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In competing risk settings, the Cox model gives correct HR's if we censor at other event types (i.e. the Cause Specific Model):

https://statisticalhorizons.com/for-causal-analysis-of-competing-risks/

Is it valid to use this censoring approach in a sampled nested case control dataset, on which we subsequently fit a conditional logistic regression model? Im guessing that the resulting HR's will be valid estimates under a competing risk setting, since the conditional logistic regression is equivalent to a Cox model with a particular data structure:

https://www.rdocumentation.org/packages/survival/versions/3.4-0/topics/clogit

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