A Renovated Cook's Distance Based On The Buckley-James Estimate In Censored Regression
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.
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 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.
 Belsley, D. A., Kuh, E. and Welsch, R. E. (1980). Regression diagnostics identifying influential data and sources of colinearity, John Wiley & Sons, New York.
 Buckley, J. and James, I. (1979). Linear regression with censored data, Biometrika 66(3): 429-436.
 Chatterjee, S. and Hadi, A. S. (1988). Sensitivity analysis in linear regression, John Wiley, United States.
 Cook, R. D. (1977). Detection of influential observation in linear regression, Technometrics 19(1).
 Cook, R. D. and Weisberg, S. (1982). Residuals and Influence in regression, Chapman and Hall, New York.
 Crowley, J. and Hu, M. (1977). Covariance analysis of heart transplant survival data, Journal of the American Statistical Association 72(357): 27- 36.
 Currie, I. D. (1996). A note on Buckley-James estimators for censored data, Biometrika 83(4): 912-915.
 Glasson, S. (2007). Censored Regression Techniques for Credit Scoring, PhD thesis, RMIT University.
 Heller, G. and Simonoff, J. S. (1990). A comparison of estimators for regression with a censored response variable, Biometrika 77(3): 515-520.
 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.
 Hillis, S. L. (1993). A comparison of three Buckley-James variance estimators, Communication in Statistics B 22(4): 955-973.
 Hillis, S. L. (1994). A heuristic generalisation of smith-s Buckley- James variance estimator, Communications in statistics. Simulation and computation 23: 713-831.
 Hillis, S. L. (1995). Residual plots for the censored data linear regression model, Statistics in Medicine 14: 2023-2036.
 James, I. R. and Smith, P. J. (1984). Consistency results for linear regression with censored data, The Annals of Statistics 12(2): 590-600.
 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.
 Lee, E. T. (1980). Statistical methods for survival data analysis, Lifetime Learning, California.
 Lin, J. S. and Wei, L. J. (1992). Linear regression analysis based on Buckley-James estimating equation, Biometrics 48(3): 679-681.
 Miller, R. and Halpern, J. (1982). Regression with censored data, Biometrika 69(3): 521-531.
 Smith, P. J. (1986). Estimation in linear regression with censored response, Pacific Statistical Congress, Amsterdam, Holland, pp. 261-265.
 Smith, P. J. (1995). On plotting renovated samples, Biometrics 51: 1147- 1151.
 Smith, P. J. (2002). Analysis of failure and survival data, Chapman & Hall, United States.
 Smith, P. J. (2004). Using linear regression techniques with censored data, International Journal of Reliability, Quality and Safety Engineering 11(2): 163-173
 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.
 Smith, P. J. and Zhang, J. (1995). Renovated scatterplots for censored data, Biometrika 82(2): 447-452.
 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.
 Velleman, P. F. and Welsch, R. E. (1981). Efficient computing of regression diagnostics, The American Statistician 35(4): 234-242.
 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.
 Weissfeld, L. A. and Schneider, H. (1990). Influence diagnostics for the normal linear model with censored data, Australian Journal Statistics 32(1): 11-20.