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"Censoring in survival analysis should be “non-informative,” i.e., participants who drop out of the study should do so due to reasons unrelated to the study. Informative censoring occurs when participants are lost to follow-up due to reasons related to the study, e.g., in a study comparing disease-free survival after two treatments for cancer, the control arm may be ineffective, leading to more recurrences and patients becoming too sick to follow-up." from this paper

In my field of medicine, which is rheumatology, drug survival analysis is quite common. One of my interests is the drug survival of tumor necrosis factor inhibitors (TNFis) in patients with spondyloarthritis (a chronic rheumatic disease). Several papers have analyzed drug retention rates. An event is considered when a patient discontinues treatment at time T. Observations were censored if the patients stopped treatment due to remission or other reasons than lack of efficacy or adverse events. In my opinion, these are not examples of non-informative censoring since stopping due to remission is related to treatment, and other reasons are vague but could also be related to treatment. Here are some examples in papers I have found.

Citation from the Paper 1:

Drug withdrawal was assessed in prespecified categories: lack of efficacy and adverse events. Lack of efficacy was defined in the individual registries and transferred as one variable to the dataset. Patients who withdrew due to remission and other reasons (e.g. planning for pregnancy) were censored.

Citation from Paper 2 (high ranking journal):

"Observations were censored by: (1) the date of data extraction; (2) date of death; or (3) end of registry follow-up, whichever came first; (4) withdrawal from treatment for other reasons than lack of efficacy (LOE) and adverse events (AE), that is, remission or other reasons such as planning for pregnancy.."

Other examples:

Paper 3. Paper 4.

Since many manuscripts have used this, I think that my reasoning must be flawed.

Question: If patiënts discontinue TNFi treatment for other reasons or remission, can this be considered an example of informative censoring? What kind of bias is to be expected from this? Or should they have modeled the events in a multi-state model?

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  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Mar 16, 2022 at 20:01
  • $\begingroup$ Editied the post and provided a question as requested $\endgroup$
    – Pashtun
    Mar 16, 2022 at 20:41
  • $\begingroup$ you're communicating that there's a time-varying exposure, not that patients are no longer under observation, correct? $\endgroup$
    – user551504
    Mar 16, 2022 at 20:43
  • $\begingroup$ Well I am not sure if I would call it AM exposure. There is a time varying outcome: treatment discontinuation at time t. The data however is also censored if the event happens because of remission rather than side effects or lack of efficacy. $\endgroup$
    – Pashtun
    Mar 16, 2022 at 20:56
  • 3
    $\begingroup$ Thanks, this is a classic competing risks problem. Towards that, could you elaborate on the definition of event? It's still not clear. You write an event is when a patient "discontinues treatment". Then the next sentence vaguely suggests you actually meant to say "discontinues treatment due to efficacy or lack of adverse event". How are these determined? $\endgroup$
    – user551504
    Mar 17, 2022 at 13:58

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Dual-trained medical oncologist and biostatistician here.

In theory, censoring should be noninformative because informative censoring causes bias. In practice, not all bias is clinically important. Papers 1 and 2 are only talking about (A) how they've chosen to define their outcome; what counts as an event, what counts as a censoring. They make no claim about (B) whether these censorings are informative or noninformative. (A) and (B) are two separate issues that should not be mixed together.

If the desired event is a composite of stopping due to inefficacy or toxicity, you are (B) technically correct in that censoring due to remission is informative (for brevity, I'm going to focus on stopping due to remission). This is because a patient in remission obviously has a very different risk of inefficacy compared to the average patient under observation. These remissions will bias the drug to look worse (think of it as "cherry-picking away the cream of the crop"). This bias could be important in theory if there was some huge difference in the pattern of remissions between different drugs but is unimportant in practice because remissions comprised a tiny proportion of drug discontinuations.

But let's take a step back. We're using the composite outcome of inefficacy or toxicity as a construct for measuring the drug's "badness." Lower risk of an event means a less bad drug. Obviously, stopping due to remission cannot count as a badness event, so (A) the investigators chose to censor instead. Sure it's informative, but let's think about whether they could have chosen any differently:

  • They could have continued counting those patients as under observation, but now they've simply traded informative censoring bias for immortal time bias, among other problems.
  • They could have used a competing risks model, which might give the "hazard ratio for inefficacy/toxicity if the remissions never happened." This might be a purer measure of "inefficacy/toxicity" on paper but is arguably a worse measure of "drug badness" which is actually what we're interested in clinically.
  • I don't see the point of a multistate model here. It's not as if remission is some sort of intermediate step between taking the drug and stopping for inefficacy/toxicity.

In summary, I think the decision to censor remissions is reasonable, but this is on (A) clinical and pragmatic grounds and has nothing to do with (B) informativeness.

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    $\begingroup$ What is being estimated when following your suggestion? $\endgroup$
    – Ben
    Sep 8, 2023 at 8:09
  • $\begingroup$ What suggestion are you referring to? I've only explained why I think the methodologies of papers 1 and 2 are reasonable. I didn't think I gave any one suggestion otherwise? $\endgroup$ Sep 8, 2023 at 8:48
  • $\begingroup$ Hi Singularity, I'm asking about censoring remissions. $\endgroup$
    – Ben
    Sep 8, 2023 at 9:06
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    $\begingroup$ Multistate models would have major benefit here and would provide much easier-to-interpret estimates such as mean time on drug and not in remission, mean time on drug and not in remission, mean time on drug or in remission, etc. The censoring problem vanishes unless a patient is lost to all follow-up assessment for a non-random reason. See this. $\endgroup$ Sep 8, 2023 at 12:12
  • $\begingroup$ @Frank Harrell, I can see the benefit of a multistate model if there were transitions such as the possibility that a person in remission can fall out of remission and may go back on the drug. Is there a benefit of a multistate model if the only two possible transitions are (1) on the drug --> stopped due to toxicity and (2) on the drug --> stopped due to remission? $\endgroup$ Sep 11, 2023 at 7:48

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