Suppose that in a given population, 200 people were diagnosed with a disease, of whom 10 died from the disease, 40 have fully recovered and the remaining 150 are alive but not cured.
To my understanding, case fatality rate is defined as the ratio Number of deaths / Number of individuals diagnosed with the disease. In this example: 10 / 200 = 5%.
I don't understand how to interpret this ratio. In the example above the majority of individuals diagnosed with the disease are neither dead nor healed, so why do they count towards the case fatality rate defined above? Depending on whether they survive or not, this will impact differently the ratio, which seems to be an undesirable property. Instead, why not compute
number of deaths / (number of deaths + number of healings) = 10/(10 + 40) = 20%
which is the fatality rate restricted to individuals that are either dead or cured. Those two ratios will agree when the disease has eventually disappeared, but at the begining of the epidemic they can take very different values. Can you explain why the former is preferred even at the begining of an epidemic? Thanks for your help!
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