• 품질경영학회지
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• 제22권4호
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• pp.59-78
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• 1994

In some observational studies, we have often random censoring model. However, the data available may be partially observable censored data consisting of the observed failure times and only those nonfailure times which are subject to follow up. In this paper, we present an extension of the problem of partially parametric estimation of the survival function to such partially observable censored data. The proposed estimator treats the observed failure times nonparametrically and uses a parametric model only for those nonfailure times which are subject to follow-up. We discuss the motivation and construction of the proposed estimator and investigate the limiting properties of the proposed estimator such as asymptotic normality. Also, when the assumed parametric model is exponential, the asymptotic variance of the estimator is obtained. Furthermore, an example is given to compare the proposed estimator with the modified Kaplan Meier(MKM) estimator. From the results, it is shown that the relative efficiency of the proposed estimator is higher than that of the MKM estimator in the follow-up study with increasing time.

• Communications for Statistical Applications and Methods
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• 제24권1호
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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 the Korean Data and Information Science Society
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• 제10권1호
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• pp.103-110
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• 1999

In this paper, we summarize some relative risk estimators under the two sample model with proportional hazard and examine the relative efficiencies of the nonparametric estimators relative to the maximum likelihood estimator of a parametric survival function under random censoring model by comparing their asymptotic variances.

• Journal of the Korean Data and Information Science Society
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• 제22권1호
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• pp.89-97
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• 2011

본 연구에서는 Buckley와 James의 방법을 이용하여 중도절단된 자료를 보완한 조건부생존함수 추정량으로부터 조건부평균잔여수명함수를 추정하는 방법을 제안하고, 모의실험을 통하여 제안된 방법의 효율성을 평가하였다. 모의실험 결과 비례위험모형이 아닌 경우 제안된 방법으로 추정한 조건부 평균잔여수명함수의 평균제곱오차가 Cox모형이나 Beran의 비모수적 방법을 이용하여 구한 추정치의 평균제곱오차보다 작게 나타났으며, 비례위험모형인 경우에는 제안된 방법으로 추정한 결과들이 Cox 모형을 이용하여 얻은 결과들과 비슷하게 나타났다. 또한 K대학교병원 외과에서 위암 수술을 받은 1,192명의 환자 자료를 이용하여 제안된 방법의 임상적 적용의 적절성을 평가하였다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• Communications for Statistical Applications and Methods
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• 제24권5호
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• pp.519-531
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• 2017

We consider goodness-of-fit test statistics for Weibull distributions when data are randomly censored and the parameters are unknown. Koziol and Green (Biometrika, 63, 465-474, 1976) proposed the $Cram\acute{e}r$-von Mises statistic's randomly censored version for a simple hypothesis based on the Kaplan-Meier product limit of the distribution function. We apply their idea to the other statistics based on the empirical distribution function such as the Kolmogorov-Smirnov and Liao and Shimokawa (Journal of Statistical Computation and Simulation, 64, 23-48, 1999) statistics. The latter is a hybrid of the Kolmogorov-Smirnov, $Cram\acute{e}r$-von Mises, and Anderson-Darling statistics. These statistics as well as the Koziol-Green statistic are considered as test statistics for randomly censored Weibull distributions with estimated parameters. The null distributions depend on the estimation method since the test statistics are not distribution free when the parameters are estimated. Maximum likelihood estimation and the graphical plotting method with the least squares are considered for parameter estimation. A simulation study enables the Liao-Shimokawa statistic to show a relatively high power in many alternatives; however, the null distribution heavily depends on the parameter estimation. Meanwhile, the Koziol-Green statistic provides moderate power and the null distribution does not significantly change upon the parameter estimation.

• International Journal of Reliability and Applications
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• 제15권2호
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• pp.125-150
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• 2014

Accelerated life tests (ALTs) are extensively used to determine the reliability of a product in a short period of time. Test units are subject to elevated stresses which yield quick failures. ALT can be carried out using constant-stress, step-stress, progressive-stress, cyclic-stress or random-stress loading and their various combinations. An ALT with linearly increasing stress is ramp-stress test. Much of the previous work on planning ALTs has focused on constant-stress, step-stress, ramp-stress schemes and their various combinations where the stress is generally increased. This paper presents an optimal design of ramp soak-stress ALT model which is based on the principle of Thermal cycling. Thermal cycling involves applying high and low temperatures repeatedly over time. The optimal plan consists in finding out relevant experimental variables, namely, stress rates and stress rate change points, by minimizing variance of reliability function with pre-specified mission time under normal operating conditions. The Burr type XII life distribution and time-censored data have been used for the purpose. Burr type XII life distribution has been found appropriate for accelerated life testing experiments. The method developed has been explained using a numerical example and sensitivity analysis carried out.

