Testing to determine population fractions – extended (updated 23apr20)

George Rebane

In ‘Testing to determine population fractions’ I introduced the reliability aspect of tests for both infection and immunity.  This is still not a serious consideration brought up in the daily WH C19 briefings, and, of course, nothing of this level of complexity is covered in the media for various reasons ranging from the acumen of their ‘journalists’ to the media-perceived acumen of their audiences.  Here we are not deterred by such deficits.

In the referenced post the strong point was made that it is not appropriate to take the uncorrected fraction of tests positive from a random sample, and apply that to the target population from which the sample was drawn.  The correction formula was derived and illustrated, along with how errors in the poorly known test sensitivities and specificities propagate into even the corrected estimates of target population fractions.  Since then I’ve done more work to graphically illustrate these mathematics in a visually accessible manner by introducing the population fraction correction surface on which these mathematical concepts can be illustrated for the non-technical reader.  The updated technical note that explains all this can be downloaded here - Download TN2004-2v200420  The figure below is a sample of the explained correction surface for a scenario in which 45% of the tested sample yielded positive test results.  Two tests of different reliability are shown in the figure, details in the technical note.

[21apr20 update]  Tonight we hear from the FDA that more than 50 different immunity testing kits are being developed by the private sector, and submitted for regulatory approval by the agency along with corroborating data derived from the companies’ “self-validations”.  But the FDA's report and subsequent questions from the nation's top reporters sitting in the WH press room are woefully inadequate for any inquiring mind.  Not one word is said about what kind of test reliability data will be required, collected, and supplied from the self-validations.  (Readers who understand and care know that the seminal information about ANY test includes first and foremost its sensitivity and specificity numbers along with their error bounds.  Without those numbers, the rest is bullshit.)  And not one word is said or asked about what kind of testing is intended to support what kind of C19 response policies.  Again, the simple inclusion of the word ‘testing’ in the media blather is considered sufficient for a nation seen as consisting overwhelmingly of double dummies.

[23apr20 update]  Bootstrapping parameters for a new test.  There may be times when we want to introduce into field use a new test for reasons having, perhaps, to do with cost, ease of application, rapid results turnaround, etc.  We want to get the new test online as quickly as possible, which requires that we also must quickly determine its performance parameters without having to go through the more lengthy and costly formal process.  Given the development in the above described TN2004-2, a method for bootstrapping such parameters for a new test is introduced in TN2004-3 which can be downloaded here -  Download TN2004-3v200425

Comments

[scenes]

Speaking of 'test positives' and the like, I have to wonder if there isn't a half-life for the efficacy of a test (in addition to immunity and vaccine efficacy)

https://www.scmp.com/news/china/science/article/3080771/coronavirus-mutations-affect-deadliness-strains-chinese-study

[George Rebane]

scenes 1140am - not sure if your "efficacy of a test" really means the re-emergence of C19's virulence (e.g. thru mutation), or if you're talking about the shelf-life of a given test in that its sensitivity and specificity would degrade over time.

[scenes]

"you're talking about the shelf-life of a given test in that its sensitivity and specificity would degrade over time."

this.

It strikes me that a half-life is a good way to think about it.

[scenes]

...and by that I mean that the virus changes, not that the tests go bad in storage or the like.

[Bill Tozer]

Lockdowns Don’t Work

https://www.thepublicdiscourse.com/2020/04/62572/

Already reports from ‘experts’ claim of those with COVID-19 antibodies is are understated by a factor of 55-80x. Herd immunity is here.

[scenes]

Speaking of tests and pulse oximetry, a not bad article.

https://www.nytimes.com/2020/04/20/opinion/coronavirus-testing-pneumonia.html

Of course, the net result of all the words is that it's useful to give people supplemental oxygen and to have them on their side or stomach in order to avoid a ventilator.

The gobsmacking angle to this is that it's probably the dozenth article I've read with the miraculous discovery of positioning patients with breathing problems. (a) it's obvious and (b)you'd think they already know all of this. The simple fact that coronavirus appears to cause relatively asymptomatic lack of takeup of oxygen should have been common knowledge in the medical community in December.