The Value of Testing

George Rebane

Trigger warning: The contents of this commentary may not be accessible to the innumerate reader.

As explained in ‘Testing, testing, …’, the value of testing comes to the fore when you have a sufficiently reliable test that can be administered on a regular and scientific basis over a suspect population.  In that case, it could be used to identify concentrations of infections that can be used for a more satisficing allocation of limited healthcare resources.  In an update to the referenced commentary, I illustrated how to determine the reliability of test results given the reliability parameters of the test administered to a walk-in member of a suspect population (country, state, county, city, region, …).

In this piece I will answer the questions many reasonable people have about testing – ‘why test if the tests are unreliable?  Why test if the test only provides a snapshot assessment which may change within the next hour?’  We start by recalling the advice from our federal and state medicos.  Given the limited availability of tests and processing labs, we are only supposed to request a test if we are symptomatic – fever, cough, headache, … .  Don’t burden the system if you are asymptomatic.

To read the remainder of this analytical commentary full of some algebra and all kinds of numbers, please download this PDF - Download The Value of Testing

Comments

[Teine Rebane Kenney]

- opens the pdf - "Teacher, may I be excused to use the bathroom?"

[Walt]

Great... Amazon delivers virus to you door.
Time to Lysol the box before touching.
https://www.the-sun.com/news/586612/six-amazon-warehouses-have-coronavirus/

[scenes]

Question. How did you determine that a suspected person has a .5 possibility?

...

The whole situation made my pea brain consider a few different aspects. Yes, no doubt you have already mentioned one or more of these, my apologies.

. It's probably more accurate to do calculations in terms of economics effect. An actuary could pump out costs of medical care, time off work, value of a person's death depending on age, etc. Death costs could be multiplied up to meet society's morality needs.

. False positives are far less harmful than false negatives.

. I'll bet that pre-symptomatic detection is the hard part in terms of accuracy. It also implies that as a sampling problem, one test is insufficient. For one thing, the time after exposure is bound to change the reliability of the test.

. A test regime should take into account the likelihood of a person infecting others. Triple bonus points for a supermarket check-out clerk, more so than even a nurse. Some people likely require regular asymptomatic testing for now. Tracking of prior contacts will become a thing.

. You sure could do a lot with universal tracking of people (via cell phone) and modern big data practices to see who to test.

. This would be a brilliant opportunity for other studies given the huge numbers of samples pouring in. Betcha there's a good case to be made for DNA sampling of most of the population.

. Asymptomatic testing. Delay of test results implies a lack of value with the exception of those who never show symptoms. By the time you get them back, you likely show symptoms if positive and anyone with any sort of flu/cold symptoms should quarantine in any case.

. Asymptomatic testing. If 18% of carriers never show symptoms. What needs to be done to push R0 down below 1? Universal simultaneous asymptomatic testing? something less ridiculous? There probably should be a lexical difference between 'asymptomatic' and 'pre-symptomatic'.

[fish]

Posted by: Teine Rebane Kenney | 24 March 2020 at 03:54 PM

You had a question for me yesterday regarding a post that I absolutely could not locate. Can you elaborate?

[George Rebane]

scenes 907am - Your good points take the discussion well beyond quantifying the reliability of tests and testing. The devising of public policies that satisfice a given utility function is both a very interesting and complex undertaking, way beyond the ken of your run-of-mill politician (that's why we mostly get crappy policies). And your point about the impact of asymptomatic testing and impact of pre-symptomatic virus spreaders I have covered elsewhere, but no doubt can be examined in more detail.

About your '0.5 question' - information theory deals heavily in probability and teaches us that information content is represented with probability distribution functions, pdfs (discrete and continuous) of the variables of interest. The highest measure of information calculates from a distribution that is peaked at the correct value of the variable (the Dirac-delta spike of a discrete distribution being the limiting case). The lowest measure of information derives from the most featureless pdf which, of course, is the flat distribution that reflects total ignorance as to the variable's value, assigning equal probability to all possibilities/alternatives.

In the case of the prior pdf for a suspect patient - who either is or is not infected - our pre-test ignorance over those two alternatives are represented by equal probabilities that sum to one - i.e. 0.5 and 0.5. This why we model our knowledge of a fair coin toss that way, and also assign 1/6 to the probability connected with each the numbers on a die.

