Informative Terminal Event Research Articles

Shared parameter modeling of longitudinal data allowing for possibly informative visiting process and terminal event.

Joint modeling of longitudinal and time-to-event data, particularly through shared parameter models (SPMs), is a common approach for handling longitudinal marker data with an informative terminal event. A critical but often neglected assumption in this context is that the visiting/observation process is noninformative, depending solely on past marker values and visit times. When this assumption fails, the visiting process becomes informative, resulting potentially to biased SPM estimates. Existing methods generally rely on a conditional independence assumption, positing that the marker model, visiting process, and time-to-event model are independent given shared or correlated random effects. Moreover, they are typically built on an intensity-based visiting process using calendar time. This study introduces a unified approach for jointly modeling a normally distributed marker, the visiting process, and time-to-event data in the form of competing risks. Our model conditions on the history of observed marker values, prior visit times, the marker's random effects, and possibly a frailty term independent of the random effects. While our approach aligns with the shared-parameter framework, it does not presume conditional independence between the processes. Additionally, the visiting process can be defined on either a gap time scale, via proportional hazard models, or a calendar time scale, via proportional intensity models. Through extensive simulation studies, we assess the performance of our proposed methodology. We demonstrate that disregarding an informative visiting process can yield significantly biased marker estimates. However, misspecification of the visiting process can also lead to biased estimates. The gap time formulation exhibits greater robustness compared to the intensity-based model when the visiting process is misspecified. In general, enriching the visiting process with prior visit history enhances performance. We further apply our methodology to real longitudinal data from HIV, where visit frequency varies substantially among individuals.

Semiparametric Reversed Mean Model for Recurrent Event Process with Informative Terminal Event

Semiparametric Reversed Mean Model for Recurrent Event Process with Informative Terminal Event

Nonparametric Estimation and Testing for Panel Count Data with Informative Terminal Event

Nonparametric Estimation and Testing for Panel Count Data with Informative Terminal Event

Semiparametric regression of panel count data with informative terminal event

Semiparametric regression of panel count data with informative terminal event

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 scale-change 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.

Nonparametric inference for reversed mean models with panel count data

Panel count data typically refer to data arising from studies with recurrent events, in which subjects are observed only at discrete time points rather than under continuous observations. We investigate a general situation where a recurrent event process is eventually truncated by an informative terminal event and we are particularly interested in behaviors of the recurrent event process near the terminal event. We propose a reversed mean model for estimating the mean function of the recurrent event process. We develop a two-stage sieve likelihood-based method to estimate the mean function, which overcomes the computational difficulties arising from a nuisance functional parameter involved in the likelihood. The consistency and the convergence rate of the two-stage estimator are established. Allowing for the convergence rate slower than the standard rate, we develop the general weak convergence theory of M-estimators with a nuisance functional parameter, and then apply it to the proposed estimator for deriving the asymptotic normality. Furthermore, a class of two-sample tests is developed. The proposed methods are evaluated with extensive simulation studies and illustrated with panel count data from the Chinese Longitudinal Healthy Longevity Study.

Variable selection in joint frailty models of recurrent and terminal events.

Recurrent event data are commonly encountered in biomedical studies. In many situations, they are subject to an informative terminal event, for example, death. Joint modeling of recurrent and terminal events has attracted substantial recent research interests. On the other hand, there may exist a large number of covariates in such data. How to conduct variable selection for joint frailty proportional hazards models has become a challenge in practical data analysis. We tackle this issue on the basis of the "minimum approximated information criterion" method. The proposed method can be conveniently implemented in SAS Proc NLMIXED for commonly used frailty distributions. Its finite-sample behavior is evaluated through simulation studies. We apply the proposed method to model recurrent opportunistic diseases in the presence of death in an AIDSstudy.

Joint regression analysis for survival data in the presence of two sets of semi-competing risks.

In many clinical trials, multiple time-to-event endpoints including the primary endpoint (e.g., time to death) and secondary endpoints (e.g., progression-related endpoints) are commonly used to determine treatment efficacy. These endpoints are often biologically related. This work is motivated by a study of bone marrow transplant (BMT) for leukemia patients, who may experience the acute graft-versus-host disease (GVHD), relapse of leukemia, and death after an allogeneic BMT. The acute GVHD is associated with the relapse free survival, and both the acute GVHD and relapse of leukemia are intermediate nonterminal events subject to dependent censoring by the informative terminal event death, but not vice versa, giving rise to survival data that are subject to two sets of semi-competing risks. It is important to assess the impacts of prognostic factors on these three time-to-event endpoints. We propose a novel statistical approach that jointly models such data via a pair of copulas to account for multiple dependence structures, while the marginal distribution of each endpoint is formulated by a Cox proportional hazards model. We develop an estimation procedure based on pseudo-likelihood and carry out simulation studies to examine the performance of the proposed method in finite samples. The practical utility of the proposed method is further illustrated with data from the motivatingexample.

