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It would seem in a emerging epidemic, where the time to resolve a disease is long, an evaluation might be used such as:

(predictive mortality rate) = (deaths) / (deaths + resolved)

Is this a standard metric? And if so what is it called?

It would seem that this kind of metric would be a predictor as to the ultimate mortality rate, unadjusted for treatment advances. The intent is to describe the demonstrated mortality of those who have acquired the disease, without influencing of the number of people who have acquired the disease. This would be helpful where R0 is large and/or Specific Interval is small. However I cannot find references to a metric similar to this. Pointers appreciated.

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The problems with the measure you've proposed have been addressed on MedicalSciences.SE:

https://medicalsciences.stackexchange.com/q/20970/8728

The short version is that this measure isn't very informative while there are unresolved cases, because it ignores what is known or expected about those unresolved cases, and it is not a standard measure.

In the long run (when almost all cases are either recovered or dead) it approaches the case fatality rate because the denominator of (resolved + deaths) becomes equal to the total number of cases. Until then, it doesn't tell you much at all.

You could track the case fatality rate over time based on time of initial diagnosis to look at effects of new treatments.

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