• Journal of the Korean Data and Information Science Society
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• v.22 no.4
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• pp.795-801
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• 2011

In machine learning and statistics it is often the case that some variables are not important, while some variables are more important than others. We propose a novel algorithm for selecting such relevant variables in the kernel Cox regression. We employ the weighted version of ANOVA decomposition kernels to choose optimal subset of relevant variables in the kernel Cox regression. Experimental results are then presented which indicate the performance of the proposed method.

• The Korean Journal of Applied Statistics
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• v.7 no.2
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• pp.53-77
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• 1994

In a certain stochastic process, Cox's regression model is used to analyze multistate survival data. From this model, the regression parameter vectors, survival functions, and the probability of being in response function are estimated based on multistate Cox's partial likelihood and nonparametric likelihood methods. The asymptotic properties of these estimators are described informally through the counting process approach. An example is given to likelihood the results in this paper.

• The Korean Journal of Applied Statistics
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• v.34 no.6
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• pp.957-968
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• 2021

Inverse censoring probability weighting (ICPW) is a popular technique in survival data analysis. In applications of the ICPW technique such as the censored regression, it is crucial to accurately estimate the censoring probability. A simulation study is undertaken in this article to see how censoring probability estimate influences model performance in censored regression using the ICPW scheme. We compare three censoring probability estimators, including Kaplan-Meier (KM) estimator, Cox proportional hazard model estimator, and local KM estimator. For the local KM estimator, we propose to reduce the predictor dimension to avoid the curse of dimensionality and consider two popular dimension reduction tools: principal component analysis and sliced inverse regression. Finally, we found that the Cox proportional hazard model estimator shows the best performance as a censoring probability estimator in both mean and median censored regressions.

• Journal for History of Mathematics
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• v.11 no.2
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• pp.63-76
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• 1998

When teaching the linear regression analysis in the class, the power transformation must be introduced to fit the linear regression model for nonlinear data. Box and Cox (1964) proposed the attractive power transformation technique which is so called Box-Cox transformation. In this paper, an effective algorithm selecting an appropriate value for Box-Cox transformation is developed which is considered to find a value minimizing error sum of squares. When the proposed algorithm is used to find a value for transformation, the number of iterations needs to be considered. Thus, the number of iterations is examined through simulation study. Since SAS is one of most widely used packages and does not provide the procedure that performs iterative Box-Cox transformation, a SAS program automatically choosing the value for transformation is developed. Hence, the students could learn how the Box-Cox transformation works, moreover, researchers can use this for analysis of data.

• Journal of the Korean Data and Information Science Society
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• v.4
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• pp.1-11
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• 1993

The Cox's regression model is frequently used for covariate effects in survival data analysis, But, much of the statistical work has focused on asymptotic behavior so the small sample evaluation has been neglected. In this paper, we compare the small or moderate sample performances of the survival function estimators for the Cox's regression model using bootstrap method. The smoothed PL type estimator and the Link estimator are slightly better than corresponding the PL type estimator and the Nelson type estimator in the sense of the achieved error rates.

• Communications for Statistical Applications and Methods
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• v.11 no.2
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• pp.227-233
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• 2004

This paper presents our work on constructing a model that is intended to predict the probability of attrition at specified points in time among customers of an insurance company. There are some difficulties in building a data-based model because a data set may contain possibly censored observations. In an effort to avoid such kind of problem, we performed logistic regression over specified time intervals while using explanatory variables to construct the proposed model. Then, we developed a Cox-type regression model for estimating the probability of attrition over a specified period of time using time-dependent explanatory variables subject to changes in value over the course of the observations.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.103-125
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• 2001

The Box-Cox transformation is a well known family of power transformation that brings a set of data into agreement with the normality assumption of the residuals and hence the response variable of a postulated model in regression analysis. This paper proposes a new method for estimating the Box-Cox transformation using maximization of the Sample Entropy statistic which forces the data to get closer to normal as much as possible. A comparative study of the proposed procedure with the maximum likelihood procedure, the procedure via artificial regression estimation, and the recently introduced maximization of the Shapiro-Francia W' statistic procedure is given. In addition, we generate a table for the optimal spacings parameter in computing the Sample Entropy statistic.

• Journal of Korean Academy of Nursing
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• v.49 no.5
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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.

• The Korean Journal of Applied Statistics
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• v.21 no.2
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• pp.327-340
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• 2008

This paper derives joint and conditional Lagrange multiplier tests based on information matrix for testing functional form and/or the presence of autocorrelation in a regression model. Small sample properties of these tests are assessed by Monte Carlo study and comparisons are made with LM tests based on Hessian matrix. The results show that the proposed $LM_E$ tests have the most appropriate finite sample performance.

• 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.