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Biostatistics Advance Access published online on January 30, 2007
Biostatistics, doi:10.1093/biostatistics/kxl043
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© The Author 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Joint frailty models for recurring events and death using maximum penalized likelihood estimation : application on cancer events

Virginie Rondeau1, Simone Mathoulin-Pelissier2, Hélène Jacqmin-Gadda1, Véronique Brouste2 and Pierre Soubeyran2

1 INSERM, U875 (Biostatistique), Bordeaux, F-33076, FRANCE
2 Université Victor Segalen Bordeaux 2, Bordeaux, F-33076, FRANCE
3 Institut Bergonié - Centre Régional de Lutte Contre le Cancer du Sud-Ouest, Bordeaux, F-33076, FRANCE

The observation of repeated events for subjects in cohort studies could be terminated by loss to follow-up, end-of-study, or a major failure event such as death. In this context, the major failure event could be correlated with recurrent events and the usual assumption of noninformative censoring of the recurrent event process by death, required by most statistical analyses, can be violated. Recently joint modelling for two survival processes has received considerable attention because it makes it possible to study the joint evolution over time of two processes and gives unbiased and efficient parameters. The most commonly used estimation procedure in the joint models for survival events is the EM algorithm. We show how maximum penalized likelihood estimation can be applied to nonparametric estimation of the continuous hazard functions in a general joint frailty model with right censoring and delayed entry. The simulation study demonstrates that this semi-parametric approach yields satisfactory results in this complex setting. As an illustration, such an approach is applied to a prospective cohort with recurrent events of follicular lymphomas, jointly modelled with death.

Keywords: joint frailty models; penalized likelihood; cancer; recurrent events

Received April 11, 2006; revised September 18, 2006; revised December 11, 2006; accepted for publication December 20, 2006.


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