Joint Frailty Models for Recurring Events and Death Using Maximum Penalized Likelihood Estimation: Application on Cancer Events

Institut National de la Santé et de la Recherche Médicale, U875 (Biostatistique), Bordeaux, F-33076, France Bordeaux, F-33076, France.
Biostatistics (Impact Factor: 2.65). 11/2007; 8(4):708-21. DOI: 10.1093/biostatistics/kxl043
Source: PubMed


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.

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Available from: Virginie Rondeau
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    • "An early locoregional recurrence significantly increased the risk of death, whereas a later one was not significantly associated with death. Furthermore, we tried to analyze jointly locoregional relapse and death by fitting a joint frailty model (Rondeau et al., 2007) using the R package Frailtypack (Rondeau et al., 2012). We noticed that locoregional relapses and death are related events. "
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    ABSTRACT: Individuals may experience more than one type of recurrent event and a terminal event during the life course of a disease. Follow-up may be interrupted for several reasons, including the end of a study, or patients lost to follow-up, which are noninformative censoring events. Death could also stop the follow-up, hence, it is considered as a dependent terminal event. We propose a multivariate frailty model that jointly analyzes two types of recurrent events with a dependent terminal event. Two estimation methods are proposed: a semiparametrical approach using penalized likelihood estimation where baseline hazard functions are approximated by M-splines, and another one with piecewise constant baseline hazard functions. Finally, we derived martingale residuals to check the goodness-of-fit. We illustrate our proposals with a real dataset on breast cancer. The main objective was to model the dependency between the two types of recurrent events (locoregional and metastatic) and the terminal event (death) after a breast cancer.
    Full-text · Article · Nov 2013 · Biometrical Journal
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    • "This dependency should be accounted for in the joint modelling of these two survival endpoints. There can be many reasons to use joint models of two survival endpoints, including giving a general description of the data, correcting for bias in survival analysis due to dependent dropout or censoring, and improving efficiency of survival analysis due to the use of auxiliary information [11]. "
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    ABSTRACT: Background Multistate models have become increasingly useful to study the evolution of a patient’s state over time in intensive care units ICU (e.g. admission, infections, alive discharge or death in ICU). In addition, in critically-ill patients, data come from different ICUs, and because observations are clustered into groups (or units), the observed outcomes cannot be considered as independent. Thus a flexible multi-state model with random effects is needed to obtain valid outcome estimates. Methods We show how a simple multi-state frailty model can be used to study semi-competing risks while fully taking into account the clustering (in ICU) of the data and the longitudinal aspects of the data, including left truncation and right censoring. We suggest the use of independent frailty models or joint frailty models for the analysis of transition intensities. Two distinct models which differ in the definition of time t in the transition functions have been studied: semi-Markov models where the transitions depend on the waiting times and nonhomogenous Markov models where the transitions depend on the time since inclusion in the study. The parameters in the proposed multi-state model may conveniently be computed using a semi-parametric or parametric approach with an existing R package FrailtyPack for frailty models. The likelihood cross-validation criterion is proposed to guide the choice of a better fitting model. Results We illustrate the use of our approach though the analysis of nosocomial infections (ventilator-associated pneumonia infections: VAP) in ICU, with “alive discharge” and “death” in ICU as other endpoints. We show that the analysis of dependent survival data using a multi-state model without frailty terms may underestimate the variance of regression coefficients specific to each group, leading to incorrect inferences. Some factors are wrongly significantly associated based on the model without frailty terms. This result is confirmed by a short simulation study. We also present individual predictions of VAP underlining the usefulness of dynamic prognostic tools that can take into account the clustering of observations. Conclusions The use of multistate frailty models allows the analysis of very complex data. Such models could help improve the estimation of the impact of proposed prognostic features on each transition in a multi-centre study. We suggest a method and software that give accurate estimates and enables inference for any parameter or predictive quantity of interest.
    Full-text · Article · Jun 2012 · BMC Medical Research Methodology
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    • "Thus, breast cancer death is likely to be an informative type of censoring, which means that those individuals who are censored by death are not as likely to have the subsequent event of interest as those who remained in the study. In order to examine this hypothesis we used a joint frailty model (using the R package "frailtypack") to analyze recurrent observations of breast cancer with death from breast cancer [22,23]. For instance, a patient recurrence rate may be positively correlated with its death rate. "
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    ABSTRACT: In the setting of recurrent events, research studies commonly count only the first occurrence of an outcome in a subject. However this approach does not correctly reflect the natural history of the disease. The objective is to jointly identify prognostic factors associated with locoregional recurrences (LRR), contralateral breast cancer, distant metastases (DM), other primary cancer than breast and breast cancer death and to evaluate the correlation between these events. Patients (n = 919) with a primary invasive breast cancer and treated in a cancer center in South-Western France with breast-conserving surgery from 1990 to 1994 and followed up to January 2006 were included. Several types of non-independent events could be observed for the same patient: a LRR, a contralateral breast cancer, DM, other primary cancer than breast and breast cancer death. Data were analyzed separately and together using a random-effects survival model. LRR represent the most frequent type of first failure (14.6%). The risk of any event is higher for young women (less than 40 years old) and in the first 10 years of follow-up after the surgery. In the combined analysis histological tumor size, grade, number of positive nodes, progesterone receptor status and treatment combination are prognostic factors of any event. The results show a significant dependence between these events with a successively increasing risk of a new event after the first and second event. The risk of developing a new failure is greatly increased (RR = 4.25; 95%CI: 2.51-7.21) after developing a LRR, but also after developing DM (RR = 3.94; 95%CI: 2.23-6.96) as compared to patients who did not develop a first event. We illustrated that the random effects survival model is a more satisfactory method to evaluate the natural history of a disease with multiple type of events.
    Full-text · Article · Dec 2010 · BMC Cancer
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