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Tied Survival Times In Survival Analysis

Year 2017, Volume 5, Issue 1, 2017, 85 - 102, 30.06.2017
https://doi.org/10.17093/alphanumeric.323833

Abstract

Survival analysis is generally defined as a set of methods for analyzing data where the outcome variable is the time until the occurrence of an event of interest. One of the methods commonly used in the survival analysis is Cox regresion model which is used to determine the factors that impact on survival times. Cox regression model has assumptions. One of them is proportional hazards assumption and the another one is there is no tied data between event times. However, in real applications, tied event times are commonly observed and Cox’s partial likelihood function needs to be modified to handle ties. It is well known methods that the Exact method, Breslow method, Efron method and Discrete method for handling tied event times. Firstly, the methods are analysed during the study, Breslow, Efron and Exact methods, which is applied on a stomach canser data set (there is tied data between event times) It was decided that Cox regression with Exact Method is the best model. Than this methods is applied Acute Myocardial Infarction data set which has no tied data between event times and it is found the same resuts at all methods.

References

  • Allison, P.D. (2010). Survival Analysis, The Reviewer’s Guide to Quantitative Methods in the Social Sciences, New York, 413-425. Arı, A., Önder, H. (2013). Farklı Veri Yapılarında Kullanılabilecek Regresyon Yöntemleri, Anadolu Tarım Bilim. Derg. , 28(3):168-174. Ata, N. (2005). Yaşam Çözümlemesinde Orantısız Hazard Modeli, Yüksek Lisans Tezi, Hacettepe Üniversitesi Fen Bilimleri Enstitüsü, Ankara. Breslow, N. (1974). Covariance Analysis of Censored Survival Data, Biometrics, 30, 89-99. Chalita, L.V. A.S., Colosimo, E.A.,Demetrio C.G.B. (2002). Reliablility and Survival Analysis, Likelihood Approximation and Discrete Models for Tied Survival Data, Commun.Statist.-Theory Meth., 31(7),1215-1229. Collett, D. (1994). Modelling Survival Data in Medical Research, Chapman &Hall. Cox, D.R. (1972). Regression models and life tables, Journal of Royal Statistical Society, Series B, 34, 187-202. DeLong, D. M., Guirguis, G. H., and So, Y. C. (1994). Efficient Computation of Subset Selection Probabilities with Application to Cox Regression, Biometrika, 81, 607–611. Efron, B. (1977). The Efficiency of Cox’s Likelihood Function for Censored Survival Data, Journal of the American Statistical Association, 72,557-565. Eroğlu A., Altınok M., Özgen K., Sertkaya D. (1997). A Multivariate Analysis of Clinical and Pathological Variables in Survival After Resection of Gastric Cancer, Türkiye Klinikleri Medical Research, 15, 1, 15-20. Johnson, R.E., Johnson, N. (1980). Survival models and data analysis, Wiley&Sons, New York. Kalbfleisch, J.D., Prentice, R.L. (1973). Marginal likelihoods based on Cox’s regression and life model, Biometrica, 60, 267-278. Kalbfleisch, J.D., Prentice, R.L. (2002). The Statistical Analysis of Failure Time Data, Second Edition, Wiley&Sons, New York. Kleinbaum, D.G. (1996). Survival Analysis: A Self-Learning Text, First Edition, Springer. Karasoy, D., Tuncer, N., (2015), Outliers in Survival Analysis, Alphanumeric Journal, 3, 2, 139-152. Lee, E.T., Wang, J.W. (2003). Statistical Methods for Survival Data Analysis, Third Edition, Wiley&Sons. Picciotto, I.H., Rockhill, B. (1997). Validity and Efficiency of Approximation Methods for Tied Survival Times in Cox Regression.Department of Epidemiology, Biometrics, 53, 1151-1156. Sertkaya, D., Ata, N., Sözer, M.T. (2005). Yaşam çözümlemesinde zamana bağlı açıklayıcı değişkenli Cox regresyon modeli, Ankara Üniversitesi Tıp Fakültesi Mecmuası, 58:153-158. Schoenfeld, D. (1982). Partial residuals for the proportional hazards regression model, Biometrika, 69, 239-241. Scheike, T.H., Sun, Y. (2007). Maximum likelihood estimation for tied survival data under Cox regression model via EM-algorithm, Lifetime Data Anal., 13:399–420. Therneau, T. M., Grambsch, P. M. (2000). Modeling Survival Data: Extending Cox Model, Springer, New York. Xin, X. (2011). A Study of Ties and Time-Varying Covariates in Cox Proportional Hazard Model, Master of Science, The Faculty of Graduate Studies of The University of Guelph. Yay,M., Çoker, E., Uysal, Ö. (2007). Yaşam Analizinde Cox Regresyon Modeli ve Artıkların incelenmesi, Cerrahpaşa Tıp Dergisi, 38: 139 – 145. Zhang, M.J. (1997). Grouped Failure Times Tied Failure Times-Two Contributions To The Encyclopedia of Biostatistics, Technical Report 24. http://www.medicine.mcgill.ca/epidemiology/hanley/c681/cox/TiesCoxModelR.txt (Aralık, 2014). Cox Proportional Hazards Regression Models, http://www4.stat.ncsu.edu/~dzhang2/st745/chap7.pdf (Aralık, 2014). Stefanescu, C., Mehrotra,D., Cox model versus generalized logrank test for time to event data with ties, http://faculty.london.edu/cstefanescu/glr.pdf ( Ekim, 2014). Semi-Parametric Duration Models: The Cox Model https://files.nyu.edu/mrg217/public/cox.pdf (Aralık, 2014).

