Dealing with the Proportional Hazards Assumption when Using the Proportional Hazards Model with a Single Independent Variable

Abstract

In order to examine the proportional hazards assumption implicit in the proportional hazards model, three types of simulations were carried out on two groups of hypothetical survival data. Simulation 1 assumed that the hazard rate for one group was higher than that for the other group but that they were not proportional. Simulation 2 was an example of hazard rates crossing each other. Simulation 3 demonstrated the effect of the extent to which the hazard rates crossed. The test statistic, Z:PH, used for testing the proportional hazards assumption was calculated, along with the logarithm of the hazard ratio with its standard error. Although the increase in number of subjects was found to favor detections of violations of the proportional hazards assumption, cases such as those in Simulation 1 were considered acceptable for clinical use. Cases such as those in Simulation 2 were not suitable for the proportional hazards model. Simulation 3 suggested that cases with a substantial degree of unproportionality could be detected to violate the proportional hazards assumption, even when groups of 100 subjects each were involved in the analysis.