frailtypack: An R Package for the Analysis of Correlated Survival Data with Frailty Models Using Penalized Likelihood Estimation or Parametrical Estimation

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 an R package called frailtypack. This package allows to fit Cox models and four 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 stratification and time-dependent covariates during analysis

Regression Modeling for Recurrent Events Possibly with an Informative Terminal Event Using R Package reReg

Recurrent event analyses have found a wide range of applications in biomedicine, public health, and engineering, among others, where study subjects may experience a sequence of event of interest during follow-up. The R package reReg offers a comprehensive collection of practical and easy-to-use tools for regression analysis of recurrent events, possibly with the presence of an informative terminal event. The regression framework is a general scalechange model which encompasses the popular Cox-type model, the accelerated rate model, and the accelerated mean model as special cases. Informative censoring is accommodated through a subject-specific frailty without any need for parametric specification. Different regression models are allowed for the recurrent event process and the terminal event. Also included are visualization and simulation tools

Bayesian survival analysis with INLA

This tutorial shows how various Bayesian survival models can be fitted using the integrated nested Laplace approximation in a clear, legible, and comprehensible manner using the INLA and INLAjoint R-packages. Such models include accelerated failure time, proportional hazards, mixture cure, competing risks, multi-state, frailty, and joint models of longitudinal and survival data, originally presented in the article "Bayesian survival analysis with BUGS" (Alvares et al., 2021). In addition, we illustrate the implementation of a new joint model for a longitudinal semicontinuous marker, recurrent events, and a terminal event. Our proposal aims to provide the reader with syntax examples for implementing survival models using a fast and accurate approximate Bayesian inferential approach

Joint Frailty Mixing Model for Recurrent Event Data with an Associated Terminal Event: Application to Hospital Readmission Data

Recurrent events like repeated hospitalization, cancer tumour recurrences, and many others occur frequently. The follow-up on recurrent events may be stopped by a terminal event like death. It is obvious that if the frequencies of recurrent events are more, then it may lead to a terminal event and in this case terminal event becomes ‘dependent’. In this article, we study a joint modelling and analysis of recurrent events with a dependent terminal event. Here, the proportional intensity model for the recurrent events process and the proportional hazard model for the terminal event time are taken. To account for the association between recurrent events and terminal events, mixing frailty or random effect is studied rather than available pure frailty. In our case, the distribution of frailty is introduced as a mixture of folded normal distribution and gamma distribution rather than using pure gamma distribution. An estimation procedure in the joint frailty model is applied to estimate the parameters of the model. This method is close to the method of minimum chi-square rather than a complicated one. An extensive simulation study has been performed to estimate the model parameters and the performances are evaluated based on bias and MSE criteria. Further from an application point of view, the method is illustrated to a hospital readmission data for colorectal cancer patients

Joint Modelling in Liver Transplantation

In the setting of liver transplantation, clinical trials and transplant registries regularly collect repeated measurements of clinical biomarkers which may be strongly associated with a time-to-event such as graft failure or disease recurrence. Multiple time-to-event outcomes are routinely collected. However, joint models are rarely used. This thesis will describe important considerations for joint modelling in the setting of liver transplantation. We will focus on transplant registry data from the United States. We develop a new tool for joint modelling in the context where a critical health event can be tracked in the longitudinal biomarker and often presents as a non-linear trajectory with a sharp jump. We capture this non-linearity with a sin- gle change-point longitudinal component that is linked to the survival model via random effects in a way that incorporates the size of this change, which is a novel way to use a sharp change in the subject-specific random effect as a linkage in a joint model. We also propose an alternative to time dependent analysis of treatment effects by using a joint survival outcome model with a time-to-drug-failure event and a terminal event in graft failure that is more appropriate to use in drug effectiveness studies where subjects are discontinued from an immunosuppressant (in favour of alternative treatment) due to health reasons. Modelling drug regime failures as a time-to-event process has not been previously considered in transplant studies. We show that this method shows a significant association of time-to-drug-failure with time-to-graft-failure, whether applied with a longitudinal component or on its own in a joint survival outcome model

Tutorial in Joint Modeling and Prediction: A Statistical Software for Correlated Longitudinal Outcomes, Recurrent Events and a Terminal Event

