Time-to-event data and censoring

In many cases an endpoint directly measures time from the point of randomisation to some well-defined event, for example time to death (survival time) in oncology or time to rash healing in Herpes Zoster. The data from such an endpoint invariably has a special feature, known as censoring. For example, suppose the times to death for a group of patients on a particular treatment in a 24 month oncology study are as follows  

Statistical Thinking for Non-Statisticians in Drug Regulation Richard Kay 2007 John Wiley Sons. Ltd ISBN 978-0-470-31971-0 

It is this specific feature that has led to the development of special methods to deal with data of this kind. If censoring were not present then we would probably just takes logs of the patient survival times and undertake the unpaired t-test or its extension ANCOVA to compare our treatments. Note that the survival times, by definition, are always positive and frequently the distribution is positively skewed so taking logs would often be successful in recovering normality. 

The special methods we are going to discuss in this section were first developed primarily in the 1970s and applied in the context of analysing time to death and this is why we generally refer to the topic as survival analysis . As time has gone on, however, we have applied these same techniques to a wide range of time-to-event type endpoints. The list below gives some examples  

Throughout this section we will adopt the conventions of the area and refer to survival analysis and survival curves, accepting that the methods are applied more widely to events other then death. 

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