NON-PROPORTIONAL HAZARDS WITH APPLICATION TO KIDNEY TRANSPLANT DATA

Year 2007, , 55 - 63, 01.02.2007

Emel Başar

https://doi.org/10.1501/Commua1_0000000196

Abstract

The Cox proportional hazards (PH) model is the popular methodfor modelling censored survival data.Cox PH model is the proportionality of hazards in which the hazard ratiois linear in the covariates. However this assumption may not hold in somesurvival studies. Therefore, diğerent non-parametric regression methods havebeen proposed to estimate the hazard ratio as a function of time when theproportionality of hazards can not be assumed.In this study a piecewisemodel and a non-parametric regression spline model have been considered forthe non-proportional hazards. The models have been illustrated with kidneytransplant data

Keywords

Cox regression, Proportional hazards, Regression splines, Survivalanalysis

References

• Abrahamowicz, M., MacKenzie, T., Esdaile, J. M., Time-dependent hazard ratio: modelling and hypothesis testing with application in lupus nephritis, Journal of the American Statistical Association, 91(1996), 1432-1439.
• Ba¸sar, E., Applications of some statistical technique used in life table analysis to the kidney transplantation data, Unpublished Ph. D., thesis, Science Institute of Hacettepe University. 1993.
• Cai, Z., Sun, Y., Local linear estimation for time-dependent coe¢ cients in Cox’s regression models, Scandinavian Journal of Statistics, 30(2003), 93-111.
• Cox, D. R. Regression models and life tables, Journal of the Royal Statistical Society, Ser. B, 34(1972), 187-220.
• De Boor, C., A Practical Guide to Splines, Springer, New York, 1978.
• Eilers, P. H. C., Marx, B. D., Flexible smoothing with B-splines and penalties, Statistical Science, 89(1996), 89-121.
• Eisen, A. E., Agalliu, I., Thurston, S. W., Coull, B. A., Checkoway, H., Smoothing in occu- pational cohort studies: an illustration based on penalised splines, Occupational and Envi- ronmental Medicine, 61(2004), 854-860.
• Grambsch, P. M., Therneau T. M., Proportional hazards test and diagnostics based on weight residuals, Biometrika, 81(1994), 515-526.
• Gray, R. J., Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis, Journal of the American Statistical Association, 87(1992), 942-951. [10] Gray, R. J., Spline-based test in survival analysis, Biometrcs, 50(1994), 640-652.
• Hastie, T., Tibshirani, R., Varying-coe¢ cient models, Journal of the Royal Statistical Society, Ser. B, 55(1993), 757-796.
• Hess, K. R., Assessing time-by-covariate interactions in proportional hazards regression mod- els using cubic spline functions, Statistics in Medicine, 13(1994), 1045-1062.
• Kooperberg, C., Stone, C. J., Truong, Y. K., Hazards regression, Journal of the American Statistical Association, 90(1995), 78-94.
• Lin, D. Y., Wei, L. J., Goodness-of-…t test for the general Cox regression model, Statistica Sinica, 1(1991), 1-17.
• Moreau, T., O’Quigley, J., Mesbah, M. A., A global goodness-of-…t statistic for the propor- tional hazards model, Applied Statistics, 34(1985), 212-218.
• Quantin, C., Abrahamowicz, M., Moreau, T., Bartlett, G., MacKenzie, T., Tazi, M. A., Lalonde, L., Faivre, J., Variation over time of the eğects of prognostic factors in a population- based study of colon cancer: comparison of statistical models, American Journal of Epidemi- ology, 150(1999), 1188-1200.
• Rosenberg, P. S., Hazard function estimation using B-splines, Biometrics, 51(1995), 874-887. [18] Sleeper, A. L., Harrington, D. P., Regression splines in the Cox model with application to covariate eğects in liver disease, Journal of the American Statistical Association, 85(1990), 941-949.
• Therneau, T. M., Grambsch, P. M., Modelling Survival Data: Extending the Cox Model, Springer, New York, 2000.
• Fen-Edebiyat Fak., ·Istatistik Bölümü, 06500, Teknikokullar, Ankara, Türkiye
• E-mail address : [e-mail]