By Douglas Moran
Obsolete Guesstimates Keeping Businesses ClosedUploaded: May 28, 2020
If you had a mathematic model that produced the same result despite substantial changes in crucial parameters, would you use it in important policy decisions? Apparently the State government does. Case in point, counties cannot proceed to the next stage in opening up from the lockdown until they are daily testing 0.15% of its population (and other criteria). Santa Clara County doesn't qualify because its testing rate is only 0.10%. From what I can find, the 0.15% testing rate was chosen back when testing rates were far lower because of shortages of test kits, and this figure was chosen as what a county should be capable of. This number seemed to be nothing more than a guesstimate because there wasn't a proper statistical basis for setting it. What statistics were being gathered had inconsistent and conflicting definitions, shifting qualifications for being tested, and multiple changes in these. Thus, multiple apples-to-oranges problems were created. Furthermore, there were various incentives for misreporting.
In contrast to those days when there were enough tests available to test those who should have been tested, the reverse now exists: more tests are available than those seeking testing. Think about that. The combination of the doctors and patients doesn't produce enough people needed to be tested to meet the State's arbitrary threshold -- to their criteria, too few tests being needed is a deciding sign that COVID-19 is out-of-control in Santa Clara County.
A common argument for performing unneeded tests is that it will provide a profile useful for tracking the progression of infections. That might be true if the selection of people being tested created a representative sample of the population, but the sample is self-selected. This blog was inspired by a social media posting encouraging people to get tested to get the number up to the threshold so that County residents could get haircuts. That will certainly help get a representative sample (sarcasm)!
If you are curious about the effect of increasing daily testing in SCC from 0.10% to 0.15%, it would increase the number of detected cases by 46 people, from 67 to 113. If you want to explore this, I have provided an ^XLSX spreadsheet^ for you to get started (you must make your own copy to modify values). Because I couldn't find the accuracy of the test kits being used by SCC, I used an unrealistic best-case value of 100% accurate (sensitivity and specificity).
A complexity I chose not to pursue was the infectiousness of the people detected as having an active case of COVID-19. Some research indicates that people are most likely to spread the disease in the days just before and after the onset of symptoms. CDC currently says most infectious during first 5 days, and effectively not infectious after 10. The 35-50% of people who are infected are asymptomatic, although a portion of this may be pre-symptomatic.
The guesstimate is that 80% of the people who are infected will have mild to moderate symptoms. This number was established before the prevalence of asymptomatic people was discovered, and has been updated to include asymptomatic cases with no change in the percentage itself.
----Antibody (serological) test----
A closely related issue is testing for the proportion of the population that has already had COVID-19 by looking for the presence of antibodies in the blood. Because these tests are currently at best only 90-95% accurate, they are effectively useless. With a low percentage of people having been infected, if you test positive, it is several times more likely that you aren't than you are. At 90% accuracy and 5% of the population already infected, only 32% of the positive tests are correct. At 2% infected, that drops to 15.5%. You can also play with this in the ^provided spreadsheet^.
If you are interested in this counter-intuitive effect, it is known as the ^Base Rate Fallacy^ (and other names).
An ^abbreviated index by topic and chronologically^ is available.
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