• Communications for Statistical Applications and Methods
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• 제24권6호
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• pp.583-604
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• 2017

The most popular regression model for the analysis of time-to-event data is the Cox proportional hazards model. While the model specifies a parametric relationship between the hazard function and the predictor variables, there is no specification regarding the form of the baseline hazard function. A critical assumption of the Cox model, however, is the proportional hazards assumption: when the predictor variables do not vary over time, the hazard ratio comparing any two observations is constant with respect to time. Therefore, to perform credible estimation and inference, one must first assess whether the proportional hazards assumption is reasonable. As with other regression techniques, it is also essential to examine whether appropriate functional forms of the predictor variables have been used, and whether there are any outlying or influential observations. This article reviews diagnostic methods for assessing goodness-of-fit for the Cox proportional hazards model. We illustrate these methods with a case-study using available R functions, and provide complete R code for a simulated example as a supplement.

• Journal of the Korean Data and Information Science Society
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• 제9권2호
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• pp.173-177
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• 1998

This paper presents the asymptotic relative efficiency of the nonparametric estimator relative to the parametric maximum likelihood estimator of the reliability function under the proportional hazards model of random censorship. Also we examine the efficiency loss due to censoring proportions and misson times.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2002년도 정기학술대회
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• pp.415-415
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• 2002

Proportional hazards model can be used to develop a realistic approach to determine the performance of a system. The proportional hazards model is typically applied for a group of equipments to assess the importance of factors that may influence the reliability of a system. In this paper we considered the interarrival times of a maintained system for the analysis of reliability, maintainability and availability. In order to demonstrate the proposed approach, an example is presented.

• Journal of the Korean Statistical Society
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• 제35권3호
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• pp.251-260
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• 2006

The proportional hazards model (PHM) can be associated with a non- homogeneous Markov chain (NHMC) in the sense that sample alignments in the PHM correspond to trajectories of the NHMC. As a result the partial likelihood widely used for the PHM is a probabilistic function of the trajectories of the NHMC. In this paper, we show that, as the total number of subjects involved increases, the trajectories of the NHMC, i.e. sample alignments in the PHM, converges to the solution of an ordinary differential equation which, subsequently, characterizes the almost sure limit of the partial likelihood.

• Journal of the Korean Data and Information Science Society
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• 제15권2호
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• pp.347-353
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• 2004

We propose a simple nonparametric estimator of relative risk in the two sample case of the proportional hazards model for complete data. The asymptotic distribution of this estimator is derived using a functional equation. We obtain the asymptotic normality of the proposed estimator and compare with Begun's estimator by confidence interval through simulations.

• International Journal of Reliability and Applications
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• 제10권2호
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• pp.101-107
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• 2009

In the accelerated tests, the importance of correct failure analysis must be strongly emphasized. Understanding the failure mechanisms is requisite for designing and conducting successful accelerated life test. Under this presumption, a rational method must be identified to relate the results of accelerated tests quantitatively to the reliability or failure rates in use conditions, using a scientific acceleration transform. Most widely used models for relating the results of accelerated tests quantitatively to the reliability or failure rates in use conditions are an accelerated failure time model and a proportional hazards model. The purpose of this research is to compare the usability of the accelerated failure time model and proportional hazards model in the accelerated life tests.

• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.379-402
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• 1994

Graphical and numerical methods for checking the assumption of proportional hazards of Cox model for censored survival data are discussed. The strenths and weaknessess of several goodness of fit tests for the propotional hazards for the two-sample problem are evaluated with Monte Carlo simulations, and the tests of Schoenfeld (1980), Andersen (1982), Wei (1984), and Gill and Schumacher (1987) are considered. The goodness of fit methods are illustrated with the survival data of patients who had chronic liver disease and had been treated with the endoscopy injection sclerotheraphy. Two other examples of data known to have nonpropotional hazards are also used in the illustration.

• 응용통계연구
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• 제15권2호
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• pp.233-250
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• 2002

Cox의 비례위험모형(proportional hazards model)은 생존자료(survival data)에 대한 회귀모형으로 경제학 및 의·공학을 비롯한 여러 응용 분야에서 가장 널리 쓰이고 있는 모형 중 하나이다. 그러나, 이 모형은 일반선헝모형에 비해 잔차 분석을 통한 회귀 진단의 연구가 널리 알려져 있지 않아, 국내의 실제 자료 분석에서는 잔차 분석에 대한 활용이 거의 이루어지지 않고 있는 실정이다. 이에 본 논문에서는 그 동안 제안된 여러 잔차들을 비교 분석하고, S-plus 프로그램을 이용한 PBC(primary biliary cirrhosis) 자료분석을 통해 각 잔차들의 의미를 고찰하고자 한다.

• 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.

• 응용통계연구
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• 제20권1호
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• pp.39-52
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• 2007

협심증 치료의 신약에 대한 교차계획 임상시험(crossover clinical trials)에서 신약의 효능을 알아보는 운동테스트(treadmill exercise test) 결과는 중도절단 생존시간(censored survival times)으로 측정된다. 이 논문에서는 교차계획에서 수집된 중도절단 생존자료의 여러 가지 분석법에 대해 설명한다. 중도절단을 감안한 비모수적 방법들과 층화 Cox 비례위험모형 (stratified Cox proportional hazards model)에 근거한 분석법이 제시되었다. 한편, 교차계획의 두 시기에 걸쳐 수집된 생존시간의 차(difference)로부터 구간절단자료(interval censored data)가 생성되며 이에 근거한 분석법으로서 이 논문에서는 구간절단자료에 대한 Cox 비례위험모형 (proportional hazards model)의 가능성을 알아보며, 예제 자료로써 여러 방법들의 결과를 비교해 본다.