Analysis of recurrent failure times data: should the baseline hazard be stratified?

Over the past two decades, a variety of fruitful statistical methods for the analysis of recurrent events has been proposed for the estimation of covariates effect using the Cox proportional hazard model. Besides frailty modelling, two simple trends of modelling have been developed: the first one uses stratification on the rank of the event, whereas the second one, more closely related to Poisson processes theory, does not use stratification. Although they both take into account the correlation of the unit failure times, each of these approaches emphasizes a different aspect of the underlying point process and there is still an ongoing debate concerning the most appropriate method. The aim of this paper is to stress current interests and trends concerning these two approaches. For each model, main statistical methods for estimating the covariates effects are presented. Methods are illustrated and compared in two randomized clinical trials which involve recurrences of severe adverse events following chemotherapy in 938 patients with chronic lymphocytic leukaemia, and recurrences of infectious rhinitis episodes in 327 patients. The discussion, based on the previous examples and on the properties of underlying statistical inference, deals with the appropriateness of the model choice, which is closely related to the data structure.