What the Statistics Tell Us about CoVid-19

by Michael Alexander, PhD 

Not only are we all scared of CoVid-19, we’re all victims of the confusion and anxiety from conflicting claims about the disease. We don’t have to be. This paper will discuss the data that is available, what it tells us, and different ways to look at it.

In the interest of full disclosure, I am a doctor, but not a physician. I am a doctor of economics, specializing in statistical analysis of data, with several decades of experience in that area.

At a recent event, I was asked my favorite way to lie with statistics. In response, I quoted an old Brewster Rocket cartoon, “85% of all statistics are made up on the spot, including this one. And five people out of four, don’t understand them.” In fact, the best way to lie with statistics, is simply to present numbers and then incorrectly interpret them for people. This paper will help you be aware of the misleading statements and statistics out there on the Corona virus.

We’ve seen scary numbers like this:

Worldwide1

Coronavirus cases: 1,141,069

Deaths 61,199

Usually, we don’t hear one other important statistic

Recovered 238,492

In other words, 20% (238,492/1,141,069) of the people who have contracted CoVid-19 have already recovered, that is is roughly four times (238,492/61,199 = 3.9) as many people have recovered from the disease as have died from it. What else does the actual data show us?

First, an explanation, CoVid-19 is the Coronavirus disease, caused by SARS-CoV-2 Severe Acute Respiratory Syndrome Coronavirus 2. It is called a “coronavirus” because of the way it sits like a crown (“corona”) on the surface.

Now, back to the statistics:

The six countries with the highest reported Coronavirus cases are as follows:

Table 1

And within the United States the top ten number of cases are distributed as follows

Table 2

 Clearly, the United States has a larger number of cases than any other country, (more than one quarter of the cases world wide), and New York has the largest number of cases of any state in the USA. But, that does not present an accurate picture.

First, I want to want the reader that I am only analyzing the official numbers, and they probably are not right. As an example, look at the reported cases in China:

 Not only are they reporting no new cases, but they also are reporting a rate of recovery of 96% which is not credible, given the experience in the rest of the world (technically, the 96% is “recovered or released,” and not necessarily “released healthy”):

 And, of course, there are a number of untested people worldwide, and that means the data is approximate, not exact, but that is all we have to work with. So, take all of these numbers with a grain of salt, and remember, the purpose of this paper is to give you new ways of thinking about the data.

If we look at Table 1 again, which shows that the US has the largest number of cases, we should remind ourselves that the US population is much larger than that of the other countries (except for China, who’s data is suspect) that we see on that list. If we look at the number of cases and deaths per person, we see a different result.

Table 3

 The USA has less cases per million than any other country in the top 5, and less deaths per million than all of them except for Germany. The media keeps saying that the USA is now the epicenter of the disease, but in fact, 180 countries have more cases per million than the USA, and 126 countries have more deaths per million than the USA.

What can we tell about how fast the CoVid-19 is spreading? Normally we see graphs like these

 But, while these tell us the number of cases is accelerating, they are hard to interpret. Let’s look at it this way, if one person infects another person, then there are two people with the disease. If the next day, they both infect one person then there are four people with the disease (the first two, plus the two newly infected.) Then there will be eight people, and so on. On the other hand, if one person infects two people, then the next day there will be three people with the disease, then nine, then 27, and so on.

This is called “exponential growth,” and is to be expected in cases of contagious diseases, and would be expected to look like the two graphs above. But those graphs don’t give us a feeling of whether the rate of infection is getting better or worse.

Mathematicians know that if one plots an experiential growth rate on a semi-log graph, the curves will look more like lines, the slopes of the lines showing how fast the rate of contagion (the rate at which the number of cases is increasing or decreasing, in this case) is. So, instead of looking at the data using graphs like the above, we should look at graphs on a logarithmic scale like the following:

 These show that the rate of growth in the number of cases slowed in mid – February and then picked up again after about a month. We will come back to this concept a little later.

Before I do, however, I want to talk about how dangerous the disease actually is. Originally, we were told that doctors expected the fatality rate would be about 2 or 3 percent. What does the data actually show?

Table 4

Worldwide 5.36% of the cases have already resulted in death (which is more than the 2-3% estimate) and 2.76% of the cases in the USA have, the USA has had a lower mortality rate than the rest of the world, but it has also had a lower recovery rate (4.56% for the USA vs. 20.90% worldwide… but, of course, China’s dubious numbers will affect the worldwide comparison). But, of course, not every case has been resolved, presumably more currently infected people will die, raising that number. Note that if you look not just at deaths, but also at “serious cases” (which include major long term respiratory scaring, among other permanent concerns) the numbers are 4.74 percent of cases to date in the USA, and 8.84% of cases worldwide.

Our numbers are, of course, colored by the fact that worldwide only 26.26% of cases have been resolved (either through recovery or death), and the number for the USA is lower, 7.22% But, this also leads to the question, what percent of the resolved cases ended in death? The answer is 20.42% worldwide, and 36.92% in the USA.

One more question which the data may help us to understand. Are the quarantine and “stay and home” orders working? To answer that question, lets go back to the logarithmic graphs. In theory, if the rate of infection is slowing, then the graph should become flatter. That is, in fact, what we see.  

Comparisons between countries may also prove instructive. The USA and Taiwan reported their first cases on the same day, Jan 20, 2020. Yet, the resulting number of cases and deaths are very different. The USA has 279,355 cases or 844 per million in population, whereas Taiwan has only 355 cases, or 15 per million. USA’s recovery rate is 4.56% as opposed to Taiwan’s 14.08 recovery rate.

Table 5

 The statistics do not give us the reason for Taiwan’s more desirable experience, but one theory is that, while Taiwan does not have stay at home orders, wearing medical masks is common place for them (One can even see their news anchors wearing masks on the air), and, while we have been told that wearing medical masks does not stop one from getting the disease, it does stop someone with the disease from spreading it, which means that wearing a mask is a form of preventative quarantine.

Looking at the data, seems to bear out the effectiveness of the masks. The initial rate of infection in Taiwan was slow, however, due to the increased demand, they encountered a shortage of masks in early March which meant that two weeks later (the incubation period of CoVid-19) the number of cases took a sharp rise. However, after a short delay, Taiwan was able to make and distribute new masks to their population. The data shows the effects both of the shortage and the return to a significantly slower infection rate:

I am hopeful that you find this sort of analysis useful, and that it permits you a different view of the situation than just listening to the pundits would. Feel free to download some data, load it into a spreadsheet, and play around with it. Maybe you want to look at how well countries with socialized medicine do with respect to ones who don’t have it. Maybe you want to compare the results from different countries with different climates. My point is, that you can look at and play with the data. Which, if nothing else, gives you something to do while sheltered in place.

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Michael Alexander has a PhD in Economics from the University of Minnesota. He is currently the operating as an expert witness and economic consultant with Alexander Economics, and as a public speaker with Alexander Talks. He is a Fellow of the International Innovative Institute. For more information, consult his Linked-In page: linkedin.com/in/alexander0

1All numbers and tables are based on the data as of April 4, 2020 My primary data source was https://www.worldometers.info/coronavirus/#countries and https://www.worldometers.info/coronavirus/country/us/