Random, independent, non-informative: the censoring promise you make to the reader

Every survival curve rests on a promise you never say out loud. To follow only the patients still at risk, you drop the ones who fell out of view. That works if the dropouts were like the patients who stayed. If they weren’t, the curve is wrong. So when you publish a Kaplan–Meier curve, you’re quietly promising the reader that the people who vanished from your data were no different from the people who remained. This post is about what that promise says, and when it’s a lie.

The promise has three names

Statisticians have three words for it, and papers use them as if they mean the same thing. They don’t.

The one that matters is independent censoring. It says that within each group you’re comparing, the patients who get censored have the same risk as the patients who stay. The dropouts are a fair sample of the people still being followed, inside each arm. That’s the assumption Kaplan–Meier, the log-rank test, and the Cox model all lean on. Break it and your estimate is off.

Random censoring is the same idea, but stronger. It asks the dropouts to look like the whole at-risk pool, without splitting into groups at all. If censoring is random, it’s automatically independent too — representing the whole pool means representing each group inside it. But censoring can be independent without being random. The difference only shows up when you have groups. Say one treatment arm loses far more patients to follow-up than the other. That alone doesn’t break independent censoring, as long as, inside each arm, the ones who left resemble the ones who stayed. It does break random censoring, because pooled across arms the dropouts no longer match the pool. The useful news is that you don’t need random. Independent is enough.

The third term is non-informative censoring. Loosely, it means the pattern of who gets censored, and when, carries no hidden clue about when events happen. It almost always holds when censoring is independent. So of the three words, independent is the one you actually have to earn.

When the promise breaks

The failure that should worry you is non-independent censoring. Picture the RCC cohort. Some patients come off targeted therapy because the toxicity became too much. Suppose those patients are also the ones doing worse. Then the people leaving your data are sicker than the people staying. Drop them as if they were average, and the curve you draw is too optimistic. Their hidden progressions get counted as non-events. Survival looks better than it is.

You can’t check it — you argue it

Here’s the hard part. You can’t test this promise against your data. The censored patients are censored precisely because you don’t know what happened to them. Nothing in the numbers will tell you whether they were like the ones who stayed. So independent censoring isn’t something you verify. It’s something you defend, using what you know about why each patient left.

That’s where it gets practical, because patients get censored for three quite different reasons.

Some are censored by the calendar. The study closed, or the data was pulled for analysis, while they were still progression-free. That reason has nothing to do with their tumor. It’s the safe kind.

Some are lost to follow-up. They stopped coming to imaging. Now you have to ask why. A patient who moved away is one thing. A patient who got too sick to travel is another — and if that’s common, your dropouts are the sick ones, and the promise breaks.

Some withdraw. They came off study, often for toxicity. Whether that’s safe depends entirely on whether the reason for leaving is tied to their prognosis.

Same δ = 0 in every row. Very different levels of trust. The dataset records that a patient was censored. It doesn’t record whether you should believe a curve that treats them as average.

What I’m taking away

Independent censoring sits under every survival curve I’ve ever read, and I’d never once seen it defended. Usually it isn’t. The curve gets drawn, and the assumption rides along unspoken. What I want to carry is a habit: for any censored patient, ask one question. Why did they leave, and is that reason tied to how they were doing? The calendar is innocent. Disappearance and toxicity are not, until shown otherwise. The promise is only as good as the reasons behind it.

Kleinbaum, D. G., & Klein, M. (2012). Survival analysis: A self-learning text (3rd ed.). Springer. https://doi.org/10.1007/978-1-4419-6646-9*