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 Ŷ ∗ i (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.