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Biostatistics Advance Access originally published online on January 30, 2007
Biostatistics 2007 8(4):708-721; doi:10.1093/biostatistics/kxl043
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© The Author 2007. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

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

Virginie Rondeau*

Institut National de la Santé et de la Recherche Médicale, U875 (Biostatistique), Bordeaux, F-33076, France and Université Victor Segalen Bordeaux 2, Bordeaux, F-33076, France virginie.rondeau{at}isped.u-bordeaux2.fr

Simone Mathoulin-Pelissier

Institut Bergonié—Centre Régional de Lutte Contre le Cancer du Sud-Ouest, Bordeaux F-33076, France

Hélène Jacqmin-Gadda

Institut National de la Santé et de la Recherche Médicale, U875 (Biostatistique), Bordeaux, F-33076, France and Université Victor Segalen Bordeaux 2, Bordeaux, F-33076, France

Véronique Brouste and Pierre Soubeyran

Institut Bergonié—Centre Régional de Lutte Contre le Cancer du Sud-Ouest, Bordeaux F-33076, France

* To whom correspondence should be addressed.

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 modeling for 2 survival processes has received considerable attention because it makes it possible to study the joint evolution over time of 2 processes and gives unbiased and efficient parameters. The most commonly used estimation procedure in the joint models for survival events is the expectation maximization 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 semiparametric 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 modeled with death.

Keywords: Cancer; Joint frailty models; Penalized likelihood; Recurrent events

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


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