• 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.22 no.3
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• pp.595-606
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• 2009

Two tests were introduced for comparing several survival functions with doubly interval-censored data and illustrated with data surveyed by Korean Cancer Prevention Study (Jee et al., 2005). The test which extended Kim et al. (2006)'s test to the doubly interval-censored data has an advantage over Sun (2006)'s test in terms of saving computation time because the proposed test only depends on the size of risk set, and also the proposed test is applicable to continuous failure time data as well as discrete failure time data unlike Sun's test. Comparing male with female groups on the incubation time of diabetes was highly different and the survival of female group was longer than that of male one. Regardless of gender, the difference in survival functions of four age groups was highly significant with p-value of less than 0.001. This trend was more remarkable for female group than for male one. Simulation results showed that the significance level of both tests was well controlled and the proposed test was better than Sun's test in terms of power.

• Communications for Statistical Applications and Methods
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• v.17 no.5
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• pp.689-696
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• 2010

Interval-censored data are commonly found in studies of diseases that progress without symptoms, which require clinical evaluation for detection. Several techniques have been suggested with independent assumption. However, the assumption will not be valid if observations come from clusters. Furthermore, when the cluster size relates to response variables, commonly used methods can bring biased results. For example, in a study on lymphatic filariasis, a parasitic disease where worms make several nests in the infected person's lymphatic vessels and reside until adulthood, the response variable of interest is the nest-extinction times. Since the extinction times of nests are checked by repeated ultrasound examinations, exact extinction times are not observed. Instead, data are composed of two examination points: the last examination time with living worms and the first examination time with dead worms. Furthermore, as Williamson et al. (2008) pointed out, larger nests show a tendency for low clearance rates. This association has been denoted as an informative cluster size. To analyze the relationship between the numbers of nests and interval-censored nest-extinction times, this study proposes a joint model for the relationship between cluster size and clustered interval-censored failure data.

• 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).

• 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.

• Journal of the Korean Data and Information Science Society
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• v.8 no.1
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• pp.21-30
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• 1997

In accelerated life tests, the failure time of an item is observed under a high stress level, and based on the time the performances of items are investigated at the normal stress level. In this paper, when the mean of the prior of a failure rate is known in the exponential lifetime distribution with censored accelerated failure time data, we utilize the empirical Bayesian method by using the moment estimators in order to estimate the parameters of the prior distribution and obtain the empirical Bayesian predictive density and predictive intervals for a future observation under the normal stress level.

• The Korean Journal of Applied Statistics
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• v.33 no.6
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• pp.777-789
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• 2020

COVID-19 has been rapidly spread world wide since late December 2019. In this paper, our interest is to estimate distribution of incubation time defined as period between infection of virus and the onset. Due to the limit of accessibility and asymptomatic feature of COVID-19 virus, the exact infection and onset time are not always observable. For estimation of incubation time, interval censoring technique is implemented. Furthermore, a competing risk model is applied to estimate the case fatality and cure fraction. Based on the result, the mean incubation time is about 5.4 days and the fatality rate is higher for older and male patient and the cure rate is higher at younger,female and asymptomatic patient.