Corona Update 24, Mathematical proof self-tests are only 3% correct, 97% false positives !
3% of the corona/covid 19 self-tests are correct, 97% are false positives !
The mathematical proof has been delivered (using Bayes' theorem):
Roche's corona self-test has a sensitivity of 96.52% and a specificity of 99.68%.
If "C19" stands for the presence of the disease COVID-19 ("corona") and
+ and − respectively for a positive and negative result of the test, this means:
sensitivity: P( + | C19 ): 0.9652
specificity: P( - | not C19): 0.9968
That seems very high. But if the prevalence is only 1 in 10,000, i.e
prevalence: P( C19 ): 0.0001
Corona Update 24, Mathematical proof self-tests are only 3% correct, 97% false positives !
3% of the corona/covid 19 self-tests are correct, 97% are false positives !
The mathematical proof has been delivered (using Bayes' theorem):
Roche's corona self-test has a sensitivity of 96.52% and a specificity of 99.68%.
If "C19" stands for the presence of the disease COVID-19 ("corona") and
+ and − respectively for a positive and negative result of the test, this means:
sensitivity: P( + | C19 ): 0.9652
specificity: P( - | not C19): 0.9968
That seems very high. But if the prevalence is only 1 in 10,000, i.e
prevalence: P( C19 ): 0.0001
This implies:
P( + ) = P( + | C19 ) P( C19 ) + P( + | not C19 ) P ( not C19 ) =
= 0.9652 x 0.0001 + 0.0032 x 0.9999 = 0.0033
and
P( C19 | + ) = ( P( + | C19 ) P( C19 ) ) / P( + ) =
= ( 0.9652 x 0.0001 ) / 0.0033 = 0.03
If 10,000 people are tested with this test, including probably 1 infected person,
then the infected person will almost certainly get a positive result.
But of the 9,999 uninfected people, 32 will get a false positive result.
The 9967 people with a negative result are almost certain that they are not infected.
But of the 33 with a positive result, only 1 is infected,
only it is unknown who that is.
So the chance that an individual is actually infected after a positive result
is only slightly more than 3% in this scenario.
This self-test is therefore of little use to determine whether you are infected with corona,
unless the prevalence is around 1% or higher.
(This information has been known and published since 20 june 2021 !)
(This information has been known and published since 20 june 2021 !)
This sounds serious. Maybe you should tell someone about it?
On 17/02/2022 19:39, skybuck2000 wrote:
Corona Update 24, Mathematical proof self-tests are only 3% correct,
97% false positives !
Deliberately misleading tosh based on a false assumption.
3% of the corona/covid 19 self-tests are correct, 97% are false
positives !
The mathematical proof has been delivered (using Bayes' theorem):
Roche's corona self-test has a sensitivity of 96.52% and a specificity
of 99.68%.
If "C19" stands for the presence of the disease COVID-19 ("corona") and
+ and − respectively for a positive and negative result of the test,
this means:
sensitivity: P( + | C19 ): 0.9652
specificity: P( - | not C19): 0.9968
That seems very high. But if the prevalence is only 1 in 10,000, i.e
prevalence: P( C19 ): 0.0001
That is a *VERY* big if though.
Right now in the UK Covid prevalence is 0.05, 5% or 1 in 20.
https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/16february2022
It will be a very long while before the Covid prevalence here is
anything like 1:10000. It would be nice just to get it under 1%.
IOW in a room with 14 people in it there is a 50:50 chance that at least
one of them has Covid-19. False positives are irrelevant at the moment.
It is an even worse 1 in 13 in Northern Ireland for some reason.
False negatives are far more dangerous when they are being misused as a permission to do something. Testing misses about 20% of real positives.
On 17/02/2022 23:39, Martin Brown wrote:
On 17/02/2022 19:39, skybuck2000 wrote:
Corona Update 24, Mathematical proof self-tests are only 3% correct,
97% false positives !
Deliberately misleading tosh based on a false assumption.
3% of the corona/covid 19 self-tests are correct, 97% are false
positives !
The mathematical proof has been delivered (using Bayes' theorem):
Roche's corona self-test has a sensitivity of 96.52% and a specificity
of 99.68%.
If "C19" stands for the presence of the disease COVID-19 ("corona") and
+ and − respectively for a positive and negative result of the test,
this means:
sensitivity: P( + | C19 ): 0.9652
specificity: P( - | not C19): 0.9968
That seems very high. But if the prevalence is only 1 in 10,000, i.e
prevalence: P( C19 ): 0.0001
That is a *VERY* big if though.
