I agree with the other commenter and you. It doesn't make sense to have it as a classification. Especially when one of the labels is so vague and a catch all.

A bit more nuanced case with regression or pattern analysis with correlation between symptoms is more interesting. Secondly, how is your data (you don't have to reveal anything sensitive) ? Can one reliably predict death from it as a simple classification? There can be a few cases where it's super obvious but they are not the most informative ones. It's the grey area where most information can be inferred and delivered to experts / docs.

You can treat it is as a binary classification if you introduce an inverse probability weighting adjustment for censoring and certain assumptions are met. There's a big literature here and it's a bit difficult to pin down the single best reference. Here's a paper that discusses censoring-adjusted evaluation of these models using standard binary classification metrics (Blanche 2013 https://pubmed.ncbi.nlm.nih.gov/23794418/)

I think you can frame this problem as

• Regression - how long will the patient survive (because patient can’t be revived), or
• Time-series classification, perform binary classification on every time steps (don’t forget to add positional/temporal encoding). But I am not familiar these task

No, how would you answer, question like "survival probablity of a patient, 'X' days from admission" with binary classification done at the end of study.