Single word request: cancer patients' prognosis is bad (serious)
Solution 1:
I think you could use poor.
Cancer prognosis is poor.
About prognosis, M-W says it means:
the prospect of survival and recovery from a disease as anticipated from the usual course of that disease or indicated by special features of the case
The example it gives is
The prognosis is poor because of the accompanying cardiovascular disease.
This NGram also shows that charcaterising prognosis as poor is the most common:
It is also true if you search with a wild cart.