• Communications for Statistical Applications and Methods
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• 제28권5호
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• pp.411-424
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• 2021

Inference following two-stage adaptive designs (also known as two-stage randomization designs) with survival endpoints usually focuses on estimating and comparing survival distributions for the different treatment strategies. The aim is to identify the treatment strategy(ies) that leads to better survival of the patients. The objectives of this study were to assess the performance three commonly cited methods for estimating survival distributions in two-stage randomization designs. We review three non-parametric methods for estimating survival distributions in two-stage adaptive designs and compare their performance using simulation studies. The simulation studies show that the method based on the marginal mean model is badly affected by high censoring rates and response rate. The other two methods which are natural extensions of the Nelson-Aalen estimator and the Kaplan-Meier estimator have similar performance. These two methods yield survival estimates which have less bias and more precise than the marginal mean model even in cases of small sample sizes. The weighted versions of the Nelson-Aalen and the Kaplan-Meier estimators are less affected by high censoring rates and low response rates. The bias of the method based on the marginal mean model increases rapidly with increase in censoring rate compared to the other two methods. We apply the three methods to a leukemia clinical trial dataset and also compare the results.

• 응용통계연구
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• 제27권1호
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• pp.1-11
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• 2014

세 개 이상의 집단에 대한 생존분포의 비교를 위해 가중 로그순위 검정법(Weighted Logrank test)과 그의 특별한 경우인 로그순위 검정법(Logrank test)이 널리 쓰인다. 그러나 이 방법은 근사적인 분포를 이용한 방법이므로 표본 크기가 작은 경우에는 유효하지 못할 수 있으며, 각 집단의 중도절단 분포가 동일하다는 가정 또한 충족되어야 하기 때문에 이 가정이 충족되지 못할 경우에도 검정법의 유효성을 장담할 수 없다. 표본 크기가 작은 경우에 대한 대안으로, 분포에 대한 가정이 없이 관찰된 자료만으로 검정통계량의 분포를 추정하고 그 분포를 이용해 검정하는 순열 검정법(Permutation test)이 제안되었으나, 순열 검정법 또한 각 집단의 중도절단 분포가 동일하다는 가정이 충족되어야 한다. 따라서 순열 검정법을 향상시킨 순열-대치 검정법(Permutation-Imputation test)이 대안이 될 수 있는데, 이는 대치 단계(Imputation step)에서 귀무가설 하에서의 생존확률이 집단에 의존하지 않도록 자료를 조정한 후 순열 검정 단계(Permutation step)를 통해 검정하는 방법이다. 본 논문에서는 근사적 방법, 순열 검정법, 순열-대치 검정법을 로그순위 검정법과 가중 로그순위 검정법의 한 형태인 Prentice-Wilcoxon 검정법에 적용해 각 검정법의 유효성과 검정력을 비교하였다.

• Communications for Statistical Applications and Methods
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• 제26권5호
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• pp.445-461
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• 2019

It is possible that data are not always fitted with sufficient precision by the existing distributions; therefore this article presents a methodology that enables the use of families of asymmetric distributions as alternative probabilistic models for survival analysis, with censorship on the right, different from those usually studied (the Exponential, Gamma, Weibull, and Lognormal distributions). We use a more flexible parametric model in terms of density behavior, assuming that data can be fit by a distribution of stable distribution families considered unconventional in the analyses of survival data that are appropriate when extreme values occur, with small probabilities that should not be ignored. In the methodology, the determination of the analytical expression of the risk function h(t) of the $L{\acute{e}}vy$ distribution is included, as it is not usually reported in the literature. A simulation was conducted to evaluate the performance of the candidate distribution when modeling survival times, including the estimation of parameters via the maximum likelihood method, survival function ${\hat{S}}$(t) and Kaplan-Meier estimator. The obtained estimates did not exhibit significant changes for different sample sizes and censorship fractions in the sample. To illustrate the usefulness of the proposed methodology, an application with real data, regarding the survival times of patients with colon cancer, was considered.

• 응용통계연구
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• 제11권1호
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• pp.113-127
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• 1998

생존자료의 분석에 있어 두 집단간의 생존분포의 비교는 자주 관심의 대상이 되고 있다. 중도절단(censoring)이 존재하는 생존자료에 있어 두 생존분포의 동일성을 검정하는 방법으로 log-rank 통계량과 Gehan의 일반화된 Wilcoxon 통계량에 근거한 검정법이 주로 사용되어 왔다. 그러나 이 두 가지 검정통계량이 어떤 상황에서나 적절한 것은 아니고, 두 생존분포의 여러가지 형태와 중도절단의 정도에 따라 통계량의 검정력은 크게 달라진다. 따라서 본 논문에서는 두 생존분포의 비교를 위해 제안된 몇 가지 검정통계량들을 여러가지 상황에서 모의실험을 통하여 비교하고, 그 결과를 토대호 주어진 상황에서 적절한 통계량을 선택하는데 대한 유용한 정보를 제공하였다.

