Yaşam Çözümlemesinde Hızlandırılmış Başarısızlık Süresi Modelleri ve Bir Uygulama

Yaşam verileri için en yaygın kullanılan regresyon modeli Cox regresyon modelidir. Cox regresyon modelinin önemli bir varsayımı, tehlike hızlarının zaman boyunca orantılı olmasıdır. Hızlandırılmış başarısızlık süresi modeli, tehlikeler orantılı olmadığında yaşam verilerinin çözümlenmesi için alternatif bir yöntemdir. Hızlandırılmış başarısızlık süresi modelleri, belirli durumlar altında Cox modelden daha etkili parametre tahminleri sağlar. Bu çalışmada, hızlandırılmış başarısızlık süresi modelleri tanıtıldı ve mide kanseri hastalarına ait veriler kullanılarak bu modeller örneklendi ve sonuçlar tartışıldı.

Accelerated Failure Time Models in Survival Analysis and an Aplication

The Cox regression model is the most commonly used regression model for survival data. The Cox regression model has an important assumption that hazard rates are proportional over time. The accelerated failure time model is an alternative method for the analysis of survival data when hazards are not proportional. The accelerated failure time models should lead to more efficient parameter estimates than Cox model under certain circumferences. In this study, The accelerated failure time models are described. The data of stomach cancer patients is used to illustrate these models and the results are discussed.

___

  • Aalen, O.O. 1994. Effects of Frailty in Survival
  • Analysis. Statistical Methods in Medical Statistics, 3, 227-2
  • Cai, T., Huang, J., Tian, L. 2009. Regularized
  • Estimation for the Accelerated Failure Time Model. Biometrics, 65, 394-404. Collett, D. 2003. Modelling Survival Data in Medical
  • Research, Chapman and Hall, New York, 347 pp. Cox, D.R., Snell, E.J. 1968. A General Definition of
  • Residuals with Discussion. Journal of the Royal Statistical Society, Series B, 30, 248-275. Cox, D.R. 1972. Regression Models and Life-Tables.
  • Journal of the Royal Statistical Society, Series B, 34(2), 187-220. Cox, D.R., Oakes, D. 1984. Analysis of Survival Data.
  • Chapman and Hall, London, 193 pp. Hougaard, P., Myglegaard, P., Borch-Johnsen, K. 1994.
  • Heterogeneity Models of Disease Susceptibility, with Application to Diabetic Nephropathy. Biometrics, 50, 1178-1188.
  • Hougaard, P. 1995. Frailty Models for Survival Data.
  • Lifetime Data Analysis, 1, 255–273. Huang, J., Ma, S., Xie, H. 2006. Regularized Estimation in the Accelerated Failure Time Model with High
  • Dimensional Covariates. Biometrics, 62, 813-820. Kaplan, E., Meier, P. 1958. Nonparametric Estimation from Incomplete Observations. Journal of American
  • Statistical Association, 53, 457-481. Kay, R., Kinnersley, N. 2002. On the Use of the Accelerated Failure Time Model as an Alternative to the Proportional Hazards Model in the Ttreatment of
  • Time to Event Data: A Case Study in Influenza. Drug Information Journal, 36, 571-579. Keiding, N., Andersen, P.K., Klein, J.P. 1997. The Role of Frailty Models and Accelerated Failure Time
  • Models in Describing Heterogeneity Due to Omitted Covariates. Statistics in Medicine, 16, 215-224. Klein, J.P., Moeschberger, M.L. 1997. Survival
  • Analysis: Techniques for Censored and Truncated Data. Springer-Verlag, New York, 502 pp. Klembaum, D.G. 1996. Survival Analysis: A Self
  • Learning Text. Springer, New York, 324 pp. Lawless, J.F. 1982. Statistical Models and Methods for
  • Lifetime Data Analysis, Wiley and Sons, New York, 580 pp. Lee, E.T., Wang, J.W. 2003. Statistical Methods for
  • Survival Data Analysis, Wiley and Sons, New York, 513 pp. Oakes, D. 1977. The Asymptotic Information in
  • Censored Survival Data. Biometrika, 64, 441-448. Orbe, J., Ferreira, E., Nunez-Anton, V. 2002.
  • Comparing Proportional Hazards and Accelerated Failure Time Models for Survival Analysis. Statistics in Medicine, 21, 3493-3510.
  • Qi, J. 2009. Comparison of Proportional Hazards and Accelerated Failure Time Models. MSc Thesis,
  • Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada, 79p. Schoenfeld, D. 1982. Partial Residuals for the Proportional Hazards Regression Model. Biometrika, 69, 239-241.
  • Wei, L.J. 1992. The Accelerated Failure Time Model: A
  • Useful Alternative to the Cox Regression Model in Survival Analysis. Statistics in Medicine, 11, 1871- 18
  • Zeng, D., Lin, D. 2007. Efficient Estimation for the Accelerated Failure Time Model. Journal of the American Statistical Association, 102, 1387-1396.