An Evaluation of the Weibull and the Logistic Models for Cox's Proportional Hazards Model

Abstract

Cox's proportional hazards model has been widely used in medical researches to evaluate the relationship between prognostic factors of a disease and the occurrence of outcome event. On a theoretical basis, regression coefficient estimated from Cox's proportional hazards model could be approximated by using the Weibull and the logistic model. Breast cancer cases (n=86) diagnosed at the Seoul National University Hospital were selected to evaluate the possibility of some accelerated models as an approximate model to Cox's proportional hazards model. Age at operation, tumor size and lymph node metastasis were the variables concerned in this study. Parameter estimates of two variables from the Weibull model, which seemed not to violate the proportionality assumption of Cox's model, showed almost identical values to those from Cox's proportional hazards model. However, there was a substantial degree of discrepancy in the parameter estimate of another variable, which showed an apparent unproportionality. This study confirmed that both the Weibull and the logistic models could be used as approximate methods to the estimates from Cox's proportional hazards model. Particularly noteworthy was the fact that the PC-SAS system could be successfully applied to survival analysis when the parameters were going to be estimated using Cox's model.