Improving estimation efficiency for semi-competing risks data with partially observed terminal event

Semi-competing risks data arise when two types of events, non-terminal and terminal, may be observed. When the terminal event occurs first, it censors the non-terminal event. Otherwise the terminal event is observable after the occurrence of the non-terminal event. In practice, it can be hard to ascertain all terminal event information after the non-terminal event. Yu and Yiannoutsos [(2015), ‘Marginal and Conditional Distribution Estimation from Double-Sampled Semi-Competing Risks Data’, Scandinavian Journal of Statistics, 42, 87–103] considered a setting when the terminal event is ascertained via double sampling from only a subset of patients who experienced the non-terminal event. They discussed estimation for marginal and conditional distributions under this double sampled semi-competing risk data framework. We propose a more efficient estimation method in the same setting by fully utilising the non-terminal event information. The efficiency gain can be substantial as observed in our simulation study.     

Regression analysis based on conditional likelihood approach under semi-competing risks data

Medical studies often involve semi-competing risks data, which consist of two types of events, namely terminal event and non-terminal event. Because the non-terminal event may be dependently censored by the terminal event, it is not possible to make inference on the non-terminal event without extra assumptions. Therefore, this study assumes that the dependence structure on the non-terminal event and the terminal event follows a copula model, and lets the marginal regression models of the non-terminal event and the terminal event both follow time-varying effect models. This study uses a conditional likelihood approach to estimate the time-varying coefficient of the non-terminal event, and proves the large sample properties of the proposed estimator. Simulation studies show that the proposed estimator performs well. This study also uses the proposed method to analyze AIDS Clinical Trial Group (ACTG 320).     

Joint model for bivariate zero-inflated recurrent event data with terminal events

Bivariate recurrent event data are observed when subjects are at risk of experiencing two different type of recurrent events. In this paper, our interest is to suggest statistical model when there is a substantial portion of subjects not experiencing recurrent events but having a terminal event. In a context of recurrent event data, zero events can be related with either the risk free group or a terminal event. For simultaneously reflecting both a zero inflation and a terminal event in a context of bivariate recurrent event data, a joint model is implemented with bivariate frailty effects. Simulation studies are performed to evaluate the suggested models. Infection data from AML (acute myeloid leukemia) patients are analyzed as an application.     

Maximum likelihood analysis of semicompeting risks data with semiparametric regression models

The “semicompeting risks” include a terminal event and a non-terminal event. The terminal event may censor the non-terminal event but not vice versa. Because times to the two events are usually correlated, the non-terminal event is subject to dependent/informative censoring by the terminal event. We seek to conduct marginal regressions and joint association analyses for the two event times under semicompeting risks. The proposed method is based on the modeling setup where the semiparametric transformation models are assumed for marginal regressions, and a copula model is assumed for the joint distribution. We propose a nonparametric maximum likelihood approach for inferences, which provides a martingale representation for the score function and an analytical expression for the information matrix. Direct theoretical developments and computational implementation are allowed for the proposed approach. Simulations and a real data application demonstrate the utility of the proposed methodology.     

Joint covariate-adjusted score test statistics for recurrent events and a terminal event

Recurrent events data are frequently encountered and could be stopped by a terminal event in clinical trials. It is of interest to assess the treatment efficacy simultaneously with respect to both the recurrent events and the terminal event in many applications. In this paper we propose joint covariate-adjusted score test statistics based on joint models of recurrent events and a terminal event. No assumptions on the functional form of the covariates are needed. Simulation results show that the proposed tests can improve the efficiency over tests based on covariate unadjusted model. The proposed tests are applied to the SOLVD data for illustration.     

Frailty modelling approaches for semi-competing risks data

Lifetime Data Analysis - In the semi-competing risks situation where only a terminal event censors a non-terminal event, observed event times can be correlated. Recently, frailty models with an...     

Joint modeling approach for semicompeting risks data with missing nonterminal event status

Semicompeting risks data, where a subject may experience sequential non-terminal and terminal events, and the terminal event may censor the non-terminal event but not vice versa, are widely available in many biomedical studies. We consider the situation when a proportion of subjects’ non-terminal events is missing, such that the observed data become a mixture of “true” semicompeting risks data and partially observed terminal event only data. An illness–death multistate model with proportional hazards assumptions is proposed to study the relationship between non-terminal and terminal events, and provide covariate-specific global and local association measures. Maximum likelihood estimation based on semiparametric regression analysis is used for statistical inference, and asymptotic properties of proposed estimators are studied using empirical process and martingale arguments. We illustrate the proposed method with simulation studies and data analysis of a follicular cell lymphoma study.     

