Help me with the maths of PCR and Cases

Reliability of the modelling / how mamy excess deaths are due to COVID-19 / how many are infected / Infection Fatality Rate / etc.
wazzally
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Help me with the maths of PCR and Cases

Post by wazzally »

A false positive rate of 1% is ok right? Well, if the infection rate is also 1% then in 100 people tested you will have 2 positives and 50% of them false.

Conclusion, cases are at least double what the numbers say.

Can someone help me here? It seems so obvious yet I have yet to meet anyone who is outraged by this willful obfuscation.

Another massive anomaly. In one city they have 200 cases per 100k population. In another they have the same. In one they tested all of them and in the other they tested half. You can in no way compare the two. Just to see how absurd it is to compare them, say the cities each had 1m people. In the first one, where they tested everyone, they found 2000 cases out of 1m. In the other, they found 200 cases out of 500k tested. Not the same is it?

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MikeAustin
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Re: Help me with the maths of PCR and Cases

Post by MikeAustin »

wazzally wrote: Tue Apr 06, 2021 9:32 pm A false positive rate of 1% is ok right? Well, if the infection rate is also 1% then in 100 people tested you will have 2 positives and 50% of them false.

Conclusion, cases are at least double what the numbers say.

Can someone help me here? It seems so obvious yet I have yet to meet anyone who is outraged by this willful obfuscation.

Another massive anomaly. In one city they have 200 cases per 100k population. In another they have the same. In one they tested all of them and in the other they tested half. You can in no way compare the two. Just to see how absurd it is to compare them, say the cities each had 1m people. In the first one, where they tested everyone, they found 2000 cases out of 1m. In the other, they found 200 cases out of 500k tested. Not the same is it?
Out of 100 that test positive, 1 will be false and 1 will be true. Therefore half of your positive results are false. You have half the so-called 'cases' that you thought you had.

There is an online calculator by BMJ here or a downloadable Excel file that gives more accuracy (decimal places) here.

Splatt
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Re: Help me with the maths of PCR and Cases

Post by Splatt »

PCR is nowhere near 1% false positive rate for starters.

You're also forgetting that PCR requires symptoms to get a test which reduces the chance of a false positive (by increasing effective prevalence- people with covid symptoms are more likely to have covid than those without).

Your figures also exclude the false *negative* rate. Both of which are required by the formulae to give answers. Some of the negatives will be positives and vice-versa.


False positives are much more of an issue with LFDs as the calculated figure is 0.34% (although government now claim 0.1% with no real supporting data).
These are also asymptomatic so dont include the screening check as PCR has.
LFDs now make up the *majority* of the UKs testing apparatus per day.

These will keep "cases" high not PCR.

Rudolph Rigger
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Re: Help me with the maths of PCR and Cases

Post by Rudolph Rigger »

wazzally wrote: Tue Apr 06, 2021 9:32 pm A false positive rate of 1% is ok right? Well, if the infection rate is also 1% then in 100 people tested you will have 2 positives and 50% of them false.
That's about right - yes.

I often use extreme examples. I find it often helps with understanding what's going on.

So let's imagine the brilliant Dr Loon who develops a great test for a virus that doesn't even exist. So nobody has it. You test 1,000,000 people and with a 1% false positive rate per individual test you're going to have (on average) about 10,000 people testing positive for a virus nobody has!

So there is a "population" false positive (PFP) rate here of 100%. Every single one of those 10,000 positive results is not coming from an infection.

I don't know what the correct term used is but what I've called the PFP here is the percentage of positive test results that arise from test false positives. In this extreme and silly case there are no true positive results - because nobody has the virus.

Now imagine that Dr Loon actually manages to create this virus - but it's a bit weak and only infects about 1 in a million people.

So he runs his test again on a million people. You're still going to get about 10,000 positive results again, on average. Amongst those will probably be that single person who actually has the infection.

So now you have a PFP of 99.99%

It's not a scandal, or obfuscation, but a very well-known thing.

This is why all (previous) medical advice is to only test people who you strongly suspect of having the thing you're testing for (for example, the existence of symptoms).

The outrage here is that the government have been pretty much ignoring this well-known advice. Yes, they do say you should only get tested if you have symptoms - that's true. But of course with such a wide-range of symptoms and a high level of fear you're going to get lots of people coming forward who really shouldn't be.

Whether by accident, ignorance or design the government seems to have bought into the myth that asymptomatic transmission is a significant driver of infections. Total bunkum, of course, and goes against what we know about every single other respiratory virus in the whole history of viruses - but, hey, it is the "novel" coronavirus isn't it? So maybe this one has escaped all previously known bounds of biology and science, right?

So it's important for their "asymptomatics are dangerous" story (their fairy tale) that we actually find lots of people, with no symptoms at all, who get a positive test result.

Dark Age science, back in 2019, would not have considered someone with no symptoms to be "ill", to be a "case", or infectious (at least as far as respiratory viruses go).

Of course this current twice-weekly testing of asymptomatic people proposal is just off-the-scale bonkers. It's utterly deranged, and of no scientific or medical benefit whatsoever.
Conclusion, cases are at least double what the numbers say.
I'm not sure what you meant to say, but what you have written is not correct.

I would say, for your example, that true positives (positives arising from actual/potential infections) are half the number of positives found.

Now with the PCR test things get even a little more murky. It's a great scientific technique for detecting trace amounts of DNA - and that's what it does (extremely well). However, that's not the same thing at all as saying it is detecting an infection.

And there we come to another piece of wilful obfuscation by the government. They have allowed the result of a single PCR test to be labelled as a "case". Again - this is entirely a political move to support their story - to keep fear high.