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

Non-parametric Bayes in biostatistics

The main focus of this Phd project is the application of Bayesian models in Biostatistics.It has become indeed evident that healthcare management is in need for methods able to improve evidence-based practice. The first problem we consider is modelling recurrent event and survival time. Recurrent event processes generate events repeatedly over time and they arise in many applications.Typically, the focus is on modelling the rate of occurrence, accounting for the variation within and between individuals. Moreover, in applications, it is often of interest to assess the relationship between event occurrence and potential explanatory factors. Although the first focus of our work is on modelling the recurrent event process itself, we also extend the proposed model as building block in a hierarchy to describe the relationship between recurrent events and survival up to a terminating event. This is achieved by specifying a joint distribution of the gap times and event (termination) time. The second objective is to identify the most promising methods that can be applied in a network meta-analysis (NMA) across longitudinal time points, compare them and extend existing models in a B-spline setting. The network meta-analysis methods extend the standard meta-analysis methods, allowing pairwise comparison of all treatments in a network in the absence of head-to-head comparisons. We focus on the most recent methods suggested in the literature that incorporate multiple time points and allow indirect comparisons of treatment effects across different longitudinal studies. In particular, we compare the Mixed Treatment Comparison model (MTC) Dakin et al. (2011), the Bayesian evidence synthesis techniques — integrated two- component prediction (BEST-ITP) developed by Ding and Fu (2013) and the more recent method based on fractional polynomials of Jansen et al. (2015). After a comparison of these methods, we develop some models within a B-spline framework

Hierarchical models for semi-competing risks data with application to quality of end-of-life care for pancreatic cancer

Readmission following discharge from an initial hospitalization is a key marker of quality of health care in the United States. For the most part, readmission has been used to study quality of care for patients with acute health conditions, such as pneumonia and heart failure, with analyses typically based on a logistic-Normal generalized linear mixed model. Applying this model to the study readmission among patients with increasingly prevalent advanced health conditions such as pancreatic cancer is problematic, however, because it ignores death as a competing risk. A more appropriate analysis is to imbed such studies within the semi-competing risks framework. To our knowledge, however, no comprehensive statistical methods have been developed for cluster-correlated semi-competing risks data. In this paper we propose a novel hierarchical modeling framework for the analysis of cluster-correlated semi-competing risks data. The framework permits parametric or non-parametric specifications for a range of model components, including baseline hazard functions and distributions for key random effects, giving analysts substantial flexibility as they consider their own analyses. Estimation and inference is performed within the Bayesian paradigm since it facilitates the straightforward characterization of (posterior) uncertainty for all model parameters including hospital-specific random effects. The proposed framework is used to study the risk of readmission among 5,298 Medicare beneficiaries diagnosed with pancreatic cancer at 112 hospitals in the six New England states between 2000-2009, specifically to investigate the role of patient-level risk factors and to characterize variation in risk across hospitals that is not explained by differences in patient case-mix

A joint model for (un)bounded longitudinal markers, competing risks, and recurrent events using patient registry data

Joint models for longitudinal and survival data have become a popular framework for studying the association between repeatedly measured biomarkers and clinical events. Nevertheless, addressing complex survival data structures, especially handling both recurrent and competing event times within a single model, remains a challenge. This causes important information to be disregarded. Moreover, existing frameworks rely on a Gaussian distribution for continuous markers, which may be unsuitable for bounded biomarkers, resulting in biased estimates of associations. To address these limitations, we propose a Bayesian shared-parameter joint model that simultaneously accommodates multiple (possibly bounded) longitudinal markers, a recurrent event process, and competing risks. We use the beta distribution to model responses bounded within any interval (a,b) without sacrificing the interpretability of the association. The model offers various forms of association, discontinuous risk intervals, and both gap and calendar timescales. A simulation study shows that it outperforms simpler joint models. We utilize the US Cystic Fibrosis Foundation Patient Registry to study the associations between changes in lung function and body mass index, and the risk of recurrent pulmonary exacerbations, while accounting for the competing risks of death and lung transplantation. Our efficient implementation allows fast fitting of the model despite its complexity and the large sample size from this patient registry. Our comprehensive approach provides new insights into cystic fibrosis disease progression by quantifying the relationship between the most important clinical markers and events more precisely than has been possible before. The model implementation is available in the R package JMbayes2

A joint model for (un)bounded longitudinal markers, competing risks, and recurrent events using patient registry data

Joint models for longitudinal and survival data have become a popular framework for studying the association between repeatedly measured biomarkers and clinical events. Nevertheless, addressing complex survival data structures, especially handling both recurrent and competing event times within a single model, remains a challenge. This causes important information to be disregarded. Moreover, existing frameworks rely on a Gaussian distribution for continuous markers, which may be unsuitable for bounded biomarkers, resulting in biased estimates of associations. To address these limitations, we propose a Bayesian shared-parameter joint model that simultaneously accommodates multiple (possibly bounded) longitudinal markers, a recurrent event process, and competing risks. We use the beta distribution to model responses bounded within any interval (a,b) without sacrificing the interpretability of the association. The model offers various forms of association, discontinuous risk intervals, and both gap and calendar timescales. A simulation study shows that it outperforms simpler joint models. We utilize the US Cystic Fibrosis Foundation Patient Registry to study the associations between changes in lung function and body mass index, and the risk of recurrent pulmonary exacerbations, while accounting for the competing risks of death and lung transplantation. Our efficient implementation allows fast fitting of the model despite its complexity and the large sample size from this patient registry. Our comprehensive approach provides new insights into cystic fibrosis disease progression by quantifying the relationship between the most important clinical markers and events more precisely than has been possible before. The model implementation is available in the R package JMbayes2