• Title, Summary, Keyword: Cox proportional hazard model

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Cox proportional hazard model with L1 penalty

  • Hwang, Chang-Ha;Shim, Joo-Yong
    • Journal of the Korean Data and Information Science Society
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    • v.22 no.3
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    • pp.613-618
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    • 2011
  • The proposed method is based on a penalized log partial likelihood of Cox proportional hazard model with L1-penalty. We use the iteratively reweighted least squares procedure to solve L1 penalized log partial likelihood function of Cox proportional hazard model. It provide the ecient computation including variable selection and leads to the generalized cross validation function for the model selection. Experimental results are then presented to indicate the performance of the proposed procedure.

Diagnostics for the Cox model

  • Xue, Yishu;Schifano, Elizabeth D.
    • 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.

Survival Prognostic Factors of Male Breast Cancer in Southern Iran: a LASSO-Cox Regression Approach

  • Shahraki, Hadi Raeisi;Salehi, Alireza;Zare, Najaf
    • Asian Pacific Journal of Cancer Prevention
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    • v.16 no.15
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    • pp.6773-6777
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    • 2015
  • We used to LASSO-Cox method for determining prognostic factors of male breast cancer survival and showed the superiority of this method compared to Cox proportional hazard model in low sample size setting. In order to identify and estimate exactly the relative hazard of the most important factors effective for the survival duration of male breast cancer, the LASSO-Cox method has been used. Our data includes the information of male breast cancer patients in Fars province, south of Iran, from 1989 to 2008. Cox proportional hazard and LASSO-Cox models were fitted for 20 classified variables. To reduce the impact of missing data, the multiple imputation method was used 20 times through the Markov chain Mont Carlo method and the results were combined with Rubin's rules. In 50 patients, the age at diagnosis was 59.6 (SD=12.8) years with a minimum of 34 and maximum of 84 years and the mean of survival time was 62 months. Three, 5 and 10 year survival were 92%, 77% and 26%, respectively. Using the LASSO-Cox method led to eliminating 8 low effect variables and also decreased the standard error by 2.5 to 7 times. The relative efficiency of LASSO-Cox method compared with the Cox proportional hazard method was calculated as 22.39. The19 years follow of male breast cancer patients show that the age, having a history of alcohol use, nipple discharge, laterality, histological grade and duration of symptoms were the most important variables that have played an effective role in the patient's survival. In such situations, estimating the coefficients by LASSO-Cox method will be more efficient than the Cox's proportional hazard method.

Survival analysis: part II - applied clinical data analysis

  • In, Junyong;Lee, Dong Kyu
    • Korean Journal of Anesthesiology
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    • v.72 no.5
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    • pp.441-457
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    • 2019
  • As a follow-up to a previous article, this review provides several in-depth concepts regarding a survival analysis. Also, several codes for specific survival analysis are listed to enhance the understanding of such an analysis and to provide an applicable survival analysis method. A proportional hazard assumption is an important concept in survival analysis. Validation of this assumption is crucial for survival analysis. For this purpose, a graphical analysis method and a goodnessof-fit test are introduced along with detailed codes and examples. In the case of a violated proportional hazard assumption, the extended models of a Cox regression are required. Simplified concepts of a stratified Cox proportional hazard model and time-dependent Cox regression are also described. The source code for an actual analysis using an available statistical package with a detailed interpretation of the results can enable the realization of survival analysis with personal data. To enhance the statistical power of survival analysis, an evaluation of the basic assumptions and the interaction between variables and time is important. In doing so, survival analysis can provide reliable scientific results with a high level of confidence.

A Study on the Survival Probability and Survival Factors of Small and Medium-sized Enterprises Using Technology Rating Data (기술평가 자료를 이용한 중소기업의 생존율 추정 및 생존요인 분석)

  • Lee, Young-Chan
    • Knowledge Management Research
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    • v.11 no.2
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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.

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Estimation of lapse rate of variable annuities by using Cox proportional hazard model (Cox 비례위험모형을 이용한 변액연금 해지율의 추정)

  • Kim, Yumi;Lee, Hangsuck
    • Journal of the Korean Data and Information Science Society
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    • v.24 no.4
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    • pp.723-736
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    • 2013
  • The importance of lapse rate is highly increasing due to the introduction of Cash Flow Pricing system, non-refund-of-reserve insurance policy, and IFRS (International Financial Reporting System) to the Korean insurance market. Researches on lapse rate have mainly focused on simple data analysis and regression analysis, etc. However, lapse rate can be analyzed by survival analysis and can be well explained in terms of several covariates with Cox proportional hazard model. Guaranteed minimum benefits embedded in variable annuities require more elegant statistical analysis of lapse rate. Hence, this paper analyzes data of policyholders with variable annuities by using Cox proportional hazard model. The key variables of policy holder that influences the lapse rate are payment method, premium, lapse insured to term insured, reserve-GMXB ratio, and age.

