Coronavirus: the fallibility of fatality rates

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Naturally, many of us would like to know the fatality rate of Covid-19. But at this stage it is guesswork. Here are some of the problems with two of the most popular fatality rates.

The most popular calculation involves dividing the number deaths by the number of cases. Epidemiologists call this a naive case fatality rate (CFR). There are two ways to calculate this rate.

The all-in rate

The first is to take the number of deaths so far and divide it by the total cumulative number of cases recorded. This figure is currently 1.6% (191/11,712) in Switzerland.

There are several weaknesses with this rate, the most critical is timing. At the beginning, because few patients have reached an outcome (recovery or death), the rate is misleadingly low. The fates of most cases are unknown. Currently in Switzerland, only 322 patients (3%) have reached an outcome – 191 passed away and 131 recovered. The fate of the remaining 11,390 patients is unknown. As more patients reach an outcome the current rate (1.6%) is, sadly, almost certain to rise. Essentially, it is a decent measure once all or a majority of cases have concluded. But early on it is a poor predictor.

The closed-case rate

The second method involves taking the number of deaths so far and dividing it by the sum of the number of deaths and recoveries so far. This figure is currently 59% (191/322) in Switzerland.

This number is the death rate of closed cases. It doesn’t suffer from the timing issue of the all-in rate, so it’s more meaningful.

However, its predictive power is limited. We don’t know if the remaining 97% of cases in Switzerland will die at the same rate as the 322 cases closed so far. As time goes by, this rate becomes more reliable. In Italy this rate has been around 40% for over a month.

It is possible that the first few cases in Switzerland might have had unusually poor underlying health. The remaining cases might be unusually healthy and recover at a higher rate, bringing down the overall figure. But we don’t know. Only time will tell.

Common weaknesses

Both of these simple calculations share two other weaknesses.

The biggest is uncertainty around the number of cases. This is a particular problem with Covid-19. Many cases appear to be mild or asymptomatic, especially among young people. Testing policies play a big part in the accuracy of this figure. South Korea conducted 364,942 tests and found 9,241 cases. Switzerland did 91,400 tests and discovered 10,714 cases. South Korea’s lower rate of positives (3%) suggests it cast the net wider than Switzerland (14%) and therefore has a more accurate case number.

Modelling done recently by Sunetra Gupta, an infectious disease expert at Oxford University, suggests half of the UK population might have already caught the virus. If true the CFR in the UK would drop dramatically as the number of cases relative to deaths shot up.

The next common weakness is uncertainty around the number of deaths. Every death is assigned a direct cause along with a list of things that contributed. Given that some dying with the coronavirus will have other potentially deadly illnesses, it is possible these illnesses end up as the main cause of death on the death certificates of some dying with the Covid-19 virus. In the UK, NHS England has confirmed that Covid-19 is acceptable as a direct or underlying cause of death on a death certificate. So potential for confusion exists. This can be more of a problem for people who die without going to hospital.

Beyond these simple calculations, there are many sophisticated mathematical models, however they all rely heavily on similar inputs.

As the philosopher Ludwig Wittgenstein said: “nothing is so difficult as not deceiving oneself.”

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