ABSTRACT
In this paper, we present a class of graphical tests of the proportional hazards hypothesis for two-sample censored survival data. The proposed tests are improvements over some existing tests based on asymptotic confidence bands of certain functions of the estimated cumulative hazard functions. The new methods are based on the comparison of unrestricted estimates of the said functions and their restricted versions under the hypothesis. They combine the rigour of analytical tests with the descriptive value of plots. Monte Carlo simulations suggest that the proposed asymptotic procedures have reasonable small sample properties. The power is much higher than existing graphical tests and comparable with existing analytical tests. The method is then illustrated through the analysis of a data set on bone marrow transplantation for Leukemia patients.