Coronavirus: estimating the death toll in Switzerland

COVID-19 has hit the world fast and we are racing to understand it, while struggling to come to terms with its deadly impact.

When trying to estimate the impact, it is tempting to take the current number of deaths and divide it by the number of reported cases to find a death rate. In Switzerland this rate is currently 1.2% (122 / 9,877). However, this percentage is misleading. Here’s why.

Jumping the gun

If we divide the current number of deaths in South Korea with the current number of cases so far we get a death rate of 1.3% – 120 deaths / 9,037 reported cases. If we do the same for China we get 4.0% – 3,277 deaths / 81,171 reported cases.

The problem with these calculations is that many of cases have not yet concluded in one of only two possible outcomes: recovery or death. In South Korea, 60% of current cases still have an unknown outcome.

It is therefore more meaningful to look at the death rate among concluded cases. In South Korea (120/3627) and China (3,277/76,436) these percentages are 3.3% and 4.3% respectively, far closer together than the percentages above (1.3% vs 4.0%).

The same percentages of outcome-based deaths in Italy (45.0%), Iran (17.8%), Spain (42.5%), USA (64.9%), France (25.1%), Switzerland (48.2%) and the UK (75.8%) are currently alarmingly high. Switzerland’s rate of 48.2% is calculated by taking the 122 deaths so far and dividing this by the sum of the deaths (122) and recoveries (131) so far.

Globally, this rate is currently 14.7% (18,605 deaths / 18,605 + 108,312), with the outcomes of 290,759 (70%) current 417,676 cases still unknown.

At the beginning, these outcome-based death rates are unreliable because the low number of outcomes is unlikely to be representative of total infected cases. For example, the 253 concluded cases in Switzerland might be on average more fragile than all of those infected. But we don’t know.

Interestingly, Germany’s outcome-based death rate is relatively low (4.6%). One theory is that many of the early cases in Germany were healthy young people who caught the virus skiing. So far only 10% of Germany’s cases have reached an outcome.

Not spreading the net wide enough

Testing practices vary from country to country. Some countries, like Switzerland, have limited testing capacity and have been forced to ration it. Switzerland is testing only those with severe symptoms and those in high risk groups. This will understate the number of cases of infection.

All those who are infected but aren’t tested, never end up in the reported case number so they don’t end up in the recovery or death numbers either. By inadvertently cherry picking the worst actual cases, Switzerland’s testing policy pushes up the outcome-based death rate, making it poor indicator of what might happen at a total population level.

Other places, like China and South Korea, where they track, trace and test a high percentage of suspected infections, have more complete confirmed case numbers. The reported case numbers in those places are higher and more meaningful. As a result, we would expect death rates there to be lower and more meaningful for the total population.

South Korea has tested 5,680 per million and Italy 3,020 per million. The number of tests in Switzerland is unclear. Some reports suggest a current test rate of 2,000 per day, so over the last 10 days Switzerland might have tested 20,000 people, a rate of 2,330 per million, putting it ahead of the UK which has tested fewer than 1,000 per million but behind countries like South Korea.

Another challenge is counting infected patients with mild or no symptoms. Tracking helps. If you test those without symptoms who have been in contact with someone with symptoms you’ll catch some mild and asymptomatic cases that would otherwise go uncounted. However, it is likely that some mild or asymptomatic cases will slip through the net at some point, even with rigorous testing and tracking. Some analyses suggest that even in China, a large number of infections were not identified as cases and counted. We just don’t know. Another study adjusts the fatality rate in Hubei from 5.1% down to 1.4% by modelling in an estimated number of uncounted mild or asymptomatic cases.

Skewed samples

A number of analyses have referred to the low death rates on the cruise ship Diamond Princess. However, this is a small (712 cases) unrepresentative sample. These people chose to go on a cruise. They do not represent a cross-section of the population. The outcome-based death rate on the Diamond Princess so far is 1.7% (10 / 587) with 16% of cases yet to reach a conclusion, so there is a wait and see element here too.

