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Cox Proportional Hazards and Proportional Odds Models in Survival Analysis

Year 2013, Volume: 6 Issue: 2, 70 - 78, 01.06.2013

Ayfer Ezgi Yılmaz Durdu Karasoy A. Eroğlu

Abstract

Cox Proportional Hazards and Proportional Odds Models in Survival Analysis Cox proportional hazards model is one of the most common model in survival analysis, in order to investigate the cause and effect relationship between covariates and survival time. In order to use this model, the assumption of proportional hazards has to be satisfied and when this assumption is violated, using this model is improper. In this study, the proportional odds model which is an alternative model to Cox proportional hazards model is proposed to investigate and these two models are proposed to compare. A numerical example which includes a data of stomach cancer patients is done to clarify the models.

Keywords

Cox proportional hazards model Proportional odds model Survival analysis Gastric cance

References

  • Sertkaya D., Ata N., Sözer M.T., 2005, Yaşam Çözümlemesinde Zamana Bağlı Açıklayıcı Değişkenli Cox Regresyon Modeli, Ankara Üniversitesi Tıp Fakültesi Mecmuası, 58 (1), 153-158.
  • Cox D.R., 1972, Regression Models and Life-tables (with discussion), J. R. Statist Soc., B 34 (1), 187-220. Ata N., Sertkaya Karasoy D., Sözer M.T., 2007, Orantılı Tehlikeler Varsayımının İncelenmesinde Kullanılan Yöntemler ve Bir Uygulama, Eskişehir Osmangazi Üniversitesi Müh Mim Fak Dergisi C.XX, 1 (1), 58- 80.
  • McCullagh P., 1973, Regression Models for Ordinal Data, Journal of the Royal Statistical Society, Series B 42 (2), 109-142.
  • Agresti, A., 2002, Logit Models for Multinomial Responses. Categorical Data Analysis, 2nd ed., New Jersy: John Wiley & Sons, s.274-276. http://www.stat.nus.edu.sg/~stachenz/ST5212Notes8.pdf (Erişim Tarihi: 23.04.2013).
  • Bennett S., 1983, Log-Logistic Regression Models for Survival Data, Journal of the Royal Statistical Society, 32 (2), 165-171.
  • Pettitt A.N., 1984, Proportional Odds Models for Survival Data and Estimates Using Ranks, Appl. Statist., 33 (2), 169-174.
  • Leung, T-L., 1999, Proportional Odds Model for Survival Data. Master of Philosophy, University of Hong Kong , Hong Kong.
  • Hunter D.R., Lange K., 2002, Computing Estimates in the Proportional Odds Model. Annals of the Institute of Statistical Mathematics, 54 (1), 155-168.
  • Kirmani S.N.A.U., Gupta R.C., 2001, On the Proportional Odds Model in Survival Analysis, Ann. Inst. Statist. Math., 53 (2), 203-216.
  • Bickel P.J., 1986, Efficient Testing in a Class of Transformation Model, Papers of Semiparametric Models at the ISI Centenary Session, Amsterdam, 63-81.
  • Dabrowska D.M. and Doksum K.A., 1988, Partial Likelihood in Transformation Models with Censored Data, Scandinavian Journal of Statistics, 15 (1), 1-23.
  • Cheng S.C., Wei L.J. and Ying Z., 1995, Analysis of Transformation Models with Censored Data, Biometrika, 82 (1), 835-845.
  • Murphy S.A., Rossini A.J. and Van Der Vaart A.W., 1997, Maximum Likelihood Estimation in the Proportional Odds Model, Journal of the American Statistical Association, 92 (439), 968-976.
  • Collett D., 1994, Strategy of Model, Modelling Survival Data in Medical Research, Chatfield C., Zidek J.V. (eds),1st ed., USA: Chapman&Hall, s. 79.
  • Eroğlu A., Altınok M., Özgen K. And 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.
  • Schoenfeld, D., 1892, Partial Residuals for the Proportional Hazards Regression Model, Biometrika Trust, 69 (1), 239-241. http://cran.r-project.org/web/packages/timereg/timereg.pdf (Erişim Tarihi: 26.04.2013)

Yaşam Çözümlemesinde Cox Orantılı Tehlikeler ve Orantılı Odds Modelleri

Year 2013, Volume: 6 Issue: 2, 70 - 78, 01.06.2013

Ayfer Ezgi Yılmaz Durdu Karasoy A. Eroğlu

Abstract

 Yaşam çözümlemesinde açıklayıcı değişkenler ile yaşam
süresi arasındaki neden-sonuç ilişkisi araştırılırken en yaygın kullanılan
model Cox orantılı tehlikeler modelidir. Bu modelin uygulanabilmesi için
orantılı tehlikeler varsayımının sağlanması gerekmektedir. Varsayım
sağlanmadığında bu modeli kullanmak doğru bir yaklaşım değildir. Bu çalışmada,
Cox orantılı tehlikeler modeline alternatif bir model olan orantılı odds
modelini incelemek ve bu iki modeli karşılaştırmak amaçlanmıştır.Mide kanseri
hastalarına ait verileri içeren sayısal bir örnek bu modelleri açıklamak üzere
kullanılmıştır.

