Choice of time scale for analysis of recurrent events data

Recurrent events refer to events that over time can occur several times for each individual. Full use of such data in a clinical trial requires a method that addresses the dependence between events. For modelling this dependence, there are two time scales to consider, namely time since start of the study (running time) or time since most recent event (gap time). In the multi-state setup, it is possible to estimate parameters also in the case, where the hazard model allows for an effect of both time scales, making this an extremely flexible approach. However, for summarizing the effect of a treatment in a transparent and informative way, the choice of time scale and model requires much more care. This paper discusses these choices both from a theoretical and practical point of view. This is supported by a simulation study showing that in a frailty model with assumptions covered by both time scales, the gap time approach may give misleading results. A literature dataset is used for illustrating the issues.