A comparison of alternative methods for testing proportional hazards hypothesis

Some important non-graphical methods of testing proportional hazards assumption in the Cox regression model are reviewed and compared. Methods are compared with respect to their powers and control over false positive rates through simulation studies. Simulation suggests that modelling time-covariate interactions in a Cox PH model where the covariate effects vary as the log of the cumulative baseline hazard function seems to be the best approach is most cases. This is equivalent to using log minus log survival function for modelling time varying effects of covariates in the Cox model and is a formal equivalent of the graphical approach of checking PH assumption by plotting log minus log survival function against log survival time. Almost the same power can be achieved by modelling time varying effects by defining time-dependent covariates that vary as the log survival time. Simulation results also suggest that these two tests have very good control over false positive rates in the sense that the observed significance levels have been found to be very close to the nominal level (0.05) set for rejecting the PH hypothesis. The tests are illustrated using the Gastric Carcinoma Data, which is known to violate the PH assumption and all the tests successfully detected the non-proportionality of the treatment effect for this example data. © Nova Science Publishers, Inc