The “real” number of people infected with coronavirus

This is the $ 1,000 question these days: how many people are actually infected with coronavirus? For true, there, not only what the official statistics say, because it is absolutely certain that it is not much more than the some 153,000 “laboratory confirmed cases” of the WHO. But by how much, exactly? Is it five times more than the “official” number? Or 10 times more? Or even more? Listen, a text that circulates abundantly these days on the web even advances the dropping figure by 27 times more!
The truth is that we still know nothing of it definitively. We will not really be fixed until we have completed “serological” studies, which look at the presence or absence of antibodies in the blood of a large number of people. But works like that take quite a long time to carry out, while waiting, we are reduced to being content with estimates, mathematical models, sometimes even vulgar rules of three. The results are very variable and, as is almost always the case in this kind of situation, it is the most spectacular figures – but not necessarily the most solid – which have the greatest impact on the web. Unfortunately…

The best example is undoubtedly this text which appeared on the Medium site last week and which has had literally global success, having been translated into 26 languages ​​and counting more than 28 million “visits” ( views ) countless mentions in media, blogs and websites around the world. One of its main conclusions is that the true scale of the epidemic, in terms of the number of people infected, would be 27 times greater than what the “official” figures show. Twenty-seven times!

Its author, a certain Tomas Pueyo, has obviously made a serious effort of documentation and, obviously, he can play with numbers. The problem is that his skills in this area stop there: he masters math (having two degrees in engineering) and he has done a lot of reading on the internet. For the rest, he is not particularly familiar with epidemiology and his conclusions differ greatly from analyzes carried out by real experts – but which never went viral, I will come back to this immediately.

His text is a bit confusing, in the sense that he presents several different approaches to estimate the real number of cases, and that he launches many different figures without always explaining which figure was obtained with which method. But as far as the “27 times” is concerned, it’s pretty clear. Mr. Pueyo started from the case of the city of Wuhan, where the famous public market was where the first cases of infection appeared. He took January 23 (when it was quarantined) as the cut-off date, then compared two stats: the total number of cases that had been diagnosed before January 23 (444 cases) and the number of cases whose date estimated infectionwas before January 23 (about 12,000). This means that on January 22, China had identified 444 patients in Wuhan when in reality there were 27 times more.

It is a clever way of proceeding, which undoubtedly did not deserve to be described as “picked up on nonsense” as some have done.. But the problem is that it does not come out of the confirmed case figures, it only compares the confirmed cases counted in two different ways. On the one hand, that is not what interests us, it is the real number that we want to know. On the other hand, it is a method that can be biased for the penalty if the screening effort is not constant – or precisely China has increased its efforts over time, which has logically inflated the results of M Pueyo. And then he suggests that his multiplier is applicable to the rest of the planet, which is very questionable because the surveillance measures vary from one country to another (which he also admits elsewhere).

But anyway, if not 27 times more, then what is it? If I were to do my own corner table calculations (and the rest of this paragraph is nothing more than that, I emphasize), I would simply compare the rate of mild infections with the rate of severe / critical infections . According to Chinese Public Health figures , 81% of people infected would do little more than a flu without any particular complication (or reason to go to the doctor), but the disease would degenerate into severe pneumonia in 14 % of cases and would lead the remaining 5% to intensive care. It’s pretty rude, but it already gives us what our neighbors to the south call a ballpark estimate: It is reasonable to assume that most people with severe (or worse) pneumonia will at least seek medical attention, and that these cases have a relatively slim chance of going unnoticed. There are certainly some in there who still escape public health statistics, but a priori the real number of patients should not, in principle, be enormously higher than that: 20% of serious cases, it suggests a detection rate which should be around 1 in 5.

To have a rate of 1 in 27, the majority of people in serious or critical condition would have to decide not to go to the doctor and to treat themselves at home. It does not seem very likely to me.

In what I’ve been able to find, there are two serious studies on this issue that have been done by real epidemiologists with real, solid models – not corner calculations. One has been available since this morning on the Science website and she estimates that in Wuhan before the quarantine on January 23, 1 in 7 cases was “documented” and that the others went unnoticed. This ratio can vary depending on the degree of surveillance, but in general, it would be a “worst case scenario” since practically all governments in the world have been on the alert for weeks, even months.

The other is available on merRxiv , which is a pre-publication site where articles appear without going through peer review. Its results are therefore to be taken with a grain of salt, but let us mention that a team of statisticians reviewed it and deemed it solid . This study estimates that the “official” cases represented a quarter of the total cases in the province of Hubei on February 11, therefore a ratio 1 on 4.

Add to this that epidemiologist Trevor Bedford of the Fred Hutchinson Cancer Research Center (Seattle) spoke of “detection rates of roughly 1 in 10 cases” on his Twitter account . Again, we won’t know for sure until we finish a couple of large serological studies, but all of that gives us a range – between 4 and 10 times the official cases – which is very, very likely much closer of reality as the factor of 27 which has been so much talked about since last week.

To be completely fair, it should be specified here that Mr. Pueyo does not speak explicitly of detection rate (the cases detected vs the real cases, regardless of the time it takes to find them ), but of a ratio to a specific point in time. Putting all these results in parallel as I am doing here is therefore somewhat artificial. But it must be said that Medium’s text is not always clear in this regard, and that it has been widely interpreted as a detection rate – this seems to me the most problematic.

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