I am taking a course in survival analysis where we follow the book "Survival Analysis: Techniques for Censored and Truncated Data" by John P. Klein and Melvin L. Moeschberger.
Although I like the book in general, I don't really understand the way truncation is explained in the book and my professor's explanation hasn't helped too much either - and what is worse they seem to conflict a little bit in my head.
From my current understanding censoring in survival analysis occurs when either the event we are trying to model the time to has already been triggered for an observation in the study (left-censoring) or if for the duration of the study we don't see the event occur for an observation (right-censoring). Hence censoring is (1) a local property in the sense that we talk about a observation being censored, and (2) censored observations are in the study.
From my current understanding, truncation on the other hand occurs when the study is conducted in such a way that some potential observations are left out.
So the main difference between censoring and truncation is whether or not we have access to all potential observations or not, is it not?
Now here is where the book and my professor's explanations differ a bit:
Book: A truncated observation is one that has been left out due to some restriction of the study. For instance if we are modelling time to death but only looking at people at retirement homes, we miss people under the age threshold (say 60) to be admitted to the retirement homes. Hence dead people younger than 60 are truncated in this study.
Professor: Truncation occurs when observations are only in the study given some condition. In the same example ALL observations are truncated since they have survived beyond age 60 and are only in the study because of this condition.
So from what I understand the book claims truncation is a local property, while my professor claims that it is a global property (in the sense that the data set is truncated). Which one is the correct one? If there are different conventions, then which one is the most common one?
Also, the above example is an example of left truncation. I am having a hard time coming up with a natural example of right truncation? Does anyone have a good one?