Frailty models are very useful for analysing correlated survival data, when observations are clustered into groups or for recurrent events. The aim of this article is to present the new version of ...anR package called frailtypack. This package allows to t Cox models andfour types of frailty models (shared, nested, joint, additive) that could be useful for several issues within biomedical research. It is well adapted to the analysis of recurrent events such as cancer relapses and/or terminal events (death or lost to follow-up). The approach uses maximum penalized likelihood estimation. Right-censored or left-truncated data are considered. It also allows stratication and time-dependent covariates during analysis.
Extensions in the field of joint modeling of correlated data and dynamic predictions improve the development of prognosis research. The R package frailtypack provides estimations of various joint ...models for longitudinal data and survival events. In particular, it fits models for recurrent events and a terminal event (frailtyPenal), models for two survival outcomes for clustered data (frailtyPenal), models for two types of recurrent events and a terminal event (multivPenal), models for a longitudinal biomarker and a terminal event (longiPenal) and models for a longitudinal biomarker, recurrent events and a terminal event (trivPenal). The estimators are obtained using a standard and penalized maximum likelihood approach, each model function allows to evaluate goodness-of-fit analyses and provides plots of baseline hazard functions. Finally, the package provides individual dynamic predictions of the terminal event and evaluation of predictive accuracy. This paper presents the theoretical models with estimation techniques, applies the methods for predictions and illustrates frailtypack functions details with examples.
During their follow-up, patients with cancer can experience several types of recurrent events and can also die. Over the last decades, several joint models have been proposed to deal with recurrent ...events with dependent terminal event. Most of them require the proportional hazard assumption. In the case of long follow-up, this assumption could be violated. We propose a joint frailty model for two types of recurrent events and a dependent terminal event to account for potential dependencies between events with potentially time-varying coefficients. For that, regression splines are used to model the time-varying coefficients. Baseline hazard functions (BHF) are estimated with piecewise constant functions or with cubic M-Splines functions. The maximum likelihood estimation method provides parameter estimates. Likelihood ratio tests are performed to test the time dependency and the statistical association of the covariates. This model was driven by breast cancer data where the maximum follow-up was close to 20 years.
Extensions in the field of joint modeling of correlated data and dynamic predictions improve the development of prognosis research. The R package frailtypack provides estimations of various joint ...models for longitudinal data and survival events. In particular, it fits models for recurrent events and a terminal event (frailtyPenal), models for two survival outcomes for clustered data (frailtyPenal), models for two types of recurrent events and a terminal event (multivPenal), models for a longitudinal biomarker and a terminal event (longiPenal) and models for a longitudinal biomarker, recurrent events and a terminal event (trivPenal). The estimators are obtained using a standard and penalized maximum likelihood approach, each model function allows to evaluate goodness-of-fit analyses and provides plots of baseline hazard functions. Finally, the package provides individual dynamic predictions of the terminal event and evaluation of predictive accuracy. This paper presents the theoretical models with estimation techniques, applies the methods for predictions and illustrates frailtypack functions details with examples.
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.
Objective:
We aimed at identifying distinct trajectories of functioning and at describing their respective clinical characteristics in a cohort of individuals with bipolar disorders.
Methods:
We ...included a sample of 2351 individuals with bipolar disorders who have been followed-up to 3 years as part as the FondaMental Advanced Centers of Expertise in Bipolar Disorders cohort. Global functioning was measured using the Functioning Assessment Short Test. We used latent class mixed models to identify distinct longitudinal trajectories of functioning over 3 years. Multivariable logistic regression models were used to identify the baseline factors that were associated with the membership to each trajectory of functioning.
Results:
Three distinct trajectories of functioning were identified: (1) a majority of individuals (72%) had a stable trajectory of mild functional impairment, (2) 20% of individuals had a stable trajectory of severe functional impairment and (3) 8% of individuals had a trajectory of moderate functional impairment that improved over time. The membership to a trajectory of stable severe versus stable mild functional impairment was associated with unemployment, a higher number of previous hospitalizations, childhood maltreatment, a higher level of residual depressive symptoms, higher sleep disturbances, a higher body mass index and a higher number of psychotropic medications being prescribed at baseline. The model that included these seven factors led to an area under the curve of 0.85.
Conclusion:
This study enabled to stratify individuals with bipolar disorders according to three distinct trajectories of functioning. The results regarding the potential determinants of the trajectory of severe functional impairment needs to be replicated in independent samples. Nevertheless, these potential determinants may represent possible therapeutic targets to improve the prognosis of those patients at risk of persistent poor functioning.
