Yesterday, we reached into our toolkit and pulled out behavioral economics and Bayesian Inference.

Our big conclusion in that post was that if C-19 tests are 90% accurate and 5% of the people in our reference group are walking around infected, then roughly __2/3’s__ of all people who get positive test results are not infected … they’re so-called __false positives.__

*See our prior post If I test positive for COVID, am I infected?**for an explanation of the method and a walk-thru of the analysis leading to that conclusion.*

Now, let’s change one of our assumptions.

In the prior post, we assumed that we were __asymptomatic__, have been __sheltering-in-place__ (i.e. minimal social contacts outside of our homes) and __don’t work in a COVID-prevalent environment __… and we used **5%** as our base rate (of virus prevalence among our reference group).

Now, let’s assume that the reference group we’re working with is __elderly__, has a __comorbid__ medical history of respiratory and heart problems and is experiencing COVID-like __symptoms__ (high fever, persistent cough), have __had contact__ with an infected person. That’s essentially the only group that initially qualified for coronavirus testing. Lets, assume that** 75%** of the people in that reference group are, in fact, infected with the virus.

Here’s the Bayesian results chart would look like:

**The question: what is the likelihood that the people who fit this profile are correctly diagnosed as having the virus (or not)?**

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We plugged in our key assumptions: **90% testing accuracy** (the yellow box above Colum 2) and **75% infection prevalence** for this specific reference group (the yellow box in Column 3, Row 3).

Again, refer back to ourprior postfor a walk-through of the calculations done to construct the table.

The answer to our headline question: “I tested negative, so I’m not infected, right?” is “maybe but…”

Since the test is 90% accurate, 90% of the infected people will, by definition, test positive … but there’s a statistically significant number of infected people who get a negative test reports (Column3, Row 2) … i.e. they are __false__ negatives.

In fact, **25%** of the people from this high infection reference group **who get negative test results are infected.**

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Note that in Column 5, 70% of the sample get positive test results.

But, we assumed that the reference group being tested has a 75% infection rate.

Where did the other 5% go?

Again, it’s those 75 people who are infected but get negative test results – the __false__ negatives.

These people — depending on the severity of their symptoms — would quite possibly be diagnosed as having pneumonia (or some other infliction), prescribed some medicine and sent home to recuperate.

The good news: a hospital bed wouldn’t be allocated to them (which was a very high priority in the early days of the pandemic).

The bad news: there’s always the risk that their condition will deteriorate … and, anybody who comes in contact with them during their recovery would be put at risk of getting infected.

**The simple solution to avoid inadvertently putting infected people back into the population ****is to give people from a highly likely to be infected group ( think: those with symptoms) who test negative a second test to confirm the diagnosis.**

Trust me, if the retest is done by a different medical crew on a different day using a different test kit, it’s statistically very unlikely that they would get another false negative test result. If they test negative again, they’re virtually certainly not infected.

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__Takeaways__:

Bayesian Inference tells us to always consider __specific observations__ (i.e. test results, witness accounts) in the __broader context__ (i.e. the __base rates__ of the reference group being evaluated.

The base rate depends on __virus prevalence__ in the relevant local area (town, workplace, hangouts), __mitigation behavior__ and__ symptomology__.

For COVID, that means, at a minimum, sorting people into at least 2 categories: asymptomatics who have a relatively low probability of being infected and those presenting with symptoms who have a relatively high probability of being infected.

For the former group, the asymptomatics, the biggest risk lies in false positives that potentially waste test & track resources on wild goose chases.

The risks for the symptomatics are false negatives — failing to provide appropriate, timely treatment and returning infected people back into the population, quite possibly spreading the virus.

90% testing accuracy is good. but not good enough.

To mitigate the risks (false positives for asymptomatics; false negatives for those with symptoms):

- Retest positive testing asymptomatics before contact tracing based on their test result, and
- Retest those with symptoms who test negative before returning them to the general population).

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