# Is there any significance in reporting COVID-19 cases by population?

Many news outlets are reporting total COVID-19 cases by country and then comparing them to other countries. For example, comparing the total cases in the United States vs the total cases in China. As of April 3rd, 2020 this shows that the U.S. has more cases than China. However, there is virtually no mention of comparing total cases of each country by population which would put the U.S. far below the top. Is there a reason why comparing cases by population wouldn't be significant (from a medical or statistical point of view)? These statistics seem to be ignored by news outlets or are not mentioned at all.

• Apr 4, 2020 at 0:30

As long as the numbers are small, the per capita numbers don't really matter much. Epidemics of infectious diseases spread initially in localized populations, so imagine the case of a disease spreading mostly around a hospital, which is common early on:

• In one country, a hospital at the epicenter has 50 infected patients. That country has 5,000,000 people.

• In another country, a hospital at the epicenter has 50 infected patients. That country has 500,000,000 people.

The situation is basically the same in both countries: they have a single epicenter with a bunch of patients. There are probably a similar number of unknown cases in the community. If you divided by the total population, you might think one situation is 100X worse, but it really isn't: it's one center. The vast majority of both are still unaffected, and the severity at the epicenter is exactly the same.

Now we are at the point of extensive community spread in many places. So now per capita might start to be meaningful, but there are some remaining limitations:

Testing is not uniform

100 cases in a place with extensive testing does not mean the same as 100 cases in a place without, so case counts aren't very informative. When the numerators aren't comparable it doesn't matter so much that the denominators are different: you have to consider each number on a case-by-case basis (and the "race" in the media is not really that relevant).

Some argue deaths are a better measure, and I would agree, but those are also limited by reporting differences.

Cases are not distributed randomly within borders

Taking the United States as an example, the US per capita number of cases doesn't tell the whole story, which is that certain geographic locations like New York City and New Orleans have substantially more cases per capita than the rest of the country. Same for Lombardy in Italy; Wuhan in China. Averaging those cases over the entire country doesn't do much to reflect the concentration of cases in places where the health care system is stressed to its limit.

So what should we use instead? In many cases I would recommend looking at logarithmic scale data. These tell you what the rate of change is. Even these are not perfect, as both testing and mortality can vary over time (both because of availability of tests and triage as the situation gets more serious), and they may not be the best data for a specific purpose. What they do show is how the rate of increase differs in different countries, and how the rate of increase changes over time in a single country.

For the US, these data: https://www.us-covid-tracker.com/?log=0&consistentY=1&per100k=1&field=deaths&time=1mo might be helpful for assessing the extent to which different states have been affected (and shows why California is not making as much news despite having a lot of cases). I think this is one case where non-log-scale per-capita data are informative.

It's the simplest measure, the absolute number of cases. The second graph you showed gives us the relative case rate based on a per million of population. Now if for instance the while population of a country succumbed to the disease, the population is now zero. So their number of cases now becomes zero because everyone is decreased. So, that's extreme but the absolute number doesn't have that fault in it.

Most people are more interested in the acceleration curves which is simply the number of diagnosed cases over time. And that's what they show us.

There's no perfect statistic.

Percentage and raw counts serve different purpose:

• Raw counts are one way to get a feeling of the impact on the population (50k deaths gives a different perspective than 0.1%, especially for people who don't know population sizes).
• Percentage are another way to get a feeling of the impact on the population (e.g., black plague is estimated to have wiped out up to 50% of the European population) and also allow for comparison (e.g., a random walk in Switzerland is significantly more dangerous than in China).

Note that, as {1} mentions, case and death counts depend on how testing is done and on how testing is done and how to decide that a death is due to COVID-19.

FYI, updated percentages for all countries: https://www.worldometers.info/coronavirus/

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