Infected groups in places where they acted preemptively, such as in Guangdong province in China, are likely to be skewed too. In Guangdong, which has a population of 113m, only 1,428 people were infected and only 8 have died so far. The outcome-based death rate among those infected in Guangdong is currently 0.6%. We can speculate that this group were healthier than average, perhaps because they were younger working people who had early contact with the virus. But this is a guess. By contrast, the death rate among those infected in China’s Hubei province was 5.0% (3,160 / 3,160 + 60,324). Here we can speculate that the disease hit a broader cross-section of society, providing a figure more meaningful for the total population.

Counting and cause

Counting deaths is far from clear cut. Every death is assigned a direct cause of death 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 Covid-19 victims. In the UK, NHS England confirmed that Covid-19 is acceptable as a direct or underlying cause of death for a death certificate. However, the potential for confusion remains. In addition, establishing the cause of death of people dying outside of the hospital system where there is little medical intervention can be difficult.

How many could die in Switzerland?

Currently, Switzerland has 9,877 recorded cases, 131 recoveries and 122 deaths. The current outcome-based death rate is 48% – this is calculated by taking the 122 deaths so far and dividing this by the sum of the deaths (122) and recoveries (131) so far.

Given Switzerland’s testing and tracking policy and the time elapsed since the beginning of the outbreak, the actual number of infections is likely to be substantially higher than the 9,877 reported cases. If we assume that Switzerland should have a similar outcome-based death rate to China (4.3%), then the current actual number of cases of infection in Switzerland would be more than 110,000 (48%/4.3% x 9,877).

However, this case estimate of 110,000 cases should to be taken with a pinch of salt. Switzerland current outcome-based death rate of 48% is based only 2.6% (253 / 9,877) of cases.

Given the unreliability of both the death rate so far (48%) and the number of reported infections (9,877), can we instead use Chinese data to predict the number of deaths in Switzerland?

Maybe.

Given Switzerland didn’t respond preemptively like the Chinese did in Guangdong and other provinces outside Hubei with low death rates, it is highly unlikely to follow this path. Places like this probably acted before the virus infected a broader cross section of the population, and, they avoided overloading their hospitals.

China’s Hubei province might be a better fit, although it could be argued that Hubei’s 5.0% mortality rate needs to be reduced to reflect the estimated number of mild or symptom free cases that went unrecorded. If we assume 50% of cases went undetected, Hubei’s infection rate would drop to 2.5% – others have gone further.

To reflect the likely continued spread in Switzerland we could take a guess at the percentage of the population that will end up being infected. So, hypothetically, if 10% of Switzerland’s population became infected (857,000) around 21,000 would die, if we applied the adjusted Hubei reported case death rate of 2.5%. Using the same maths, if 50% of Switzerland’s population became infected (4,285,000) around 107,000 would die.

If Switzerland’s hospitals coped better than Hubei’s, the death rate might be lower. On the other hand, if Switzerland’s population proves less resilient than Hubei’s it could swing the other way. On top of this, it is difficult to know what percentage of Switzerland’s population will become infected – a leaked government document in the UK estimates that up to 80% of the population there could eventually be infected. The extent and rate of spread is in Switzerland is unknown too. Testing and tracking has been too patchy in Switzerland to know how many are infected and where the number might go. Mild and asymptomatic cases add to this challenge.

A paper by pandemic experts suggests considering a range of fatality rates from 0.25% to 3%. Another study adjusts the fatality rate in Hubei down to 1.4% by modelling in an estimated number of uncounted mild or asymptomatic cases. These rates are all higher than the fatality rate of flu, which is around 0.1% – CDC estimate for the US.

In reality, we will only know the true number of Covid-19 deaths in hindsight. And even then, given the ambiguity around assigning a cause of death, we won’t know for sure.

More on this:
Underlying numbers from Worldometers.info (in English)

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