A Numerical Study on Statistical Diagnostics on Cox Proportional Hazards Models for Survival Data Analysis

There have been proposed so far many methods of statistical diagnostics in Cox regression for checking the goodness of the estimated model or checking the adequacy of the data. The former type contains the checking of the overall goodness of fit, the validity of the assumption of proportional hazards and the proper functional forms of the effects of covariates. While the latter type contains the checking whether there exist singly and/or jointly influential observations in the data set. In the present paper we study numerically the performances of various methods of diagnostics including our method of influence analysis for multiple-case diagnostics (Sung and Tanaka, 2003) by analyzing a real data set of lung cancer patients.