 

Keywords

Cox orantılı tehlikeler modeli Orantılı odds modeli Yaşam çözümlemesi; Mide kanseri

References

  • Sertkaya D., Ata N., Sözer M.T., 2005, Yaşam Çözümlemesinde Zamana Bağlı Açıklayıcı Değişkenli Cox Regresyon Modeli, Ankara Üniversitesi Tıp Fakültesi Mecmuası, 58 (1), 153-158.
  • Cox D.R., 1972, Regression Models and Life-tables (with discussion), J. R. Statist Soc., B 34 (1), 187-220. Ata N., Sertkaya Karasoy D., Sözer M.T., 2007, Orantılı Tehlikeler Varsayımının İncelenmesinde Kullanılan Yöntemler ve Bir Uygulama, Eskişehir Osmangazi Üniversitesi Müh Mim Fak Dergisi C.XX, 1 (1), 58- 80.
  • McCullagh P., 1973, Regression Models for Ordinal Data, Journal of the Royal Statistical Society, Series B 42 (2), 109-142.
  • Agresti, A., 2002, Logit Models for Multinomial Responses. Categorical Data Analysis, 2nd ed., New Jersy: John Wiley & Sons, s.274-276. http://www.stat.nus.edu.sg/~stachenz/ST5212Notes8.pdf (Erişim Tarihi: 23.04.2013).
  • Bennett S., 1983, Log-Logistic Regression Models for Survival Data, Journal of the Royal Statistical Society, 32 (2), 165-171.
  • Pettitt A.N., 1984, Proportional Odds Models for Survival Data and Estimates Using Ranks, Appl. Statist., 33 (2), 169-174.
  • Leung, T-L., 1999, Proportional Odds Model for Survival Data. Master of Philosophy, University of Hong Kong , Hong Kong.
  • Hunter D.R., Lange K., 2002, Computing Estimates in the Proportional Odds Model. Annals of the Institute of Statistical Mathematics, 54 (1), 155-168.
  • Kirmani S.N.A.U., Gupta R.C., 2001, On the Proportional Odds Model in Survival Analysis, Ann. Inst. Statist. Math., 53 (2), 203-216.
  • Bickel P.J., 1986, Efficient Testing in a Class of Transformation Model, Papers of Semiparametric Models at the ISI Centenary Session, Amsterdam, 63-81.
  • Dabrowska D.M. and Doksum K.A., 1988, Partial Likelihood in Transformation Models with Censored Data, Scandinavian Journal of Statistics, 15 (1), 1-23.
  • Cheng S.C., Wei L.J. and Ying Z., 1995, Analysis of Transformation Models with Censored Data, Biometrika, 82 (1), 835-845.
  • Murphy S.A., Rossini A.J. and Van Der Vaart A.W., 1997, Maximum Likelihood Estimation in the Proportional Odds Model, Journal of the American Statistical Association, 92 (439), 968-976.
  • Collett D., 1994, Strategy of Model, Modelling Survival Data in Medical Research, Chatfield C., Zidek J.V. (eds),1st ed., USA: Chapman&Hall, s. 79.
  • Eroğlu A., Altınok M., Özgen K. And 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.
  • Schoenfeld, D., 1892, Partial Residuals for the Proportional Hazards Regression Model, Biometrika Trust, 69 (1), 239-241. http://cran.r-project.org/web/packages/timereg/timereg.pdf (Erişim Tarihi: 26.04.2013)
There are 16 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Ayfer Ezgi Yılmaz

Durdu Karasoy

A. Eroğlu This is me

Publication Date June 1, 2013
Published in Issue Year 2013 Volume: 6 Issue: 2

Cite

IEEE A. E. Yılmaz, D. Karasoy, and A. Eroğlu, “Yaşam Çözümlemesinde Cox Orantılı Tehlikeler ve Orantılı Odds Modelleri”, JSSA, vol. 6, no. 2, pp. 70–78, 2013.