Open Access
February 2020 Consistent semiparametric estimators for recurrent event times models with application to virtual age models
Eric Beutner, Laurent Bordes, Laurent Doyen
Bernoulli 26(1): 557-586 (February 2020). DOI: 10.3150/19-BEJ1140


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. Here we show that consistent estimators can be constructed by smoothing the profile log-likelihood function appropriately. We show that our general result 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. A simulation study is provided to illustrate our consistency results together with an application to real data.


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Eric Beutner. Laurent Bordes. Laurent Doyen. "Consistent semiparametric estimators for recurrent event times models with application to virtual age models." Bernoulli 26 (1) 557 - 586, February 2020.


Received: 1 March 2018; Revised: 1 July 2019; Published: February 2020
First available in Project Euclid: 26 November 2019

zbMATH: 07140509
MathSciNet: MR4036044
Digital Object Identifier: 10.3150/19-BEJ1140

Keywords: effective age process , recurrent event data , semiparametric inference , smoothed profile likelihood , virtual age process

Rights: Copyright © 2020 Bernoulli Society for Mathematical Statistics and Probability

Vol.26 • No. 1 • February 2020
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