Right now in the UK Covid prevalence is 0.05, 5% or 1 in 20.
https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/16february2022
It will be a very long while before the Covid prevalence here is
anything like 1:10000. It would be nice just to get it under 1%.
IOW in a room with 14 people in it there is a 50:50 chance that at least
one of them has Covid-19. False positives are irrelevant at the moment.
It is an even worse 1 in 13 in Northern Ireland for some reason.
False negatives are far more dangerous when they are being misused as a
permission to do something. Testing misses about 20% of real positives.
The relevant number is not the prevalence of Covid in the population at large, but the prevalence of Covid amongst people taking a self-test.
Since self-tests are usually taken by people with symptoms, or people
with very close contact to people who have Covid, the number is not
going to be 1 in 20 but more like 1 in 3 or 4.
On 18/02/2022 08:40, David Brown wrote:
On 17/02/2022 23:39, Martin Brown wrote:
On 17/02/2022 19:39, skybuck2000 wrote:
Corona Update 24, Mathematical proof self-tests are only 3% correct,
97% false positives !
Deliberately misleading tosh based on a false assumption.
3% of the corona/covid 19 self-tests are correct, 97% are false
positives !
The mathematical proof has been delivered (using Bayes' theorem):
Roche's corona self-test has a sensitivity of 96.52% and a specificity >>>> of 99.68%.
If "C19" stands for the presence of the disease COVID-19 ("corona") and >>>> + and − respectively for a positive and negative result of the test, >>>> this means:
sensitivity: P( + | C19 ): 0.9652
specificity: P( - | not C19): 0.9968
That seems very high. But if the prevalence is only 1 in 10,000, i.e
prevalence: P( C19 ): 0.0001
That is a *VERY* big if though.
Right now in the UK Covid prevalence is 0.05, 5% or 1 in 20.
https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/16february2022
It will be a very long while before the Covid prevalence here is
anything like 1:10000. It would be nice just to get it under 1%.
IOW in a room with 14 people in it there is a 50:50 chance that at least >>> one of them has Covid-19. False positives are irrelevant at the moment.
It is an even worse 1 in 13 in Northern Ireland for some reason.
False negatives are far more dangerous when they are being misused as a
permission to do something. Testing misses about 20% of real positives.
The relevant number is not the prevalence of Covid in the population at
large, but the prevalence of Covid amongst people taking a self-test.
Since self-tests are usually taken by people with symptoms, or people
with very close contact to people who have Covid, the number is not
going to be 1 in 20 but more like 1 in 3 or 4.
The UK publishes those figures too and they are very age dependent.
Quoting a paragraph from the source I referenced above:
"In England, the percentage of people testing positive for COVID-19
varied substantially across age groups, with the highest for those aged
2 years to school Year 6 at 7.60% (95% confidence interval: 6.89% to
8.35%) and lowest for those aged 70 years and over at 2.23% (95%
confidence interval: 2.03% to 2.45%), in the week ending 12 February 2022."
School age children it is 7+/-2%.
Over 70's it is 2.2 +/- 0.2%
UK is doing quite a lot of population testing. There are quite a few
other infections that give Covid like symptoms this time of year!
The numbers I quoted are from the population survey which does a 100k
samples from apparently healthy people chosen at random. It does have a couple of notable biasses - downwards in that someone with Covid who
doesn't want the hassle of self isolating will not bother to return it
and upwards in that it detects shedding viral DNA which continues for a
while afterwards. Week on week it is a clear comparable measure though.
Worried well hypochondriacs seem to be burning up LF tests on a near
daily basis and they have a roughly 0.1% chance of a false positive. I
have been randomly sampled by REACT a couple of times and taken a test
in anger once, my wife twice after being pinged by the tracing app. They
go short supply from time to time especially when Covid levels are so
high. Many people have switched off their tracing app and UK so-called
Test and Trace has been a complete disaster from the very beginning.
Apply them to a few million people when the Covid rate is actually low
and you do get a serious fraction of false positive with nuisance value.
In the past the rule was LF positive then do a "definitive" PCR test but
that has been scrapped. Give it a week now and you won't even be legally obliged to self isolate after a positive Covid test(madness).
Part of the save The Boris distraction scam.
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