• 지식경영연구
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• 제11권2호
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• pp.95-109
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• 2010

The objectives of this study are to identify the survival function (hazard function) of small and medium enterprises by using technology rating data for the companies guaranteed by Korea Technology Finance Corporation (KOTEC), and to figure out the factors that affects their survival. To serve the purposes, this study uses Kaplan-Meier Analysis as a non-parametric method and Cox proportional hazards model as a semi-parametric one. The 17,396 guaranteed companies that assessed from July 1st in 2005 to December 31st in 2009 are selected as samples (16,504 censored data and 829 accident data). The survival time is computed with random censoring (Type III) from July in 2005 as a starting point. The results of the analysis show that Kaplan-Meier Analysis and Cox proportional hazards model are able to readily estimate survival and hazard function and to perform comparative study among group variables such as industry and technology rating level. In particular, Cox proportional hazards model is recognized that it is useful to understand which technology rating items are meaningful to company's survival and how much they affect it. It is considered that these results will provide valuable knowledge for practitioners to find and manage the significant items for survival of the guaranteed companies through future technology rating.

• Communications for Statistical Applications and Methods
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• 제26권5호
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• pp.431-443
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• 2019

Goodness-of-fit techniques are an important topic in statistical analysis. Censored data occur frequently in survival experiments; therefore, many studies are conducted when data are censored. In this paper we mainly consider test statistics based on the empirical distribution function (EDF) to test normal distributions with unknown location and scale parameters when data are randomly censored. The most famous EDF test statistic is the Kolmogorov-Smirnov; in addition, the quadratic statistics such as the $Cram{\acute{e}}r-von$ Mises and the Anderson-Darling statistic are well known. The $Cram{\acute{e}}r-von$ Mises statistic is generalized to randomly censored cases by Koziol and Green (Biometrika, 63, 465-474, 1976). In this paper, we generalize the Anderson-Darling statistic to randomly censored data using the Kaplan-Meier estimator as it was done by Koziol and Green. A simulation study is conducted under a particular censorship model proposed by Koziol and Green. Through a simulation study, the generalized Anderson-Darling statistic shows the best power against almost all alternatives considered among the three EDF statistics we take into account.

• Asian-Australasian Journal of Animal Sciences
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• 제32권9호
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• pp.1349-1354
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• 2019

Objective: The objective of this study was to determine the best approach for handling missing records of first to successful insemination (FS) in Japanese Black heifers. Methods: Of a total of 2,367 records of heifers born between 2003 and 2015 used, 206 (8.7%) of open heifers were missing. Four penalty methods based on the number of inseminations were set as follows: C1, FS average according to the number of inseminations; C2, constant number of days, 359; C3, maximum number of FS days to each insemination; and C4, average of FS at the last insemination and FS of C2. C5 was generated by adding a constant number (21 d) to the highest number of FS days in each contemporary group. The bootstrap method was used to compare among the 5 methods in terms of bias, mean squared error (MSE) and coefficient of correlation between estimated breeding value (EBV) of non-censored data and censored data. Three percentages (5%, 10%, and 15%) were investigated using the random censoring scheme. The univariate animal model was used to conduct genetic analysis. Results: Heritability of FS in non-censored data was $0.012{\pm}0.016$, slightly lower than the average estimate from the five penalty methods. C1, C2, and C3 showed lower standard errors of estimated heritability but demonstrated inconsistent results for different percentages of missing records. C4 showed moderate standard errors but more stable ones for all percentages of the missing records, whereas C5 showed the highest standard errors compared with noncensored data. The MSE in C4 heritability was $0.633{\times}10^{-4}$, $0.879{\times}10^{-4}$, $0.876{\times}10^{-4}$ and $0.866{\times}10^{-4}$ for 5%, 8.7%, 10%, and 15%, respectively, of the missing records. Thus, C4 showed the lowest and the most stable MSE of heritability; the coefficient of correlation for EBV was 0.88; 0.93 and 0.90 for heifer, sire and dam, respectively. Conclusion: C4 demonstrated the highest positive correlation with the non-censored data set and was consistent within different percentages of the missing records. We concluded that C4 was the best penalty method for missing records due to the stable value of estimated parameters and the highest coefficient of correlation.