Introduction

Survival data or more generally speaking “time-to-event” data considers the time from a given origin to the occurrence of an event of interest, for example the time from the diagnosis of a certain disease to the death of the patient. The classical survival data analysis techniques encompass estimation, hypothesis tests, and regression models. Such regression models are useful to analyse simultaneously the impact of several factors on the time-to-event under investigation. For example, in the context of a clinical trial, such regression models are often used to estimate the treatment effect on time to death while adjusting for important prognostic factors such as the stage of disease at randomization. A classical assumption in survival analysis is that if the follow-up would be long enough, all observations under study would experience the event of interest. In other words, one assumes that all observations are at risk for the event of interest.