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Title: Semiparametric methods for recurrent event times models with application to virtual age models Authors:  Eric Beutner - Vrije Universiteit Amsterdam (Netherlands) [presenting]
Laurent Bordes - University of Pau (France)
Laurent Doyen - Univ Grenoble Alpes (France)
Abstract: Virtual age models are very useful to analyse recurrent events. Among the strengths of these models is their ability to account for treatment (or intervention) effects after an event occurrence. Despite their flexibility for modeling recurrent events the number of applications is limited. This seems to be a result of the fact that in the semiparametric setting all the existing results assume the virtual age function that describes the treatment (or intervention) effects to be known. This shortcoming can be overcome by considering semiparametric virtual age models with parametrically specified virtual age functions. Yet, fitting such a model is a difficult task. Indeed it has recently been shown that for these models the standard profile likelihood method fails to lead to consistent estimators. We can consider statistical properties of estimators constructed by smoothing the profile log-likelihood function appropriately. We show that our general results derived by smoothing can be applied to most of the relevant virtual age models of the literature. Our approach shows that empirical process techniques may be a worthwhile alternative to martingale methods for studying asymptotic properties of these inference methods.