Sometimes I wonder whether it’s appropriate to focus solely on the event of interest in survival analysis. For example, if I’m studying dementia, is it valid to simply censor individuals who die during follow-up?
I recently explored the Fine-Gray model and came away with a few takeaways:
- In the standard (cause-specific) survival model, censored individuals—including those who die—are removed from the risk set at the time of censoring.
- In contrast, the Fine-Gray model treats deaths as competing risks: these individuals remain in the risk set but contribute with diminishing weights, since they can no longer develop the event of interest unlike those who are censored but still theoretically at risk.
- As a result, the cumulative incidence estimated by the Fine-Gray model is typically lower than that from a cause-specific model, due to a larger at-risk population.
For example, if younger (Group A) and older (Group B) individuals have the same theoretical event rate, but more deaths occur in Group B, the observed incidence in Group B may appear lower. While counterintuitive at first, it’s expected under a competing risks framework.
Since my primary interest is in biological mechanisms rather than population-level incidence, I think it’s reasonable to continue using the cause-specific model in most cases.
Experimental code and data here
Happy to hear your thoughts and discuss further!
Disclaimer: This is my personal reflection, I may be completely wrong 
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@hirotaka - this is fascinating. I would say if you are interested in “biology” then you don’t really care about the magnitude of effect. The upside of the Fine-Gray is that with the larger sample size the confidence intervals will be narrower (and thus, smaller p-values)… right? Otherwise, if the competing event is neglible.. then it doesn’t really matter which approach.
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@fbbriggs — really interesting point about the effective sample size! You’re right — in my example, the Fine-Gray model produced a smaller standard error (0.628 vs. 0.707 in the cause-specific model). I agree with your comment: when competing risks are negligible, the model choice may not matter much. And in cohorts with long follow-up (e.g., 10+ years), where deaths accumulate, running both models can be informative.
That said, I wonder if one could argue that the cause-specific model is more appropriate in certain contexts. For biological studies, assuming that individuals who died could have developed the event if they had lived — and treating them as standard censoring — may better reflect the underlying disease mechanism. This aligns with the example I gave, where the true event rate was assumed to be the same across groups. In that case, the cause-specific model returned an HR of 1.0, while the Fine-Gray model gave 0.78 (But it is subdistribution HR), likely reflecting differences in mortality rather than differences in the event risk itself.
So while the Fine-Gray model appropriately captures real-world incidence, it may obscure biological associations when competing risks differ across groups.
Do you think this line of reasoning would be acceptable to reviewers?
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@hirotaka I think this is an excellent reasoning - especially the point about subpopulation differences in competing risk
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