Saturday, September 5, 2020

Published September 05, 2020 by with 1 comment

Interesting Statistical Paradoxes You Might See With COVID-19

Some trends might appear baffling but have really simple explanations. Here's my guess on two that we might see. They are both examples of sampling bias.

Wages might increase as the economy suffers

Depending on how it's calculated/reported, you might see wages increase even though the economy is suffering. For an example of why this might happen, consider the following simplified workforce:

100 people making $100,000/year, and 100 people making $20,000/year

If you just take the average wage for each worker, you'll find that it's $60,000/year. Now, imagine that due to covid-19, 5% of the high-earners and 25% of the low-earners lose their jobs. Now the workforce is:

95 people making $100,000/year, and 75 people making $20,000/year

The average wage for each worker is now ~$65,000/year. Average wages increased by ~8%. 

The real wage distribution is obviously not that simple, but the basic principle holds. If more low-earners than high-earners are laid off (which is the case...restaurants, basic travel services, etc. have had way more layoffs than software companies), you will paradoxically see wages increase with a poorer economy. To get a better feel for this, we'd need to report something like 'median monthly pay per working age adult'.

Case fatality rates might lower without the virus becoming less deadly

We locked down early on, it's been summer, and children don't work. Thus, children have not really been as exposed to the virus as much as adults have. Imagine as a simple example that the case fatality rate by age is:
  • 5% for 70 and up
  • 0.01% for 10 and down
  • 1% in-between those two
Imagine then that from June through August, the cases were:
  • 10,000 70 and up
  • 10,000 10 and down
  • 100,000 for all others
You would have expected 1501 deaths out of 120,000 cases, so the case fatality rate would be ~1.3%. Now, imagine that schools open and children are all exposed to the virus. Everyone else keeps getting it, so imagine that September through November results in the following cases:
  • 10,000 70 and up
  • 100,000 10 and down
  • 100,000 for all others
Now, you would expect 1510 deaths out of 210,000 cases, so the case fatality rate would be ~0.7%. The virus didn't get any less deadly and the infection rate for adults didn't slow down, but the exposed population changed so the fatality rate went down.

There is a similar one to this one with death reporting. New York reports Covid-19 deaths more accurately than many other states (Texas and Florida for example) and was hit hard early on. If New York reports 90% of Covid-19 deaths accurately and Texas reports 50% of them accurately, then even if the virus is just as deadly in Texas as New York, it will appear that the virus became much less deadly while really it is just being reported less accurately. We saw this early on in Europe also with Belgium reporting more accurately than other countries and showing an apparently higher death rate. The best way to handle this will likely be to look back at excess deaths after a year.


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