Yaşam Çözümlemesinde Eş Zamanlı Yaşam Süreleri

Year 2017, Volume 5, Issue 1, 2017, 85 - 102, 30.06.2017
https://doi.org/10.17093/alphanumeric.323833

Abstract

Yaşam çözümlemesi, tanımlanan herhangi bir olayın belirli bir başlangıç noktasından, ortaya çıkmasına kadar geçen sürenin incelenmesinde kullanılan istatistiksel yöntemler topluluğudur. Yaşam çözümlemesinde sıkça kullanılan yöntemlerden biri yaşam süresi üzerinde etkili olan faktörlerin belirlenmesinde kullanılan Cox regresyon modelidir Cox regresyon modelinin orantılı tehlikeler varsayımına ek olarak bir diğer varsayımı ise eş zaman durumunun meydana gelmemiş olmasıdır. Ancak çalışmalarda genellikle eş zamanlı olarak meydana gelen başarısızlıklara rastlanmaktadır ve bu durum özel çözüm gerektirmektedir. Kesin yöntem, Breslow yöntemi, Efron yöntemi ve Kesikli yöntem olarak bilinen yöntemler bu özel çözümlemelerdir. Çalışma boyunca incelenen yöntemlerden Breslow yöntemi, Efron yöntemi ve Kesin yöntem, eş zamanlı gözlemlerin olduğu duruma örnek olarak mide kanseri verilerine uygulanmış Kesin yöntem ile Cox regresyon modelinin en iyi model olduğuna karar verilmiştir. Daha sonra ise eş zamanlı gözlemlerin olmadığı Akut Miyokard İnfarktüsü verilerine uygulanmış ve sonuçların aynı olduğu gözlenmiştir.

