A Simulation Study on Cox Regression with Weighted Estimations


Abstract


Cox regression model has an important and glaring place in survival analysis. The key assumption is proportional hazards and violation of this assumption can invalidate outcomes of a study. Our approach will be to use Cox regression model with weighted estimation for a survival data set that includes both proportional and nonproportional hazards.  We carried out a simulation study, considering different censoring rates, sample sizes, and tied observations. Simulation results are interpreted and discussed with the results obtained by traditional Cox regression model. Cox regression model with N-Prentice weighting function serves as a better model under all simulation scenarios

DOI Code: 10.1285/i20705948v7n1p26

Keywords: Cox regression model; hazard ratio; log-rank test; nonproportional hazards; survival analysis; weighting function

References


. Altshuler, B.(1970). Theory for the measurement of competing risks in animal experiments. Mathematical Bioscience, 6, 1-11.

. Andersen, P.K., Borgan, G., Keiding N. (1982). Linear nonparametric tests for comparison of counting process with application to censored survival data. International Statistical Review, 50, 219-258.

. Arjas, E. (1988). A graphical method for assessing goodness of fit in Cox’s proportional hazards model. Journal of the American Statistical Association, 83, 204-212.

. Ata, N., Demirhan, H. (2013). Weighted estimation in Cox regression model: An application to breast cancer data. Gazi University Journal of Science, 26(1), 63-72.

. Bewick, V., Cheek, L., Ball, J. (2004). Statistical review 12: Survival analysis. Critical Care, 8, 389-394.

. Breslow, N.E.(1974). Covariance analysis of censored survival data. Biometrics, 30, 89-99.

. Collett, D. (2003). Modelling survival data in medical research. Chapman&Hall, London.

. Cox, D.R. (1972). Regression models and life-tables. Journal of the Royal Statistical Society Series B, 34, 187-220.

. Frankel, P., Longmate, J. (2002). Parametric models for accelerated and long-term survival: a comment on proportional hazards. Statistics in Medicine, 21, 3279-3289.

. Gehan, E.A. (1965). A generalized Wilcoxon test for comparing arbitrarily singly-censored samples. Biometrika, 52, 203-223.

. Gill, R.D., Schumacher, M. (1987). A simple test for the proportional hazards assumption. Biometrika, 74, 289-300.

. Harris, E.K., Albert, A. (1991). Survivorship analysis for clinical studies, Marcel Dekker.

. Jinnah, A. (2007). Inference for Cox’s Regression Model via A New Version of Empirical Likelihood. Unpublished Master of Science Thesis, Georgia State University.

. Kaplan, E.L., Meier, P. (1958). Nonparametric estimation from incomplete observations. Journal of the American Statistical Association, 53, 457-481.

. Leton, E., Zuluaga, P. (2001). Equivalence between score and weighted tests for survival curves. Communications in Statistics-Theory and Methods, 30(4), 591-608.

. Moreau, T., Maccario, J., Lellouch, J., Huber, C. (1992). Weighted log rank statistics for comparing two distributions. Biometrika, 79, 195-198.

Perperoglou, A., Keramopoullos, A., Houwelingen, H.C. (2007). Approaches in modelling long-term survival: An application to breast cancer. Statistics in Medicine, 26(13), 2666-2685.

Persson, I., Khamis, H. (2005). Bias of the Cox model hazard ratio. Journal of Modern Applied Statistical Methods, 4(1), 90-99.

Prentice, R.L. (1978). Linear rank tests with right censored data. Biometrika, 65,167-179.

Prentice, R.L., Marek, P. (1979). A qualitative discrepancy between censored data rank tests. Biometrics, 35, 861-867.

Putter, H., Sasako, M., Hartgrink, H.H., van de Velde, C.J.H., van Houwelingen, J.C. (2005). Long-term survival with non-proportional hazards: results from the Dutch Gastric Cancer Trial. Statistics in Medicine, 24(18), 2807-2821.

Sasieni, P. (1993). Maximum weighted partial likelihood estimators for the Cox model. Journal of the American Statistical Association, 88, 421, 144-152.

Schemper, M. (1992). Cox analysis of survival data with nonproportional hazards functions. The Statistician, 41, 455–465.

Schoenfeld, D. (1982). Partial residuals for the proportional hazards model. Biometrika, 69, 551-555.

Therneau, T.M., Grambsch, P.M. (2000). Modelling survival data: Extending the Cox model. New York: Springer-Verlang.


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