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A Renovated Cook's Distance Based On The Buckley-James Estimate In Censored Regression

Authors: Nazrina Aziz, Dong Q. Wang


There have been various methods created based on the regression ideas to resolve the problem of data set containing censored observations, i.e. the Buckley-James method, Miller-s method, Cox method, and Koul-Susarla-Van Ryzin estimators. Even though comparison studies show the Buckley-James method performs better than some other methods, it is still rarely used by researchers mainly because of the limited diagnostics analysis developed for the Buckley-James method thus far. Therefore, a diagnostic tool for the Buckley-James method is proposed in this paper. It is called the renovated Cook-s Distance, (RD* i ) and has been developed based on the Cook-s idea. The renovated Cook-s Distance (RD* i ) has advantages (depending on the analyst demand) over (i) the change in the fitted value for a single case, DFIT* i as it measures the influence of case i on all n fitted values Yˆ∗ (not just the fitted value for case i as DFIT* i) (ii) the change in the estimate of the coefficient when the ith case is deleted, DBETA* i since DBETA* i corresponds to the number of variables p so it is usually easier to look at a diagnostic measure such as RD* i since information from p variables can be considered simultaneously. Finally, an example using Stanford Heart Transplant data is provided to illustrate the proposed diagnostic tool.

Keywords: Buckley-James estimators, censored regression, censored data, diagnostic analysis, product-limit estimator, renovated Cook's Distance.

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[1] Aziz, N. and Wang, D. Q. (2009). Local influence for Buckley-James censored regression, submitted for publication to the Communication in Statistics-Theory and Method.
[2] Belsley, D. A., Kuh, E. and Welsch, R. E. (1980). Regression diagnostics identifying influential data and sources of colinearity, John Wiley & Sons, New York.
[3] Buckley, J. and James, I. (1979). Linear regression with censored data, Biometrika 66(3): 429-436.
[4] Chatterjee, S. and Hadi, A. S. (1988). Sensitivity analysis in linear regression, John Wiley, United States.
[5] Cook, R. D. (1977). Detection of influential observation in linear regression, Technometrics 19(1).
[6] Cook, R. D. and Weisberg, S. (1982). Residuals and Influence in regression, Chapman and Hall, New York.
[7] Crowley, J. and Hu, M. (1977). Covariance analysis of heart transplant survival data, Journal of the American Statistical Association 72(357): 27- 36.
[8] Currie, I. D. (1996). A note on Buckley-James estimators for censored data, Biometrika 83(4): 912-915.
[9] Glasson, S. (2007). Censored Regression Techniques for Credit Scoring, PhD thesis, RMIT University.
[10] Heller, G. and Simonoff, J. S. (1990). A comparison of estimators for regression with a censored response variable, Biometrika 77(3): 515-520.
[11] Heller, G. and Simonoff, J. S. (1992). Prediction in censored survival data: A comparison of the proportional hazards and linear regression models, Biometrika 48(1): 101-115.
[12] Hillis, S. L. (1993). A comparison of three Buckley-James variance estimators, Communication in Statistics B 22(4): 955-973.
[13] Hillis, S. L. (1994). A heuristic generalisation of smith-s Buckley- James variance estimator, Communications in statistics. Simulation and computation 23: 713-831.
[14] Hillis, S. L. (1995). Residual plots for the censored data linear regression model, Statistics in Medicine 14: 2023-2036.
[15] James, I. R. and Smith, P. J. (1984). Consistency results for linear regression with censored data, The Annals of Statistics 12(2): 590-600.
[16] Lai, T. L. and Ying, Z. (1991). Large sample theory of a modified Buckley-James estimator for regression analysis with censored data, The Annals of Statistics 19(3): 1370-1402.
[17] Lee, E. T. (1980). Statistical methods for survival data analysis, Lifetime Learning, California.
[18] Lin, J. S. and Wei, L. J. (1992). Linear regression analysis based on Buckley-James estimating equation, Biometrics 48(3): 679-681.
[19] Miller, R. and Halpern, J. (1982). Regression with censored data, Biometrika 69(3): 521-531.
[20] Smith, P. J. (1986). Estimation in linear regression with censored response, Pacific Statistical Congress, Amsterdam, Holland, pp. 261-265.
[21] Smith, P. J. (1995). On plotting renovated samples, Biometrics 51: 1147- 1151.
[22] Smith, P. J. (2002). Analysis of failure and survival data, Chapman & Hall, United States.
[23] Smith, P. J. (2004). Using linear regression techniques with censored data, International Journal of Reliability, Quality and Safety Engineering 11(2): 163-173
[24] Smith, P. J. and Peiris, L. W. (1999). Added variable plots for linear regression with censored data, Communication in Statistics-Theory and Method 28(8): 1987-2000.
[25] Smith, P. J. and Zhang, J. (1995). Renovated scatterplots for censored data, Biometrika 82(2): 447-452.
[26] Stare, J., Heinzl, H. and Harrell, F. (2000). On the use of buckley and james least squares regression for survival data, New Approach in Applied Statistics 12: 125-134.
[27] Velleman, P. F. and Welsch, R. E. (1981). Efficient computing of regression diagnostics, The American Statistician 35(4): 234-242.
[28] Wang, D. Q., Smith, P. J. and Aziz, N. (2009). Renovated partial residuals and properties for censored regression, submitted for publication to the Computational Statistics and Data Analysis.
[29] Weissfeld, L. A. and Schneider, H. (1990). Influence diagnostics for the normal linear model with censored data, Australian Journal Statistics 32(1): 11-20.