• 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.

• 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.

• Journal of the Korean Statistical Society
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• 제36권1호
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• pp.129-148
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• 2007

Frailty estimates from the proportional hazards frailty model often lead us to conjecture the heterogeneity in frailty such that the variance of the frailty varies over different covariate groups (e.g. male group versus female group). For such systematic heterogeneity in frailty, we consider a regression model for the variance components in the proportional hazards frailty model, denoted by the MLFM. However, in many cases, the observed data do not show any statistically significant preference between the homogeneous frailty model and the heterogeneous frailty model. In this paper, we propose a Bayesian model averaging procedure with the reversible jump Markov chain Monte Carlo which selects the appropriate model automatically. The resulting regression coefficient estimate ignores the model uncertainty from the frailty distribution in view of Bayesian model averaging (Hoeting et al., 1999). Finally, the proposed model and the estimation procedure are illustrated through the analysis of the kidney infection data in McGilchrist and Aisbett (1991) and a simulation study is implemented.

• 대한간호학회지
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• 제49권5호
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• pp.575-585
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• 2019

Purpose: The purpose of this study was to develop predictive models for pressure ulcer incidence using electronic health record (EHR) data and to compare their predictive validity performance indicators with that of the Braden Scale used in the study hospital. Methods: A retrospective case-control study was conducted in a tertiary teaching hospital in Korea. Data of 202 pressure ulcer patients and 14,705 non-pressure ulcer patients admitted between January 2015 and May 2016 were extracted from the EHRs. Three predictive models for pressure ulcer incidence were developed using logistic regression, Cox proportional hazards regression, and decision tree modeling. The predictive validity performance indicators of the three models were compared with those of the Braden Scale. Results: The logistic regression model was most efficient with a high area under the receiver operating characteristics curve (AUC) estimate of 0.97, followed by the decision tree model (AUC 0.95), Cox proportional hazards regression model (AUC 0.95), and the Braden Scale (AUC 0.82). Decreased mobility was the most significant factor in the logistic regression and Cox proportional hazards models, and the endotracheal tube was the most important factor in the decision tree model. Conclusion: Predictive validity performance indicators of the Braden Scale were lower than those of the logistic regression, Cox proportional hazards regression, and decision tree models. The models developed in this study can be used to develop a clinical decision support system that automatically assesses risk for pressure ulcers to aid nurses.

• Journal of the Korean Statistical Society
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• 제26권1호
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• pp.117-130
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• 1997

We study the asymptotic behavior of the maximum partial likelihood estimator in the Cox proportional hazards model in the presence of nuisance parameters when the entry of patients is staggered. When entry of patients is simultaneous and there is only one regression parameter in the Cox model, the efficient score process of the partial likelihood is martingale and converges weakly to a time-chnaged Brownian motion. Our problem is to get a similar result in the presence of nuisance parameters when entry of patient is staggered.

• Journal of the Korean Data and Information Science Society
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• 제5권1호
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• pp.59-66
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• 1994

Heller and Simonoff(1990) compared several methods of estimating the regression coefficient in a modified proportional hazards model, when the response variable is subject to censoring. We give another method of estimating the parameters in the model which also allows the dependent variable to be censored and the error distribution to be unspecified. The proposed method differs from that of Miller(1976) and that of Buckely and James(1979). We also obtain the variance estimator of the coefficient estimator and compare that with the Buckely-James Variance estimator studied by Hillis(1993).

• 한국학교ㆍ지역보건교육학회지
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• 제23권4호
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• pp.81-93
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• 2022

Objectives: The purpose of this study was to develop a model for comprehensively evaluating the risk of sarcopenia in Korean adults and to generate the sarcopenia risk scorecard model based on the results. Methods: The participants of the study were 7,118 adults without sarcopenia in the first basic survey, and a longitudinal analysis was conducted using data from the 1st to 8th survey (2006-2020) of the Korean Longitudinal Study of Aging (KLoSA). The data were analyzed using Rao-Scott chi-square test and weighted Cox proportional hazards regression of complex sampling design. The sarcopenia risk scorecard model was developed by Cox proportional hazards regression using points to double the odds (PDO) method. Results: The findings show that the risk factors for sarcopenia in Korean adults were gender, age, marital status, socioeconomic status, body mass index (BMI), regular exercise, diabetes and arthritis diagnosis. In the scorecard results, the case of exposure to the highest risk level was 100 points. The highest score range were given in the order of age over 65, low BMI, and low socioeconomic status. Conclusions: The significance of this study is that the causal relationship between various factors and the occurrence of sarcopenia in Korean adults was identified. Also, the model developed in this study is expected to be useful in detecting participants with risk of sarcopenia in the community early and preventing and managing sarcopenia through appropriate health education.

• 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).

• 한국수자원학회논문집
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• 제42권6호
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• pp.445-455
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• 2009

본 논문에서는 연구대상 지역의 150 mm 주철 상수관로의 첫 번째 파손으로부터 일곱 번째 파손사건에 대한 비례 위험모형을 구축하였다. 모형의 구축과정에서 공변수의 위험률에 대한 비례위험 가정을 검사하여 이를 위배할 경우 시간종속형 공변수로 모형화하였다. 그 결과 첫 번째 파손에 대해서는 관로의 제원 및 연결 방식과 급수인구가, 그리고 두 번째 파손 사건에 대해서는 급수인구의 영향이 시간에 따라 변하는 것으로 나타났다. 각 생존시간군의 기저위험률에 대한 분석으로부터 첫 번째와 두 번째 파손에 대해서는 대체적으로 파손 위험률이 시간에 따라 계속해서 증가하는 것으로 나타났으며, 세 번째 파손으로부터 일곱번째 파손사건에 대해서는 파손 위험률이 감소하다가 시간이 지나면 증가하는 욕조 모양으로 추정되었다. 또한 시간과 파손횟수에 따른 기저위험률의 변화 및 각 생존시간군의 중간생존시간으로부터 연구대상 상수관로들은 파손횟수가 증가할수록 전반적인 관로의 상태가 악화되는 것으로 판단된다. 추정된 공변수의 회귀계수와 위험비율을 이용하여 관로파손에 미치는 인자와 그 시간적 영향에 대하여 분석하였으며, 구축된 모형의 이탈잔차를 이용하여 모형의 적합도를 검증하였다.

• 품질경영학회지
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• 제18권1호
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• pp.9-20
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• 1990

The purpose of this paper is to propose the modified semiparametric estimators for survival function in the Cox's regression model with randomly censored data based on Tsiatis and Breslow estimators, and present their asymptotic variances estimates. The proposed estimators are compared to Tsiatis, Breslow, and Kaplan-Meier estimators through a small-sample Monte Carlo study. The simulation results show that the proposed estimators are preferred for small sample sizes.