• The Korean Journal of Applied Statistics
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• v.23 no.4
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• pp.715-724
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• 2010

Recurrent event data occurs when a subject experience the event of interest several times and has been found in biomedical studies, sociology and engineering. Several diverse approaches have been applied to analyze the recurrent events (Cook and Lawless, 2007). In this study, we analyzed the YTOP(Young Traffic Offenders Program) dataset which consists of 192 drivers with conviction dates by speeding violation and traffic rule violation. We consider a subject-specific effect, frailty, to reflect the individual's driving behavior and extend to time-varying frailty effect. Another feature of this study is about the redefinition of risk set. During the study, subject may be under suspension and this period is regarded as non-risk period. Thus the risk variables are reformatted according to suspension and termination time.

• The Korean Journal of Applied Statistics
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• v.28 no.6
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• pp.1209-1216
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• 2015

Competing-risks events are often observed in a clustered clinical study such as a multi-center clinical trial. We propose a joint modelling approach via a shared frailty term for competing risks survival data from a cluster. For the inference we use the hierarchical likelihood (or h-likelihood), which avoids an intractable integration. We derive the corresponding h-likelihood procedure. The proposed method is illustrated via the analysis of a practical data set.

• The Korean Journal of Applied Statistics
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• v.18 no.1
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• pp.67-81
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• 2005

Most of the previously proposed methods for the frailty model do not work well when there are many tied observations. This is partly because the empirical likelihood used is not suitable for tied observations. In this paper, we propose a new method for the frailty model with many ties. The proposed method obtains the posterior distribution of the parameters using the binomial form empirical likelihood and Bayesian bootstrap. The proposed method yields stable results and is computationally fast. To compare the proposed method with the maximum marginal likelihood approach, we do simulations.

• The Korean Journal of Applied Statistics
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• v.23 no.5
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• pp.871-882
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• 2010

In animal tumorigenicity data, the occurrence time of tumor is not observed because the existence of a tumor is examined only at either time of natural death or time of sacrifice for the animal. A three-state model (Health-Tumor onset-Death) is widely used to model the incomplete data. In this paper, we employed a frailty effect into the three-state model to incorporate the dependency of death on tumor occurrence when the time of natural death works as an informative censoring against the tumor onset time. For the inference of parameters, then the EM algorithm is considered in order to deal with missing quantities of tumor onset time and random frailty. The proposed method is applied to the bladder tumor data taken from Lindsey and Ryan (1993, 1994) and a simulation study is performed to show the behavior of the proposed estimators.

• Journal of the Korean Data and Information Science Society
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• v.27 no.2
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• pp.499-510
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• 2016

It is very important to select relevant variables in regression models for survival analysis. In this paper, we introduce a penalized variable-selection procedure in multi-level frailty models based on the "frailtyHL" R package (Ha et al., 2012). Here, the estimation procedure of models is based on the penalized hierarchical likelihood, and three penalty functions (LASSO, SCAD and HL) are considered. The proposed methods are illustrated with multi-country/multi-center bladder cancer survival data from the EORTC in Belgium. We compare the results of three variable-selection methods and discuss their advantages and disadvantages. In particular, the results of data analysis showed that the SCAD and HL methods select well important variables than in the LASSO method.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.965-976
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• 2015

Determining relevant variables for a regression model is important in regression analysis. Recently, a variable selection methods using a penalized likelihood with various penalty functions (e.g. LASSO and SCAD) have been widely studied in simple statistical models such as linear models and generalized linear models. The advantage of these methods is that they select important variables and estimate regression coefficients, simultaneously; therefore, they delete insignificant variables by estimating their coefficients as zero. We study how to select proper variables based on penalized hierarchical likelihood (HL) in semi-parametric frailty models that allow three penalty functions, LASSO, SCAD and HL. For the variable selection we develop a new function in the "frailtyHL" R package. Our methods are illustrated with breast cancer survival data from the Medical Center at Chonnam National University in Korea. We compare the results from three variable-selection methods and discuss advantages and disadvantages.

