A comparison of various rate functions of a recurrent event process in the presence of a terminal event

Several different rate functions of the recurrent event process have been proposed for analysing recurrent event data when the observation of a study subject can be terminated by a failure event, such as death. When the terminal event is correlated with the underlying recurrent event process, these rate functions have different interpretations; however, recognition of the differences has been lacking theoretically and practically. In this article, we study the relationship between these rate functions and demonstrate that models based on an inappropriate rate function may lead to misleading scientific conclusions in various scenarios. An analysis of data from an AIDS clinical trial is presented to emphasise the importance of cautious model selection.