You said,
"First you have to demonstrate what happened or failed to happen, i.e. the inadequacy, then you have to demonstrate that it resulted from negligence." That's actually not how it works. In medical malpractice cases, you just have to prove what should've been done (i.e. what the standard of care is, a.k.a. what doctors/nurses/etc. are supposed to do in such a situation). If that wasn't done, then the defendant is negligent.
Medical negligence just means "not doing what doctors are supposed to do" (or nurses, or respiratory therapists, or whatever the defendant is). You don't have to "demonstrate that [what happened/failed to happen] resulted from negligence," because care that was inadequate according to normal medical standards IS negligence:
"Stated simply, medical malpractice, or
medical negligence, is medical care or treatment that falls below the accepted standard of care and causes actual harm to a patient."
https://www.natlawreview.com/article/medical-malpractice-cau...