Extensions of cox model for non-proportional hazards purpose

Cox proportional hazard model is one of the most common methods used in time to event analysis. The idea of the model is to define a hazard level as a dependent variable which is explained by the time-related component (so-called baseline hazard) and the covariates- related component. The model is based on several restrictive assumptions one of which is the assumption of proportional hazard. However, if this assumption is violated, this does not necessarily prevent an analyst from using Cox model. The current paper presents two ways of model modification in the case of non-proportional hazards: introducing interactions of selected covariates with function of time and stratification model. Calculations performed give the evidence that both methods result in better model fit as compared with the original model. Additionally, they allow interpreting the parameters estimates more precisely, taking into account the effect of the covariate at the hazard level that is changing over time. The choice of the appropriate method of tied events handling however is not straightforward and should be adjusted to the particular analysis purpose