• Proceedings of the Korean Reliability Society Conference
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• 2005.06a
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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.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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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.

• Communications for Statistical Applications and Methods
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• v.21 no.4
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• pp.285-296
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• 2014

The quantile residual life function has been effectively used to interpret results from the analysis of the proportional hazards model for censored survival data; however, the quantile residual life function is not always estimable with currently available semi-parametric regression methods in the presence of heavy censoring. A parametric regression approach may circumvent the difficulty of heavy censoring, but parametric assumptions on a baseline hazard function can cause a potential bias. This article proposes a Bayesian semi-parametric regression approach for inference on an unknown baseline hazard function while adjusting for available covariates. We consider a model-based approach but the proposed method does not suffer from strong parametric assumptions, enjoying a closed-form specification of the parametric regression approach without sacrificing the flexibility of the semi-parametric regression approach. The proposed method is applied to simulated data and heavily censored survival data to estimate various quantile residual lifetimes and adjust for important prognostic factors.

• International Journal of Reliability and Applications
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• v.3 no.4
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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.

• Journal of Korea Water Resources Association
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• v.42 no.6
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• pp.445-455
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• 2009

In this paper proportional hazards models for the first through seventh break of 150 mm cast iron pipes in a case study area are established. During the modeling process the assumption of the proportional hazards for covariates on the hazards is examined to include the time-dependent covariate terms in the models. As a result, the pipe material/joint type and the number of customers are modeled as time-dependent for the first failure, and for the second failure only the number of customers is modeled as time-dependent. From the analysis on the baseline hazard functions the failure hazards are found to be generally increasing for the first and second failure, while the hazards of the third break and beyond showed a form of a bath-tub. Furthermore, the changes in the baseline hazard rates according to the time and number of break reflect that the general condition of the pipes is deteriorating. The factors causing pipe break and their effects are analyzed based on the estimated regression coefficients and their hazard ratios, and the constructed models are verified using the deviance residuals of the models.

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.433-444
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• 1996

In contrast to the multiplicative risk model, the additive risk model specifies that the hazard function with covariates is the sum of, rather than product of, the baseline hazard function and the regression function of covariates. We, in this paper, propose a method for checking the adequacy of the additive risk model based on partial-sum of matingale residuals. Under the assumed model, the asymptotic properties of the proposed test statistic and approximation method to find the critical values of the limiting distribution are studied. Several real examples are illustrated.

• The Korean Journal of Applied Statistics
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• v.31 no.6
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• pp.761-769
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• 2018

Simulations are important for survival analyses that deal with censored data. Cox models are widely used in survival analyses, therefore, we investigate how to generate censored data that can simulate the Cox model. Bender et al. (Statistics in Medicine, 24, 1713-1723, 2005) provided a parametric method for generating survival times, but we need to generate censoring times as well as survival times to simulate the censored data. In addition to the parametric method for generating censored data, a nonparametric method is also proposed and applied to a real data set.

• Journal of Preventive Medicine and Public Health
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• v.30 no.3 s.58
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• pp.630-642
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• 1997

The purpose of this study was to examine the mortality risk associated with cognitive impairment among the rural elderly. The subjective of study was 558 of 'A Study on the Depression and Cognitive Impairment in the Rural Elderly' of Jung Ae Rhee and Hyang Gyun Jung's study(1993). Cognitive impairment and other social and health factors were assessed in 558 elderly rural community residents. For this study, a Korean version of the Mini-Mental State Examination(MMSEK) was used as a global indicator of cognitive functioning. And mortality risk factors for each cognitive impairment subgroup were identified by univariate and multivariate Cox regression analysis. At baseline 22.6% of the sample were mildly impaired and 14.2% were severely impaired. As the age increased, the cognitive function was more impaired. Sexual difference was existed in the cognitive function level. Also the variables such as smoking habits, physical disorders had the significant relationship with cognitive function impairment. Across a 3-year observation period the mortality rate was 8.5% for the cognitively unimpaired, 11.1% for the mildly impaired, and 16.5% for the severly impaired respendents. And the survival probability was .92 for the cognitively unimpaired, .90 for the mildly impaired, and .86 for the severly impaired respondents. Compared to survival curve for the cognitively unimpaired group, each survival curve for the mildly and the severely impaired group was not significantly different. When adjustments models were not made for the effects of other health and social covariates, each hazard ratio of death of mildly and severely impaired persons was not significantly different as compared with the cognitively unimpaired. But, as MMSEK score increased, significantly hazard ratio of death decreased. Employing Cox univariate proportional hazards model, statistically other significant variables were age, monthly income, smoking habits, physical disorders. Also when adjustments were made for the effects of other health and social covariates, there was no difference in hazard ratio of death between those with severe or mild impairment and unimpaired persons. And as MMSEK score increased, significantly hazard ratio of death did not decrease. Employing Cox multivariate proportional hazards model, statistically other significant variables were age, monthly income, physical disorders. Employing Cox multivariate proportional hazards model by sex, at men and women statistically significant variable was only age. For both men and women, also cognitive impairment was not a significant risk factor. Other investigators have found that cognitive impairment is a significant predictor of mortality. But we didn't find that it is a significant predictor of mortality. Even though the conclusions of our study were not related to cognitive impairment and mortality, early detection of impaired cognition and attention to associated health problems could improve the quality of life of these older adults and perhaps extend their survival.