Estimation of hazard function and hazard change-point for the rectal cancer data (직장암 데이터에 대한 위험률 함수 추정 및 위험률 변화점 추정)

  • Lee, Sieun;Shim, Byoung Yong;Kim, Jaehee
    • Journal of the Korean Data and Information Science Society
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    • v.26 no.6
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    • pp.1225-1238
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    • 2015
  • In this research, we fit various survival models and conduct tests and estimation for the hazard change-point with the rectal cancer data. By the log-rank tests, at significance level ${\alpha}=0.10$, survival functions are significantly different according to the uniporter of glucose (GLUT1), clinical stage (cstage) and pathologic stage (ypstage). From the Cox proportional hazard model, the most significant covariates are GLUT1 and ypstage. Assuming that the rectal cancer data follows the exponential distribution, we estimate one hazard change-point using Matthews and Farewell (1982), Henderson (1990) and Loader (1991) methods.

Identifying the Factors Affecting the First Traffic Violation Duration by Novice Drivers (초보운전자 생애 첫 교통법규 위반기간에 영향을 미치는 요인)

  • Kang, Gyungmi;Kim, Do-Gyeong
    • International Journal of Highway Engineering
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    • v.15 no.5
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    • pp.203-215
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    • 2013
  • PURPOSES : This study deals with first traffic violations occurred by novice drivers, which may be associated with traffic accidents. The objective of this study is to identify what kinds of drivers' characteristics influence on duration till the first traffic violation. METHODS : For the study, Survival Analysis and Cox proportional hazard model, that are usually used in the medical field, were employed. Survival Analysis was conducted to investigate whether there exist differences in survival duration by each covariate, whereas Cox proportional hazard model was used to identify significant factors that affect survival duration till novice drivers violate traffic regulations for the first time after getting a driver license. RESULTS : The results of Survival Analysis indicate that female, age (less than 21), low-frequency examinee of written exam, and non-crash involved drivers have longer duration till the first violation compared to male, greater than 21 years old, high-frequency examinee of written exam, and crash involved drivers, respectively. For the Cox proportional hazard model, license class 1 acquisitor was found to increase the survival duration till the first traffic violation was made, while male, age of 21-24, age of 25-34, age of 45-54, and crash involved drivers were more likely to reduce the survival duration. CONCLUSIONS : Absolutely, traffic violation is closely related to traffic accidents and all of the drivers should keep the traffic regulations to enhance highway safety. The results of this study might provide some insights to construct safe road environments by controlling the factors that reduce the traffic violation duration of novice drivers.

Survival analysis of bank loan repayment rate for customers of Hawassa commercial bank of Ethiopaia

  • Kitabo, Cheru Atsmegiorgis;Kim, Jong Tae
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.6
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    • pp.1591-1598
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    • 2014
  • The reviews of the balance sheet of commercial banks showed that loan item constitutes the largest portion of bank's assets. Although the sector has highest rate of profit, it possesses the greatest risk. Identifying factors that can contribute in lifting-up the loan repayment rate of customers of Hawassa district commercial bank is the major goal of this study. A sample of 183 customers who took loan from October, 2005 to April, 2012 was taken from the bank record. Kaplan-Meier estimation method and univariate Cox proportional hazard model were applied to identify factors affecting bank loan repayment rate. The result from Kaplan-Meier survival estimation revealed that the loan repayment rate is significantly related with loan type, and previous loan experience, educational level and mode of repayment. The log-rank test indicates that the survival probability of loan customers is not statistically different in repaying the loan among groups classified by sex. Moreover, the univariate Cox proportional hazard model result portrayed that educational level, having previous loan experience, mode of repayment, collateral type and purpose of loan are significantly related with loan repayment rate of customers commercial bank. Hence, banks should design loan strategies giving special emphasis on the significant factors while they are giving loans to their customers.

Bayesian Variable Selection in the Proportional Hazard Model

  • Lee, Kyeong-Eun
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.3
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    • pp.605-616
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    • 2004
  • In this paper we consider the proportional hazard models for survival analysis in the microarray data. For a given vector of response values and gene expressions (covariates), we address the issue of how to reduce the dimension by selecting the significant genes. In our approach, rather than fixing the number of selected genes, we will assign a prior distribution to this number. To implement our methodology, we use a Markov Chain Monte Carlo (MCMC) method.

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