Pseudo Self-Consistent Estimation of a Copula Model with Informative Censoring

Abstract.  We consider the case where a terminal event censors a non-terminal event, but not vice versa. When the events are dependent, estimation of the distribution of the non-terminal event is a competing risks problem, while estimation of the distribution of the terminal event is not. The dependence structure of the event times is formulated with the gamma frailty copula on the upper wedge, with the marginal distributions unspecified. With a consistent estimator of the association parameter, pseudo self-consistency equations are derived and adapted to the semiparametric model. Existence, uniform consistency and weak convergence of the new estimator for the marginal distribution of the non-terminal event is established using theories of empirical processes, U -statistics and Z -estimation. The potential practical utility of the methodology is illustrated with simulated and real data sets.     

Analysis of censored longitudinal data with skewness and a terminal event

In HIV/AIDS study, the measurements viral load are often highly skewed and left-censored because of a lower detection limit. Furthermore, a terminal event (e.g., death) stops the follow-up process. The time to terminal event may be dependent on the viral load measurements. In this article, we present a joint analysis framework to model the censored longitudinal data with skewness and a terminal event process. The estimation is carried out by adaptive Gaussian quadrature techniques in SAS procedure NLMIXED. The proposed model is evaluated by a simulation study and is applied to the motivating Multicenter AIDS Cohort Study (MACS).     

A Marginal Additive Rates Model for Recurrent Event Data with a Terminal Event

Recurrent events data with a terminal event often arise in many longitudinal studies. Most of existing models assume multiplicative covariate effects and model the conditional recurrent event rate given survival. In this article, we propose a marginal additive rates model for recurrent events with a terminal event, and develop two procedures for estimating the model parameters. The asymptotic properties of the resulting estimators are established. In addition, some numerical procedures are presented for model checking. The finite-sample behavior of the proposed methods is examined through simulation studies, and an application to a bladder cancer study is also illustrated.     

Quantile regression based on a weighted approach under semi-competing risks data

In this article, we investigate the quantile regression analysis for semi-competing risks data in which a non-terminal event may be dependently censored by a terminal event. Due to the dependent censoring, the estimation of quantile regression coefficients on the non-terminal event becomes difficult. In order to handle this problem, we assume Archimedean Copula to specify the dependence of the non-terminal event and the terminal event. Portnoy [Censored regression quantiles. J Amer Statist Assoc. 2003;98:1001–1012] considered the quantile regression model under right-censoring data. We extend his approach to construct a weight function, and then impose the weight function to estimate the quantile regression parameter for the non-terminal event under semi-competing risks data. We also prove the consistency and asymptotic properties for the proposed estimator. According to the simulation studies, the performance of our proposed method is good. We also apply our suggested approach to analyse a real data.     

Regression analysis of multivariate recurrent event data with a dependent terminal event

Recurrent event data occur in many clinical and observational studies (Cook and Lawless, Analysis of recurrent event data, 2007) and in these situations, there may exist a terminal event such as death that is related to the recurrent event of interest (Ghosh and Lin, Biometrics 56:554–562, 2000; Wang et al., J Am Stat Assoc 96:1057–1065, 2001; Huang and Wang, J Am Stat Assoc 99:1153–1165, 2004; Ye et al., Biometrics 63:78–87, 2007). In addition, sometimes there may exist more than one type of recurrent events, that is, one faces multivariate recurrent event data with some dependent terminal event (Chen and Cook, Biostatistics 5:129–143, 2004). It is apparent that for the analysis of such data, one has to take into account the dependence both among different types of recurrent events and between the recurrent and terminal events. In this paper, we propose a joint modeling approach for regression analysis of the data and both finite and asymptotic properties of the resulting estimates of unknown parameters are established. The methodology is applied to a set of bivariate recurrent event data arising from a study of leukemia patients.     