Since I understand you to be technically astute, I'll share a little insight on how to generate the optimal search policy for anything the location of which initially is known to within a prior pdf. The optimal strategy is the one that flattens the pdf the most and the quickest. That is the equivalent of sucking out the prior pdf's information content the fastest way possible (using Bayes of course). Competing strategies are therefore easy to compare by just computing the time history of the posterior pdf's information content as the search proceeds. Hope this helps.

[scenes]

Obliquely related to testing, I was considering small populations this morning.

Even starting with 'clean' humans, will an isolated group always eventually produce a germ/virus/bacteria/other nasty that wipes out everyone at some point? Enough generations of relatively fast evolution of preexisting critters and...voila'.

From a practical standpoint, would an Easter Island always eventually die because of non-viability due to an epidemic given enough time? If you put all your eggs in one boat, sinking is assured?

If that's true, you can think of a couple of modern variants.

1) Permanent space colonies, especially the super long term variants like generation starships (a bit far off, but worth considering).
2) The world as one big community. The globalist project.

At least in terms of globalism, the epidemic will always be stopped and produce survivors as travel collapses.

[scenes]

" probability distribution functions,"

Outside of my wheelhouse, but I think I can grasp the idea from the name. I'll spend a bit of time attempting to get the 10k ft. view. It sounds like something applicable to machine learning, another thing I could stand to know more about as all the cool kids are into it. I do see your point in assigning a 50% chance in a case where there are two outcomes.

[George Rebane]

scenes 1226pm - total ignorance of alternatives or of futures is always represented by a flat pdf - everything is equally un/likely. Knowledge is always represented by structured pdfs, the more bunched here than there, the better. For a great (and I do mean great) text from which to learn probability, I strongly recommend to my students 'The Probability Tutoring Book' by Carol Ash - it could not be more clearly written. It's hefty price testifies to its acknowledged utility among professionals; but the used copies are just as good ;-) (It's also published by IEEE, which itself is an impressive imprimatur. I have had my copy for years.) For an equivalent book on calculus, again look for Carol Ash co-authored by her hubby.
https://smile.amazon.com/Probability-Tutoring-Book-Revised-Printing/dp/0780310519/

[George Rebane]

scenes 1226pm - of starships and such. I don't think our ancestors will be worrying much about such contagious epidemics. From my perch this is 'the last great century of Man', bio-life is a transitory phase in the rise and development of intelligent civilizations. We're about at the end of that phase with the coming Singularity - soon trans-humans will rule, and their bio-progenitors will die out and their replicable DNA will be digitally preserved on some storage device. Or else, we'll simply destroy ourselves.

[Bill Tozer]

My two cents....which is worth less than a half cent.

https://i2.wp.com/www.powerlineblog.com/ed-assets/2020/03/Screen-Shot-2020-03-22-at-9.34.41-AM.png?w=996&ssl=1

https://i1.wp.com/www.powerlineblog.com/ed-assets/2020/03/Screen-Shot-2020-03-22-at-4.51.42-PM.png?w=1002&ssl=1

[Bertie]

speaking of testing.. the Russians version of the CDC, who closed the borders with China at the end of January, say they have created and are maintaining a reserve of 700,000 test kits as the virus begins to spread. In the meantime Americans are still waiting for test kits as the US becomes the world leader in confirmed cases. Don't worry folks it will all be over by Easter and we will be back in business.... because who really cares about other people's lives when the economy is more important.. right?

[George Rebane]

Bertie 548pm - You really ought to watch something more than MSNBC. Besides, bitching about playing catch up on test kits which 1) would not have stopped the progress of the disease in the last month, and 2) should be contributed under 'Hunker Down ...' where I talk about what wasn't done by the feds during the last couple of decades.

[Scott O]

Bertie 5:48 - "...say they have created and are maintaining a reserve of 700,000 test kits as the virus begins to spread."
And if Putin says it's true, it must be, right Bertie?
Moreover - "In the meantime Americans are still waiting for test kits as the US becomes the world leader in confirmed cases."
Hey - shit-for-brains - The only way you can confirm a case of CV19 is to have an accurate test.
If we lead the world in confirmed cases then it follows we lead the world in test kits.
Bertie makes stupid look good and that ain't easy.
We eagerly await the next post from Putin's lap dog.

[Bill Tozer]

Tiger At Bronx Zoo Tests Positive For Coronavirus, Other Animals Suspected Of Having Disease

https://www.dailywire.com/news/tiger-at-bronx-zoo-tests-positive-for-coronavirus-other-animals-suspected-of-having-disease?

Well, bats are mammals too!