• Communications for Statistical Applications and Methods
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• 제14권1호
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• pp.93-109
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• 2007

In this paper we study a number of new exponentiated distributions. The survival function, failure rate and moments of the distributions have been derived using certain special functions. The behavior of the failure rate has also been studied.

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.179-185
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• 1994

To test the equality of survival distributions in the presence of arbitrary right censorship, the choice of weights which are functions of the number of individuals at risk at the time of each death is very important in increasing the power of the test. In this paper a weight by probit scale is derived and the efficiencies relative to the other weight's are also investigated.

• Asian Pacific Journal of Cancer Prevention
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• 제13권5호
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• pp.1829-1831
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• 2012

Background: The generalized gamma distribution statistics constitute an extensive family that contains nearly all of the most commonly used distributions including the exponential, Weibull and log normal. A saturated version of the model allows covariates having effects through all the parameters of survival time distribution. Accelerated failure-time models assume that only one parameter of the distribution depends on the covariates. Methods: We fitted both the conventional GG model and the saturated form for each of its members including the Weibull and lognormal distribution; and compared them using likelihood ratios. To compare the selected parameter distribution with log logistic distribution which is a famous distribution in survival analysis that is not included in generalized gamma family, we used the Akaike information criterion (AIC; r=l(b)-2p). All models were fitted using data for 369 women age 50 years or more, diagnosed with stage IV breast cancer in BC during 1990-1999 and followed to 2010. Results: In both conventional and saturated parametric models, the lognormal was the best candidate among the GG family members; also, the lognormal fitted better than log-logistic distribution. By the conventional GG model, the variables "surgery", "radiotherapy", "hormone therapy", "erposneg" and interaction between "hormone therapy" and "erposneg" are significant. In the AFT model, we estimated the relative time for these variables. By the saturated GG model, similar significant variables are selected. Estimating the relative times in different percentiles of extended model illustrate the pattern in which the relative survival time change during the time. Conclusions: The advantage of using the generalized gamma distribution is that it facilitates estimating a model with improved fit over the standard Weibull or lognormal distributions. Alternatively, the generalized F family of distributions might be considered, of which the generalized gamma distribution is a member and also includes the commonly used log-logistic distribution.

• 응용통계연구
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• 제27권6호
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• pp.891-907
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• 2014

Hjort (1990)가 제안한 베타과정은 베이지안 생존분석 또는 사건사 분석에서 널리 쓰이는 사전분포이다. 본 논문은 베타과정에 대한 최신 이론과 이를 기반으로 하는 베이지안 생존자료분석 방법을 주로 다룬다. 구체적으로는 베타과정의 생성법, 사후 분포, 대표본 이론, 베이지안 계산법, 혼합베타과정 등을 소개하기로 한다.

• Communications for Statistical Applications and Methods
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• 제25권5호
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• pp.523-544
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• 2018

Bivariate distributions play a fundamental role in survival and reliability studies. We consider a regression model for bivariate survival times under right-censored based on the bivariate Kumaraswamy Weibull (Cordeiro et al., Journal of the Franklin Institute, 347, 1399-1429, 2010) distribution to model the dependence of bivariate survival data. We describe some structural properties of the marginal distributions. The method of maximum likelihood and a Bayesian procedure are adopted to estimate the model parameters. We use diagnostic measures based on the local influence and Bayesian case influence diagnostics to detect influential observations in the new model. We also show that the estimates in the bivariate Kumaraswamy Weibull regression model are robust to deal with the presence of outliers in the data. In addition, we use some measures of goodness-of-fit to evaluate the bivariate Kumaraswamy Weibull regression model. The methodology is illustrated by means of a real lifetime data set for kidney patients.

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.925-931
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• 2022

In this article, we compare the reliability and the hazard function between a baseline distribution and the corresponding transmuted-G distribution. Some examples based on existing transmuted-G distributions in literature are used. Three tests of parameter significance are utilized to test the importance of a transmuted-G distribution over the baseline distribution, and real data is used in an application of the inference about the importance of transmuted-G distributions.