Independence of censoring time $C$ and event time $T$ for randomised entry to a study

Question

While reading through the textbook 'Modern Applied Statistics With S' by Venables and Ripley, I came across the following paragraph detailing the different types of censoring possible when dealing with survival data. Highlighted is a sentence of particular interest. Here we consider a study where individuals are entered randomly (across a fixed time interval), and those individuals for which the event of interest is not observed are censored when the trial is reviewed at some predetermined fixed time. In the text, they list this scenario as one in which the time to censoring $C$ is independent of the event time $T$.

I understand this to be uninformative censoring, but why is the independence of the two random variables $T$ and $C$ for a given individual be a reasonable assumption to make in this instance?

Answer 1

This is a very usual study design. Since exit time from the study is fixed, total time until censoring $C = t_{exit} - t_{entry}$ only depends on entry time. On the other hand, entry conditions are the same for all participants (maybe something like "every patient will be asked to enter the study the day after surgery" or such) so it is usual, and quite safe, to assume no association exists between $t_{entry}$ and survival after entering the study, which is $T$ (remind that $T= t_{event}-t_{entry}$).

An exception to this rule may occur if during the time of the study, treatment improved or there was some time trend affecting the survival chances, this is either excluded a priori, or, if measurable, controlled for with a time changing factor.