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

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