• The Korean Journal of Applied Statistics
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• v.29 no.7
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• pp.1311-1327
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• 2016

We propose a multi-state model for analyzing semi-competing risks data with interval-censored or missing intermediate events. This model is an extension of the 'illness-death model', which composes three states, such as 'healthy', 'diseased', and 'dead'. The state of 'diseased' can be considered as an intermediate event. Two more states are added into the illness-death model to describe missing events caused by a loss of follow-up before the end of the study. One of them is a state of 'LTF', representing a lost-to-follow-up, and the other is an unobservable state that represents the intermediate event experienced after LTF occurred. Given covariates, we employ the Cox proportional hazards model with a normal frailty and construct a full likelihood to estimate transition intensities between states in the multi-state model. Marginalization of the full likelihood is completed using the adaptive Gaussian quadrature, and the optimal solution of the regression parameters is achieved through the iterative Newton-Raphson algorithm. Simulation studies are carried out to investigate the finite-sample performance of the proposed estimation procedure in terms of the empirical coverage probability of the true regression parameter. Our proposed method is also illustrated with the dataset adapted from Helmer et al. (2001).

• The Korean Journal of Applied Statistics
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• v.33 no.4
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• pp.379-393
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• 2020

A terminal event such as death may censor an intermediate event such as relapse, but not vice versa in semi-competing risks data, which is often seen in medicine, public health, and epidemiology. We propose a Weibull regression model with a normal frailty to analyze semi-competing risks data when all three transition times of the illness-death model are possibly interval-censored. We construct the conditional likelihood separately depending on the types of subjects: still alive with or without the intermediate event, dead with or without the intermediate event, and dead with the intermediate event missing. Optimal parameter estimates are obtained from the iterative quasi-Newton algorithm after the marginalization of the full likelihood using the adaptive importance sampling. We illustrate the proposed method with extensive simulation studies and PAQUID (Personnes Agées Quid) data.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.327-336
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• 2014

Recurrent event data occurs when a subject experiences same type of event repeatedly and is found in various areas such as the social sciences, Economics, medicine and public health. To analyze recurrent event data either a total time or a gap time is adopted according to research interest. In this paper, we analyze recurrent event data with incomplete observation gap using a gap time scale. That is, some subjects leave temporarily from a study and return after a while. But it is not available when the observation gaps terminate. We adopt an interval censoring mechanism for estimating the termination time. Furthermore, to model the association among gap times of a subject, a frailty effect is incorporated into a model. Programs included in Survival package of R program are implemented to estimate the covariate effect as well as the variance of frailty effect. YTOP (Young Traffic Offenders Program) data is analyzed with both proportional hazard model and a weibull regression model.

• The Korean Journal of Applied Statistics
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• v.30 no.4
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• pp.539-553
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• 2017

We propose a multi-state model to analyze semi-competing risks data with interval-censored or missing intermediate events. This model is an extension of the three states of the illness-death model: healthy, disease, and dead. The 'diseased' state can be considered as the intermediate event. Two more states are added into the illness-death model to incorporate the missing events, which are caused by a loss of follow-up before the end of a study. One of them is a state of the lost-to-follow-up (LTF), and the other is an unobservable state that represents an intermediate event experienced after the occurrence of LTF. Given covariates, we employ the Lin and Ying additive hazards model with log-normal frailty and construct a conditional likelihood to estimate transition intensities between states in the multi-state model. A marginalization of the full likelihood is completed using adaptive importance sampling, and the optimal solution of the regression parameters is achieved through an iterative quasi-Newton algorithm. Simulation studies are performed to investigate the finite-sample performance of the proposed estimation method in terms of empirical coverage probability of true regression parameters. Our proposed method is also illustrated with a dataset adapted from Helmer et al. (2001).