Proportional hazard model for time-dependent covariates with repeated events

Cox's proportional hazard is potentially the most used method in life data and survival analysis. Although the method is relatively simple to understand, its major difficulties in estimation are observed when time dependent-covariates with repeated events are used as input variables. This paper presents a review and analysis of the model parameter estimation. The model's assumptions are discussed, and a detailed analysis highlights the application, advantages and potential limitations when the assumption of proportionality is violated.