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Although another post has raised a similar question - survival analysis with external non-competing events, my question seems slightly different and not addressed by the answers within the post.

Example:

A statistical analysis plan of a breast cancer study that investigates the efficacy of a new drug X stated that "competing risk survival analysis" would be used to estimate overall survival as multiple competing (new) risks were expected to emerge during the trial. For example, a patient might develop a new skin cancer (radiation-induced skin cancer) after she was treated by radiation therapy for her breast cancer (but before she was treated by the new drug X). As the new skin cancer may impact her survival, but new skin cancer is not relevant to the efficacy (or toxicity) of new drug X, new skin cancer could be considered a "competing risk" and patient's overall survival needs to take this "variable" into account.

This seems sensible. However, let's assume patients may also develop a new breast tissue pathology in the other (normal) breast when she was also being treated by new drug X for her breast cancer. Assuming that this new breast tissue pathology occurs at a high frequency in an average woman and is known not to have any impact on breast cancer patient survival. As the disease organ is breast, the study plan needs to preemptively address this type of potential events.

From the medical literature, there are at least two different approaches to this type of event:

  1. ignore the occurrence of the event and continue to follow patient's subsequent development in terms of survival
  2. censor this patient and do not follow her subsequent development in terms of survival

I can vaguely grasp the thinking process of point 2, but have no idea if point 1 is statistically justifiable.

Q1. can "time-varying covariate" be used to account for this type of "non-event" events, although this time-varying covariate model seems to assume (layman's understanding) that the non-event plays a "covariate role" to the final (survival) outcome?

Q2. does point 1 stand when we assume these "non-events" truly do not affect the survival?

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Much of the answer to your question is included on the page you link. Your question becomes how to apply the principles outlined there.

@AdamO notes:

A competing event is formally any event that "curtails the incidence" of a particular outcome.

For each of your scenarios, you have to answer the question: does this "event" affect the probability of the outcome of primary interest (e.g., overall survival)?

For the benign contralateral pathology "known not to have any impact on breast cancer patient survival" that occurs after entry into the trial for Drug X, there would seem to be no "competing risk" under that definition. In a pre-planned randomized trial (which is the situation you seem to be considering), any unexpected effect of that benign pathology on outcome would ideally be averaged out between treatment groups. As this "event" (under your assumptions) doesn't "curtail the incidence" of the outcome of interest, there is no need to censor such patients. You might include development of that pathology as a time-varying covariate for further control, or evaluate it with a multi-state model to test your assumption that it has no impact on survival or on the efficacy of Drug X.

A treatment-induced skin cancer that occurs before entry into the trial of Drug X is a bit more complicated. It's not clear to me whether such an event occurring before the trial would be considered strictly as a "competing event" if the starting point for survival analysis were the start date of the Drug X trial. As you note, however, that can't just be ignored. A trial design in practice would probably either exclude such individuals or use prior development of such skin cancer as a factor in the randomization. Analysis that stratifies on prior skin-cancer status or includes it as a covariate could be considered.

Things get much trickier if such a skin cancer develops after entry into the Drug X trial (even if it was caused by radiation therapy prior to the Drug trial). Then (1) it certainly is a competing event and (2) the skin cancer might affect other therapies received by the patient during the trial, potentially interacting with Drug X. Censoring or a formal competing-risks could help deal with this problem.

If there is confounder-treatment feedback, traditional covariate-adjustment methods might not work. For example, what if Drug X affected the probability of developing radiation-induced skin cancer, and therapy for the skin cancer then affected how well Drug X works? Hernán and Robins provide an accessible reference for how to deal with such complications in both randomized trials and observational studies.

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