Conditional Modeling of Longitudinal Data With Terminal Event

ABSTRACTWe consider a random effects model for longitudinal data with the occurrence of an informative terminal event that is subject to right censoring. Existing methods for analyzing such data include the joint modeling approach using latent frailty and the marginal estimating equation approach using inverse probability weighting; in both cases the effect of the terminal event on the response variable is not explicit and thus not easily interpreted. In contrast, we treat the terminal event time as a covariate in a conditional model for the longitudinal data, which provides a straightforward interpretation while keeping the usual relationship of interest between the longitudinally measured response variable and covariates for times that are far from the terminal event. A two-stage semiparametric likelihood-based approach is proposed for estimating the regression parameters; first, the conditional distribution of the right-censored terminal event time given other covariates is estimated and then the likelihood function for the longitudinal event given the terminal event and other regression parameters is maximized. The method is illustrated by numerical simulations and by analyzing medical cost data for patients with end-stage renal disease. Desirable asymptotic properties are provided. Supplementary materials for this article are available online.

Analyzing semi-competing risks data with missing cause of informative terminal event.

Cancer studies frequently yield multiple event times that correspond to landmarks in disease progression, including non-terminal events (i.e., cancer recurrence) and an informative terminal event (i.e., cancer-related death). Hence, we often observe semi-competing risks data. Work on such data has focused on scenarios in which the cause of the terminal event is known. However, in some circumstances, the information on cause for patients who experience the terminal event is missing; consequently, we are not able to differentiate an informative terminal event from a non-informative terminal event. In this article, we propose a method to handle missing data regarding the cause of an informative terminal event when analyzing the semi-competing risks data. We first consider the nonparametric estimation of the survival function for the terminal event time given missing cause-of-failure data via the expectation-maximization algorithm. We then develop an estimation method for semi-competing risks data with missing cause of the terminal event, under a pre-specified semiparametric copula model. We conduct simulation studies to investigate the performance of the proposed method. We illustrate our methodology using data from a study of early-stage breast cancer. Copyright © 2016 John Wiley & Sons, Ltd.

An additive-multiplicative mean model for marker data contingent on recurrent event with an informative terminal event

An additive-multiplicative mean model for marker data contingent on recurrent event with an informative terminal event

A joint frailty-copula model between tumour progression and death for meta-analysis.

Dependent censoring often arises in biomedical studies when time to tumour progression (e.g., relapse of cancer) is censored by an informative terminal event (e.g., death). For meta-analysis combining existing studies, a joint survival model between tumour progression and death has been considered under semicompeting risks, which induces dependence through the study-specific frailty. Our paper here utilizes copulas to generalize the joint frailty model by introducing additional source of dependence arising from intra-subject association between tumour progression and death. The practical value of the new model is particularly evident for meta-analyses in which only a few covariates are consistently measured across studies and hence there exist residual dependence. The covariate effects are formulated through the Cox proportional hazards model, and the baseline hazards are nonparametrically modeled on a basis of splines. The estimator is then obtained by maximizing a penalized log-likelihood function. We also show that the present methodologies are easily modified for the competing risks or recurrent event data, and are generalized to accommodate left-truncation. Simulations are performed to examine the performance of the proposed estimator. The method is applied to a meta-analysis for assessing a recently suggested biomarker CXCL12 for survival in ovarian cancer patients. We implement our proposed methods in R joint.Cox package.

An additive-multiplicative rates model for recurrent event data with informative terminal event

In this article, we propose an additive-multiplicative rates model for recurrent event data in the presence of a terminal event such as death. The association between recurrent and terminal events is nonparametric. For inference on the model parameters, estimating equation approaches are developed, and the asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is provided.

Joint Models of Longitudinal Data and Recurrent Events with Informative Terminal Event.

This article presents semiparametric joint models to analyze longitudinal data with recurrent event (e.g. multiple tumors, repeated hospital admissions) and terminal event such as death. A broad class of transformation models for the cumulative intensity of the recurrent events and the cumulative hazard of the terminal event is considered, which includes the proportional hazards model and the proportional odds model as special cases. We propose to estimate all the parameters using the nonparametric maximum likelihood estimators (NPMLE). We provide the simple and efficient EM algorithms to implement the proposed inference procedure. Asymptotic properties of the estimators are shown to be asymptotically normal and semiparametrically efficient. Finally, we evaluate the performance of the method through extensive simulation studies and a real-data application.

A semiparametric additive rate model for recurrent events with an informative terminal event

We propose a semiparametric additive rate model for modelling recurrent events in the presence of a terminal event. The dependence between recurrent events and terminal event is nonparametric. A general transformation model is used to model the terminal event. We construct an estimating equation for parameter estimation and derive the asymptotic distributions of the proposed estimators. Simulation studies demonstrate that the proposed inference procedure performs well in realistic settings. Application to a medical study is presented.

A semiparametric additive rate model for recurrent events with an informative terminal event

A semiparametric additive rate model for recurrent events with an informative terminal event