This paper discusses regression analysis of longitudinal data in which the observation process may be related to the longitudinal process of interest. Such data have recently attracted a great deal of attention and some methods have been developed. However, most of those methods treat the observation process as a recurrent event process, which assumes that one observation can immediately follow another. Sometimes, this is not the case, as there may be some delay or observation duration. Such a process is often referred to as a recurrent episode process. One example is the medical cost related to hospitalization, where each hospitalization serves as a single observation. For the problem, we present a joint analysis approach for regression analysis of both longitudinal and observation processes and a simulation study is conducted that assesses the finite sample performance of the approach. The asymptotic properties of the proposed estimates are also given and the method is applied to the medical cost data that motivated this study.