• 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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• 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.

• 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.

• 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.

• 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.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2005년도 학술발표대회 논문집
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• pp.265-269
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• 2005

Cox's proportional hazards model (PHM) has been widely applied in the analysis of lifetime data, and it can be characterized by the baseline hazard function and covariates influencing systems' lifetime, where the covariates describe operating environments (e.g. temperature, pressure, humidity). In this article, we consider the constant baseline hazard function and a discrete random variable of a covariate. The estimation procedure is developed in a parametric framework when there are not only complete data but also incomplete one. The Expectation-Maximization (EM) algorithm is employed to handle the incomplete data problem. Simulation results are presented to illustrate the accuracy and some properties of the estimation results.

• International Journal of Reliability and Applications
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• 제3권4호
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• pp.185-198
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• 2002

In the traditional life testing model, it is assumed that a certain number of identical items are tested under identical condition. This is due to statistical rather than practical considerations. The proportional hazards model can be used to develop a realistic approach to determine the performance of an item. That is also capable of modeling the failure rates of accelerated life testing when the covariates are applied stresses. The proportional hazards model is typically applied for a group of items to assess the importance of factors that may influence the reliability of an item. In this paper we considered the interarrival times of an item rather than the time to first failure for grouped items and provided the availability estimation for the determination of maintenance policy and overhaul time. In order to demonstrate the proposed approach, an example is presented.

• Communications for Statistical Applications and Methods
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• 제8권1호
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• pp.127-135
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• 2001

In this paper, we consider a simple method for testing the assumption of independent censoring on the basis of a Cox proportional hazards regression model with a time-dependent covariate. This method involves a two-stage sampling in which a random subset of censored observations is selected and followed-up until their true survival times are observed. Lee and Wolfe(1998) proposed an adjusted estimate of the survivor function for the dependent censoring under a proportional hazards alternative. This paper extends their result to obtain a bootstrap confidence interval for the adjusted survivor function under the dependent censoring. The proposed procedure is illustrated with an example of a clinical trial for lung cancer analysed in Lee and Wolfe(1998).

• Communications for Statistical Applications and Methods
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• 제4권2호
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• pp.435-444
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• 1997

The objective of this study is to investigate the problem of goodness of fit testing based on nonparametric function estimation techniques for the random censorship model. The small and large sample properties of the proposed test, $E_{mn}$, were investigated and it is shown that under the proportional hazard model $E_{mn}$ has higher power compared to the powers of the Kolmogorov -Smirnov, Kuiper, Cramer-von Mises, and analogue of the Cramer-von Mises type test statistic.

• Journal of the Korean Data and Information Science Society
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• 제28권2호
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• pp.349-359
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• 2017

본 논문에서는 미국 국립암연구소의 SEER 프로그램에서 제공하는 우측 대장암 3기 자료에 Cox 비례위험모형을 적합하여 생존분석을 하였다. 우측 대장암 3기 환자의 사망률에 유의한 영향을 미치는 공변량들을 파악하고, 관심있는 공변량들을 가진 환자의 생존율을 추정하였다. Schoenfeld 잔차를 기반한 검정과 Schoenfeld 잔차 도표, $log[-log\{{\hat{S}}(t)\}]$ 도표를 이용하여 분석에 사용된 공변량들이 비례위험 가정을 만족함을 확인하였다. 적합된 Cox 비례위험모형의 타당성을 검증하기 위해 10-fold 교차 검증을 이용하여 calibration 도표와 시간에 의존하는 ROC 곡선 아래 면적을 계산하였다. 이를 통해 적합된 Cox 비례위험모형의 타당성을 확인하였다.