# Difference between independent and non-informative censoring

I was wondering if I could get a third opinion to settle a discussion on the distinction between independent and non-informative censoring.

My definitions:

1) In independent censoring, the event and censoring rates are assumed to be the same conditional on the level of the covariates.

2) In non-informative censoring we assume that the time to censorship distribution is not related to the time-to-event distribution (e.g. if a patient in a study received the event, then another patient in the study is selected randomly to leave the study).

Adviser's definition:

1) She has not heard of/used the phrase "independent censoring".

2) Noninformative censoring is when time to event and time to censoring are independent conditional on the level of covariates.

Who's on point with regards to these two types of censoring? Are we both correct (and I just fail to see the equivalence)? both incorrect? I think the two have just very subtle differences that change the meaning of the terms.

I appreciate your insights!

• stats.stackexchange.com/questions/22497/… Commented Jul 23, 2013 at 13:04
• Thank you. I saw that previously, but I'm looking more for a big picture view rather than the mathematics. I understand the math just fine, and based on that, my definitions seem to be more on point. Commented Jul 23, 2013 at 13:09

## 1 Answer

The first set of definitions seem right to me.

Your adviser's definition two seems to be a conflation of independent and non-informative censoring assumptions. I haven't seen non-informative censoring defined before with reference to the covariate profile.

The following text is from "Survival analysis: A self-learning text" by Kleinbaum and Klein (3rd edition, 2011, Springer) where pages 37-43 deal with censoring assumptions:

p. 38 (emphasis as per original text)

Independent censoring essentially means that within any subgroup of interest, the subjects who are censored at time t should be representative of all the subjects in that subgroup who remained at risk at time t with respect to their survival experience. In other words, censoring is independent provided that it is random within any subgroup of interest.

So independent censoring is a less restrictive form of random censoring (where we would not be taking into account the survival profile by covariates).

p. 42

Non-informative censoring occurs if the distribution of survival times (T) provides no information about the distribution of censorship times (C), and vice versa.

However... and to the point of the materiality of the distinction:

p. 42 (emphasis added by me this time!)

The assumption of non-informative censoring is often justifiable when censoring is independent and/or random; nevertheless, these assumptions are not equivalent.

• Thanks for that insight. Funny you reference that text since Kleinbaum was my professor and most of my intuition I got from his class (and book). So just to make sure I'm clear - in noninformative censoring, you are saying that it does NOT depend on the covariate profile? In the post given by @ocram above, does his statement "distribution of C does not depend on the parameters of the distribution of T" mean that there is no conditioning on the covariate profile? Commented Jul 24, 2013 at 4:21
• I'll read ocram's comment later on and get back to you... Commented Jul 24, 2013 at 4:33
• Reading the linked answer from Ocram (stats.stackexchange.com/a/22605/16974) -- I think there formulae there don't consider the covariate profiles, but rather that "parameters" refers to parameters informing the right-hand side of the equation $$\Pr[T=y_i, C > y_i] = G(y_i) f(y_i).$$ --- if you're comfortable with the details of the maths on that page, you're one step ahead of me in that regard! Commented Jul 24, 2013 at 6:57