developed and the asymptotic properties of the resulting estimates are established. Numerical studies indicate that the proposed approach works well for practical situations and the methodology is applied to a skin cancer study that motivates this study.