• 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 Applied Reliability
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• v.18 no.2
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• pp.130-142
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• 2018

Purpose: The purpose of this study is to introduce regression method in the presence of competing risks and to show how you can use the method with hypothetical data. Methods: Survival analysis has been widely used in biostatistics division. But the same method has not been utilized in reliability division. Especially competing risks, where more than a couple of causes of failure occur and the occurrence of one event precludes the occurrence of the other events, are scattered in reliability field. But they are not utilized in the area of reliability or they are analysed in the wrong way. Specifically Kaplan-Meier method is used to calculate the probability of failure in the presence of competing risks, thereby overestimating the real probability of failure. Hence, cumulative incidence function is introduced. In addition, sample competing risks data are analysed using cumulative incidence function along with some graphs. Lastly we compare cumulative incidence functions with regression type analysis briefly. Results: We used cumulative incidence function to calculate the survival probability or failure probability in the presence of competing risks. We also drew some useful graphs depicting the failure trend over the lifetime. Conclusion: This research shows that Kaplan-Meier method is not appropriate for the evaluation of survival or failure over the course of lifetime in the presence of competing risks. Cumulative incidence function is shown to be useful in stead. Some graphs using the cumulative incidence functions are also shown to be informative.

• Journal of Applied Reliability
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• v.16 no.1
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• pp.56-63
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• 2016

Purpose: The purpose of this study is to point out that the Kaplan-Meier method is not valid to calculate the survival probability or failure probability (risk) in the presence of competing risks and to introduce more valid method of cumulative incidence function. Methods: Survival analysis methods have been widely used in biostatistics division. However the same methods have not been utilized in reliability division. Especially competing risks cases, where several causes of failure occur and the occurrence of one event precludes the occurrence of the other events, are scattered in reliability field. But they are not noticed in the realm of reliability expertism or they are analysed in the wrong way. Specifically Kaplan-Meier method which assumes that the censoring times and failure times are independent is used to calculate the probability of failure in the presence of competing risks, thereby overestimating the real probability of failure. Hence, cumulative incidence function is introduced and sample competing risks data are analysed using cumulative incidence function and some graphs. Finally comparison of cumulative incidence functions and regression type analysis are mentioned briefly. Results: Cumulative incidence function is used to calculate the survival probability or failure probability (risk) in the presence of competing risks and some useful graphs depicting the failure trend over the lifetime are introduced. Conclusion: This paper shows that Kaplan-Meier method is not appropriate for the evaluation of survival or failure over the course of lifetime. In stead, cumulative incidence function is shown to be useful. Some graphs using the cumulative incidence functions are also shown to be informative.

• 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.31 no.4
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• pp.529-538
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• 2018

Tuberculosis causes high morbidity and mortality. However, Korea still has the highest tuberculosis (TB) incidence and mortality among OECD countries despite decreasing incidence and mortality due to the development of modern medicine. Korea has now implemented various policy projects to prevent and control tuberculosis. This study analyzes the effects of public-private mix (PPM) tuberculosis control program on treatment outcomes and identifies the factors that affecting the success of TB treatment. We analyzed 130,000 new tuberculosis patient cohort from 2012 to 2015 using data of tuberculosis patient reports managed by the Disease Control Headquarters. A cumulative incidence function (CIF) compared the cumulative treatment success rates for each factor. We compared the results of the analysis using two popular types of competition risk models (cause-specific Cox's proportional hazards model and subdistribution hazard model) that account for the main event of interest (treatment success) and competing events (death).

• Nuclear Engineering and Technology
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• v.29 no.1
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• pp.1-6
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• 1997

This paper presents a new dynamic approach for assessing feasibility associated with the implementation of accident management strategies by the operators. This approach includes the combined use of both the concept of reliability physics and a dynamic event tree generation scheme. The reliability physics is based on the concept of a comparison between two competing variables, i.e., the requirement and the achievement parameter, while the dynamic event tree generation scheme on the continuous generation of the possible event sequences at every branch point up to the desired solution. This approach is applied to a cavity flooding strategy in a reference plant, which is to supply water into the reactor cavity using emergency fire systems in the station blackout sequence. The MAAP code and Latin Hypercube sampling technique are used to determine the uncertainty of the requirement parameter. It has been demonstrated that this combined methodology may contribute to assessing the success likelihood of the operator actions required during accidents and therefore to developing the accident management procedures.

• 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).

• Communications for Statistical Applications and Methods
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• v.24 no.1
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• pp.43-65
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• 2017

We propose a flexible cure rate survival model by assuming that the number of competing causes of the event of interest has the Poisson distribution and the time for the event follows the gamma-G family of distributions. The extended family of gamma-G failure-time models with long-term survivors is flexible enough to include many commonly used failure-time distributions as special cases. We consider a frequentist analysis for parameter estimation and derive appropriate matrices to assess local influence on the parameters. Further, various simulations are performed for different parameter settings, sample sizes and censoring percentages. We illustrate the performance of the proposed regression model by means of a data set from the medical area (gastric cancer).

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.4
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• pp.304-312
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• 2011

In an oligopolistic market, only a few firms account for most or all of total production, e.g., automobile, steel, and computer industries. For a dynamic oligopolistic market with two firms competing in quantities, we show that supervisory control theory of discrete event systems provides a novel approach to solve the dynamic oligopoly problem with the aim of maximizing the profits of both firms. Specifically, we show that the controllability, observability, and nonblocking property (which are the core concepts in supervisory control theory) are the necessary and sufficient conditions for two oligopolistic firms in disequilibrium to eventually reach equilibrium states of maximizing the profits of both firms.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.7
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• pp.244-252
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• 2013

In this paper, we show that supervisory control theory of discrete event systems can be applied to analyze the problem of power in political economy. For this purpose, we introduce the decision mechanism of control inputs based on power, and the consequent behavior of a supervised system. Specifically, this paper presents the notion of power-controllability as a necessary and sufficient condition to achieve a common control objective of competing groups (local controllers). If the power-controllability is met, a modular system controlled by local controllers with power functions is not deviated from a common control objective of them.