Survival analysis using Cox´s proportional hazards model is widely used to search for prognostic factors or covariates for which the time-to-response is influenced by other explanatory variables. This technique presumes death rates may be modelled as both log-linear functions of the covariates and proportionality of hazard ratios. It is essential to test those assumptions whenever multivariate modelling procedure is applied to any given data. In case of application to Cox´s model, the proportionality assumption should be secured to draw out valid estimate of each prognostic factor. It can be done through checking LLS (log(-log survival function)) plot of each variable, which enables to verify parallelism between cumulative survival functions according to the level of exposure.
Survival data on 86 histologically confirmed breast cancer cases at the Seoul National University Hospital, 1984-1988, were used in this analysis. Prognostic factors as age at diagnosis, tumor size, lymph node involvement, clinical stage by TNM classification, and pathological grade were dichotomized for the study purpose. A covariate, i.e. age at diagnosis, even though it was well-fitted to the Cox´s model, did not reach to a significant level by both ordinary statistical methods and the test for significance by Cox´s model. However, lymph node involvement as well as clinical stage were revealed to be significant prognostic factors, in which proportionality assumption were satisfied. Other variables, which did not show any evidence of parallelism, even crossing each other, were statistically non-significant by both ordinary tests and Cox´s method. It suggests that statistical significance in survival data analysis was affected by real difference of survivalship of each prognostic factor, as well as by the fitness to the Cox´s proportional hazards model, which can be easily assessed by a simple plotting method. Test for assumption of proprtionality is recommended in order to get a more valid estimate of relative risk, and may be valuable to expand biological knowledge on the etiology of a disease under investigation.
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