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Japanese Journal of Clinical Oncology 19:195-201 (1989)
© 1989 Foundation for Promotion of Cancer Research

research-article

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

Atsuko Shibata*, Nobuyuki Hamajima, Akiko Tamakoshi, Sadao Suzuki, Ryuichiro Sasaki and Kunio Aoki

Department of Preventive Medicine, Nagoya University School of Medicine 65 Tsurumai-cho, Showa-ku, Nagoya 466

*For reprints and all correspondence

Received March 15, 1989; accepted June 21, 1989

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 cross ing 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 cal culated, along with the logarithm of the hazard ratio with its standard error. Although the in crease 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 clini cal 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.

Key Words: Survival analysis • Proportional hazards model • Simulations


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