How is time to death calculated in terminally I’ll patients?
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From what perspective are you asking?
There’s a a group of statistical methods broadly known as survival analysis or time-to-event that are used to, amongst other things, determine the survival (or time to death) of terminally ill patients. Obviously it depends on several factors and can only be expressed in terms of estimates for the population based on observed data (true of all research) so you can never be certain of time to death in an individual. As others have noted, you might be able to say something like, for a female with stage 3 breast cancer of your age, 50% of people live longer than X years. But you could never say to someone, you will die in 3 months. Obviously the closer a person gets to death from a terminal illness, the more obvious it becomes and you can be more certain.
From another perspective, as others have noted, doctors have experience with various illnesses and can make general statements about how long a person might expect to live. But they won’t (shouldn’t) give very precise estimates because it’s very easy to be wrong. You don’t have to look very hard to find examples of people being told they only had months to live and are still kicking around years later. Unfortunately the opposite can also be true (die much sooner than expected).
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