> Your formula has the opposite problem, by looking at cases that have a known outcome you are biasing results towards cases that end quickly (in particular case that end in death).

Unless I'm mistaken, that would only be true if cases that end in death are much faster than the cases that end in recovery. I have found it difficult to find detailed statistics on the topic, so I cannot tell you that it's definitely true or not, but I agree that it's an important variable that should be taken into the equation.