# Why is CFR calculated this way it is? [duplicate]

Good afternoon everyone! I am only 17 years old, and this may sound like a stupid question...

First way

Anyway, we currently calculate the "case fatality rate" by dividing the number of patients who have died from a specific disease by the total number of those who got infected.

Second way

However, why don't we calculate the CFR by dividing the number of patients who died by the number of patients who had been successfully healed plus the ones who have died?

Explanation

I understand that maybe the data we have isn't enough nor accurate to use that reason once a country could have only 100 cases, which out of them, 70 died, and only 30 recovered - giving a false CFR having in count time.

Besides that, I also have read this article: Does COVID-19 have a mortality rate of 41%?, in which they explained why the second way of calculating CFR approaches the first one.

But that isn't necessarily true. Let's take, for example, the case of COVID-19 in Italy. Because of the older population, the mortality rate is expected to be a lot higher in Italy than in China (about 7.2% compared to 2.1%). Nevertheless, the statistics have been constant for a long time, remaining at almost 45% of death ratio (if calculated using the second way). This doesn't make any sense, but it also looks more accurate than 7.2%. If we take on mind that only 10,950 people recovered from the 20,084 closed cases, the numbers seem right.

I also have in mind that the second way of calculating the CFR doesn't apply to all ages and genders once a 40% mortality rate can't be applied to people <20 years the same way it is to people >60 years. The second way doesn't assume all of the population from a specific country. Although, neither does the first one. If we have to count the real consequences in a general way, isn't this the most appropriate way of calculating it?

Question

Why should we use the total number of cases (active cases + deaths + recoveries) to calculate CFR if the active cases didn't have an outcome yet?

• If you read my recent answer to other question, the first thing to note is that you need a confined sample for a true CFR. And besides trying to rehash that argument here, I don't quite understand what you're saying in the 2nd part of your question. Yes, obviously, if you want to apply a correction factor from one sample to another, you need to account for the different age distribution between samples. But what is your question (on that) actually? – Fizz Mar 27 '20 at 19:26
• It is obvious that 45% of people are not dying from COVID-19. The bigger concern right now is that more than 45% of people who are infected may show zero symptoms. So, the next step is to figure out why that number is so wrong rather than using it to try to argue other numbers are wrong. One reason might be that in a place where there aren't enough facilities to handle all the critically ill patients, doctors aren't making much effort to declare cases as "recovered". Another is that with exponential growth, most of the cases are still new. Hospitals in Italy are a disaster zone right now. – Bryan Krause Mar 27 '20 at 19:40
• Needs to move to biology.stackexchange.com/questions/tagged/biostatistics – Graham Chiu Mar 27 '20 at 19:53
• @BryanKrause Would this be accepted in Biology? Seems like it would be more appropriate in Cross Validated. – Carey Gregory Mar 27 '20 at 20:29
• @CareyGregory I'd prefer it closed as a dupe of the post I marked; it doesn't add anything logical that the question there doesn't already involve, and the answers there already answer it. – Bryan Krause Mar 27 '20 at 20:30