Extensions in the field of joint modeling of correlated data and dynamic predictions improve the development of prognosis research. The R package frailtypack provides estimations of various joint ...models for longitudinal data and survival events. In particular, it fits models for recurrent events and a terminal event (frailtyPenal), models for two survival outcomes for clustered data (frailtyPenal), models for two types of recurrent events and a terminal event (multivPenal), models for a longitudinal biomarker and a terminal event (longiPenal) and models for a longitudinal biomarker, recurrent events and a terminal event (trivPenal). The estimators are obtained using a standard and penalized maximum likelihood approach, each model function allows to evaluate goodness-of-fit analyses and plots of baseline hazard functions. Finally, the package provides individual dynamic predictions of the terminal event and evaluation of predictive accuracy. This paper presents theoretical models with estimation techniques, applies the methods for predictions and illustrates frailtypack functions details with examples.
Objective: We aimed at identifying distinct trajectories of functioning and at describing their respective clinical characteristics in a cohort of individuals with bipolar disorders. Methods: We ...included a sample of 2351 individuals with bipolar disorders who have been followed-up to 3 years as part as the FondaMental Advanced Centers of Expertise in Bipolar Disorders cohort. Global functioning was measured using the Functioning Assessment Short Test. We used latent class mixed models to identify distinct longitudinal trajectories of functioning over 3 years. Multivariable logistic regression models were used to identify the baseline factors that were associated with the membership to each trajectory of functioning. Results: Three distinct trajectories of functioning were identified: (1) a majority of individuals (72%) had a stable trajectory of mild functional impairment, (2) 20% of individuals had a stable trajectory of severe functional impairment and (3) 8% of individuals had a trajectory of moderate functional impairment that improved over time. The membership to a trajectory of stable severe versus stable mild functional impairment was associated with unemployment, a higher number of previous hospitalizations, childhood maltreatment, a higher level of residual depressive symptoms, higher sleep disturbances, a higher body mass index and a higher number of psychotropic medications being prescribed at baseline. The model that included these seven factors led to an area under the curve of 0.85. Conclusion: This study enabled to stratify individuals with bipolar disorders according to three distinct trajectories of functioning. The results regarding the potential determinants of the trajectory of severe functional impairment needs to be replicated in independent samples. Nevertheless, these potential determinants may represent possible therapeutic targets to improve the prognosis of those patients at risk of persistent poor functioning.
Ce travail a eu pour objectif de proposer des modèles conjoints d'intensités de processus d'événements récurrents et d'un événement terminal dépendant. Nous montrons que l'analyse séparée de ces ...événements conduit à des biais d'estimation importants. C'est pourquoi il est nécessaire de prendre en compte les dépendances entre les différents événements d'intérêt. Nous avons choisi de modéliser ces dépendances en introduisant des effets aléatoires (ou fragilités) et de travailler sur la structure de dépendance. Ces effets aléatoires prennent en compte les dépendances entre événements, les dépendances inter-récurrences et l'hétérogénéité non-observée. Nous avons, en premier lieu, développé un modèle conjoint à fragilités pour un type d'événement récurrent et un événement terminal dépendant en introduisant deux effets aléatoires indépendants pour prendre en compte et distinguer la dépendance inter-récurrences et celle entre les risques d'événements récurrents et terminal. Ce modèle a été ajusté pour des données de patients atteints de lymphome folliculaire où les événements d'intérêt sont les rechutes et le décès. Le second modèle développé permet de modéliser conjointement deux types d'événements récurrents et un événement terminal dépendant en introduisant deux effets aléatoires corrélés et deux paramètres de flexibilités. Ce modèle s'avère adapté pour l'analyse des risques de récidives locorégionales, de récidives métastatiques et de décès chez des patientes atteintes de cancer du sein. Nous confirmons ainsi que le décès est lié aux récidives métastatiques mais pas aux récidives locorégionales tandis que les deux types de récidives sont liés. Cependant ces approches font l'hypothèse de proportionnalité des intensités conditionnellement aux fragilités, que nous allons tenter d'assouplir. Dans un troisième travail, nous proposons de modéliser un effet potentiellement dépendant du temps des covariables en utilisant des fonctions B-Splines.
This work aimed to propose joint models for recurrent events and a dependent terminal event. We show how separate analyses of these events could lead to important biases. That is why it seems necessary to take into account the dependencies between events of interest. We choose to model these dependencies through random effects (or frailties) and work on the dependence structure. These random effects account for dependencies between events, inter-dependence recurrences and unobserved heterogeneity. We first have developed a joint frailty model for one type of recurrent events and a dependent terminal event with two independent random effects to take into account and distinguish the inter-recurrence dependence and between recurrent events and terminal event. This model was applied to follicular lymphoma patient’s data where events of interest are relapses and death. The second proposed model is used to model jointly two types of recurrent events and a dependent terminal event by introducing two correlated random effects and two flexible parameters. This model is suitable for analysis of locoregional recurrences, metastatic recurrences and death for breast cancer patients. It confirms that the death is related to metastatic recurrence but not locoregional recurrence while both types of recurrences are related. However, these approaches do the assumption of proportional intensities conditionally on frailties, which we want to relax. In a third study, we propose to model potentially time-dependent regression coefficient using B-splines functions.
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