References

  • Allison, P.D. (2010). Survival Analysis, The Reviewer’s Guide to Quantitative Methods in the Social Sciences, New York, 413-425. Arı, A., Önder, H. (2013). Farklı Veri Yapılarında Kullanılabilecek Regresyon Yöntemleri, Anadolu Tarım Bilim. Derg. , 28(3):168-174. Ata, N. (2005). Yaşam Çözümlemesinde Orantısız Hazard Modeli, Yüksek Lisans Tezi, Hacettepe Üniversitesi Fen Bilimleri Enstitüsü, Ankara. Breslow, N. (1974). Covariance Analysis of Censored Survival Data, Biometrics, 30, 89-99. Chalita, L.V. A.S., Colosimo, E.A.,Demetrio C.G.B. (2002). Reliablility and Survival Analysis, Likelihood Approximation and Discrete Models for Tied Survival Data, Commun.Statist.-Theory Meth., 31(7),1215-1229. Collett, D. (1994). Modelling Survival Data in Medical Research, Chapman &Hall. Cox, D.R. (1972). Regression models and life tables, Journal of Royal Statistical Society, Series B, 34, 187-202. DeLong, D. M., Guirguis, G. H., and So, Y. C. (1994). Efficient Computation of Subset Selection Probabilities with Application to Cox Regression, Biometrika, 81, 607–611. Efron, B. (1977). The Efficiency of Cox’s Likelihood Function for Censored Survival Data, Journal of the American Statistical Association, 72,557-565. Eroğlu A., Altınok M., Özgen K., Sertkaya D. (1997). A Multivariate Analysis of Clinical and Pathological Variables in Survival After Resection of Gastric Cancer, Türkiye Klinikleri Medical Research, 15, 1, 15-20. Johnson, R.E., Johnson, N. (1980). Survival models and data analysis, Wiley&Sons, New York. Kalbfleisch, J.D., Prentice, R.L. (1973). Marginal likelihoods based on Cox’s regression and life model, Biometrica, 60, 267-278. Kalbfleisch, J.D., Prentice, R.L. (2002). The Statistical Analysis of Failure Time Data, Second Edition, Wiley&Sons, New York. Kleinbaum, D.G. (1996). Survival Analysis: A Self-Learning Text, First Edition, Springer. Karasoy, D., Tuncer, N., (2015), Outliers in Survival Analysis, Alphanumeric Journal, 3, 2, 139-152. Lee, E.T., Wang, J.W. (2003). Statistical Methods for Survival Data Analysis, Third Edition, Wiley&Sons. Picciotto, I.H., Rockhill, B. (1997). Validity and Efficiency of Approximation Methods for Tied Survival Times in Cox Regression.Department of Epidemiology, Biometrics, 53, 1151-1156. Sertkaya, D., Ata, N., Sözer, M.T. (2005). Yaşam çözümlemesinde zamana bağlı açıklayıcı değişkenli Cox regresyon modeli, Ankara Üniversitesi Tıp Fakültesi Mecmuası, 58:153-158. Schoenfeld, D. (1982). Partial residuals for the proportional hazards regression model, Biometrika, 69, 239-241. Scheike, T.H., Sun, Y. (2007). Maximum likelihood estimation for tied survival data under Cox regression model via EM-algorithm, Lifetime Data Anal., 13:399–420. Therneau, T. M., Grambsch, P. M. (2000). Modeling Survival Data: Extending Cox Model, Springer, New York. Xin, X. (2011). A Study of Ties and Time-Varying Covariates in Cox Proportional Hazard Model, Master of Science, The Faculty of Graduate Studies of The University of Guelph. Yay,M., Çoker, E., Uysal, Ö. (2007). Yaşam Analizinde Cox Regresyon Modeli ve Artıkların incelenmesi, Cerrahpaşa Tıp Dergisi, 38: 139 – 145. Zhang, M.J. (1997). Grouped Failure Times Tied Failure Times-Two Contributions To The Encyclopedia of Biostatistics, Technical Report 24. http://www.medicine.mcgill.ca/epidemiology/hanley/c681/cox/TiesCoxModelR.txt (Aralık, 2014). Cox Proportional Hazards Regression Models, http://www4.stat.ncsu.edu/~dzhang2/st745/chap7.pdf (Aralık, 2014). Stefanescu, C., Mehrotra,D., Cox model versus generalized logrank test for time to event data with ties, http://faculty.london.edu/cstefanescu/glr.pdf ( Ekim, 2014). Semi-Parametric Duration Models: The Cox Model https://files.nyu.edu/mrg217/public/cox.pdf (Aralık, 2014).
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Details

Journal Section Articles
Authors

Durdu Karasoy This is me

Sena Keskin Kaplan This is me

Publication Date June 30, 2017
Submission Date June 28, 2017
Published in Issue Year 2017 Volume 5, Issue 1, 2017

Cite

APA Karasoy, D., & Keskin Kaplan, S. (2017). Tied Survival Times In Survival Analysis. Alphanumeric Journal, 5(1), 85-102. https://doi.org/10.17093/alphanumeric.323833

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