Recurrent Events Analysis in the Presence of Terminal Event and Zero-recurrence Subjects

Recurrent event data are often encountered in longitudinal follow-up studies related to biomedical science, econometrics, reliability, and demography. In many situations, a terminal event such as death can happen during the follow-up period that precludes further recurrences. In this article, we will review some existing models for recurrent event with information censoring, and then extend them to allow zero-recurrence subjects as well as a terminal event. Estimating equations and partial likelihood are employed to estimate the coefficients of covariates, accumulative rate functions and the proportions of zero-recurrence subjects. The large-sample properties ofthe estimators are established as well. Simulations are performed to evaluate the estimationprocedure and an example of application on a set of migration data is provided to illustrateour proposed models and methods.     

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.     

Semiparametric model for recurrent event data with excess zeros and informative censoring

Recurrent event data are often encountered in longitudinal follow-up studies in many important areas such as biomedical science, econometrics, reliability, criminology and demography. Multiplicative marginal rates models have been used extensively to analyze recurrent event data, but often fail to fit the data adequately. In addition, the analysis is complicated by excess zeros in the data as well as the presence of a terminal event that precludes further recurrence. To address these problems, we propose a semiparametric model with an additive rate function and an unspecified baseline to analyze recurrent event data, which includes a parameter to accommodate excess zeros and a frailty term to account for a terminal event. Local likelihood procedure is applied to estimate the parameters, and the asymptotic properties of the estimators are established. A simulation study is conducted to evaluate the performance of the proposed methods, and an example of their application is presented on a set of tumor recurrent data for bladder cancer.     

Joint modeling and estimation for longitudinal data with informative observation and terminal event times

ABSTRACT

In many longitudinal studies, there may exist informative observation times and a dependent terminal event that stops the follow-up. In this paper, we propose a joint model for analysis of longitudinal data with informative observation times and a dependent terminal event via two latent variables. Estimation procedures are developed for parameter estimation, and asymptotic properties of the proposed estimators are derived. Simulation studies demonstrate that the proposed method performs well for practical settings. An application to a bladder cancer study is illustrated.     

Quantile residual life regression based on semi-competing risks data

This paper investigates the quantile residual life regression based on semi-competing risk data. Because the terminal event time dependently censors the non-terminal event time, the inference on the non-terminal event time is not available without extra assumption. Therefore, we assume that the non-terminal event time and the terminal event time follow an Archimedean copula. Then, we apply the inverse probability weight technique to construct an estimating equation of quantile residual life regression coefficients. But, the estimating equation may not be continuous in coefficients. Thus, we apply the generalized solution approach to overcome this problem. Since the variance estimation of the proposed estimator is difficult to obtain, we use the bootstrap resampling method to estimate it. From simulations, it shows the performance of the proposed method is well. Finally, we analyze the Bone Marrow Transplant data for illustrations.     

Modeling of semi-competing risks by means of first passage times of a stochastic process

In semi-competing risks one considers a terminal event, such as death of a person, and a non-terminal event, such as disease recurrence. We present a model where the time to the terminal event is the first passage time to a fixed level c in a stochastic process, while the time to the non-terminal event is represented by the first passage time of the same process to a stochastic threshold S, assumed to be independent of the stochastic process. In order to be explicit, we let the stochastic process be a gamma process, but other processes with independent increments may alternatively be used. For semi-competing risks this appears to be a new modeling approach, being an alternative to traditional approaches based on illness-death models and copula models. In this paper we consider a fully parametric approach. The likelihood function is derived and statistical inference in the model is illustrated on both simulated and real data.     

Analyzing panel count data with a dependent observation process and a terminal event

Panel count data occur in many fields and a number of approaches have been developed. However, most of these approaches are for situations where there is no terminal event and the observation process is independent of the underlying recurrent event process unconditionally or conditional on the covariates. In this paper, we discuss a more general situation where the observation process is informative and there exists a terminal event which precludes further occurrence of the recurrent events of interest. For the analysis, a semiparametric transformation model is presented for the mean function of the underlying recurrent event process among survivors. To estimate the regression parameters, an estimating equation approach is proposed in which an inverse survival probability weighting technique is used. The asymptotic distribution of the proposed estimates is provided. Simulation studies are conducted and suggest that the proposed approach works well for practical situations. An illustrative example is provided. The Canadian Journal of Statistics 41: 174–191; 2013 © 2012 Statistical Society of Canada