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In long-term follow-up studies on recurrent events, the observation patterns may not be consistent over time. During some observation periods, subjects may be monitored continuously so that each event occurence time is known. While during the other observation periods, subjects may be monitored discretely so that only the number of events in each period is known. This results in mixed recurrent-event and panel-count data. In these data, there is dependence among within-subject events. Furthermore, if the data are collected from multiple centers, then there is another level of dependence among within-center subjects. Literature exists for clustered recurrent-event data, but not for clustered mixed recurrent-event and panel-count data. Ignoring the cluster effect may lead to less efficient analysis. In this paper, we present a marginal modeling approach to take into account the cluster effect and provide asymptotic distributions of the resulting regression parameters. Our simulation study demonstrates that this approach works well for practical situations. It was applied to a study comparing the hospitalization rates between childhood cancer survivors and healthy controls, with data collected from 26 medical institutions across North America during more than 20 years of follow-up. [ABSTRACT FROM AUTHOR]