Usually a "case" is someone who presents with symptoms. But they wanted the idea firmly planted that asymptomatic people are dangerous. It's this (false) idea that has allowed them to get away with the gross and ineffective restrictions such as lockdowns and masks (remember Ferguson stating that he didn't think "we could get away with it here"?)

But get people sufficiently scared and you can "get away" with quite a lot.
You can in no way compare the two.
Yes you can - and being able to draw sensible conclusions on different population sizes is why we have the techniques and science of statistics.

People often deride stats - but the real issue is almost never with the stats themselves but the ridiculous conclusions (some) draw from them. Stats are great when interpreted with care.

jmc
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Re: Help me with the maths of PCR and Cases

Post by jmc »

Splatt wrote: Wed Apr 07, 2021 12:46 am PCR is nowhere near 1% false positive rate for starters.

You're also forgetting that PCR requires symptoms to get a test which reduces the chance of a false positive (by increasing effective prevalence- people with covid symptoms are more likely to have covid than those without).

Your figures also exclude the false *negative* rate. Both of which are required by the formulae to give answers. Some of the negatives will be positives and vice-versa.


False positives are much more of an issue with LFDs as the calculated figure is 0.34% (although government now claim 0.1% with no real supporting data).
These are also asymptomatic so dont include the screening check as PCR has.
LFDs now make up the *majority* of the UKs testing apparatus per day.

These will keep "cases" high not PCR.
Even after all your posting here over the months you still dont seem to be able to differentiate between pure calibration test results of RT/PCR machines and actual real world testing results from large volume labs with large banks of these machines running 24 hours a day. Mass screening for a very low prevalence antigen. No matter how many times it is explained to you. And how many primary sources are linked to.

You keep quoting single test values that are only achievable when the RT/PCR machines are given high quality calibration samples in a very controlled situation with carefully prepared and checked reagents. In very high prevalence scenarios with the control. Thats the only time you even get close to the error rates you have been quoting.

The mathematics that disproves what you write is very simple. If the prevalence of what you are testing for is around 3 in 1000 and if the calibration test error rate is greater than 3 in 1000 (<99.7% true positive in calibrated tests) then more than 50% of all positive results will be false positives. Type II Errors.

This is very basic mathematics.

As the current criteria for screen testing is the complete opposite of pre March 2020 and not a valid clinical test the actual prevalence in the 1 million to 2 million people tested every day will be little higher than the general population. As proximity seems to be the main testing criteria not actual infection specific clinical symptoms. Given the probably low prevalence of SARs CoV 2 even if everyone in the country with early stage symptoms of an active infection was identified and tested it would still be less than 30K/40K tests per day. With a true negative rate of up to 70%.

Real world lab testing process error rate for even low volume lab processes on its own is in the region of 5% plus. Sometime over 10%. Year in, year out.

The cross contamination rates for samples like nasopharyngeal swabbing is at least 5% and higher. Quite separate from the whole issue of general circulation HCOV cross contamination.

The lab error rate for RT/PCR in the past with moderate volumes could be as high as 5% / 10% due to reagent, area contamination and machine calibration issues. Then there is the interpretation of the result curve. The reason why trend negative interpretation was the norm before Match 2020 was because of all of the above. And the ambiguity of marginal results with this process. The result interpretation stage introduces by itself a serious false positive bias when the process stage is now default positive rather than default negative.

So maybe stop quoting the numbers from the Thermo Fisher or Bio Rad sales literature as if it has any relevance to the real world results from mass screening labs that are processing up to 1 million test a day ( 782k yesterday) as compared to the low tens of thousands per day pre March 2020.

They are still doing mass screening with a test with a false negative rate of 50% plus and real world false positive rate of 90% plus. A screening test which is invalid by all traditional clinical test criteria and standards.

Those real world numbers are very different numbers from those found in the glossy sales brochures. Or in those very controlled not at all real world lab scenario published papers.

Splatt
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Re: Help me with the maths of PCR and Cases

Post by Splatt »

MikeAustin wrote: Tue Apr 06, 2021 11:02 pm There is an online calculator by BMJ here or a downloadable Excel file that gives more accuracy (decimal places) here.
The BMJ is frustrating as it rounds to 1% increments.
This means you cant enter a prevalence of under 1% into the thing.
At todays rough 0.2% and dropping its unusable.

I guess they never thought people would still be worried about disease levels this low!

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MikeAustin
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Re: Help me with the maths of PCR and Cases

Post by MikeAustin »

Splatt wrote: Wed Apr 07, 2021 9:58 am
MikeAustin wrote: Tue Apr 06, 2021 11:02 pm There is an online calculator by BMJ here or a downloadable Excel file that gives more accuracy (decimal places) here.
The BMJ is frustrating as it rounds to 1% increments.
This means you cant enter a prevalence of under 1% into the thing.
At todays rough 0.2% and dropping its unusable.

I guess they never thought people would still be worried about disease levels this low!
This is exactly why I provided a link to my Excel sheet! (BTW, it needs to be downloaded to run as it can only be viewed in a browser)
However, through the BMJ's rounding, they are effectively indicating that these tests should not be used for low prevalence mass testing.

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MikeAustin
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Re: Help me with the maths of PCR and Cases

Post by MikeAustin »

jmc wrote: Wed Apr 07, 2021 9:55 am
Splatt wrote: Wed Apr 07, 2021 12:46 am PCR is nowhere near 1% false positive rate for starters.
You keep quoting single test values that are only achievable when the RT/PCR machines are given high quality calibration samples in a very controlled situation with carefully prepared and checked reagents. In very high prevalence scenarios with the control. Thats the only time you even get close to the error rates you have been quoting.
Yes, of course. Look here to see the difference in quality of testing.
During last summer, Lighthouse Labs produced 7x the false positives that Cambridge Labs would have produced. And the so-called 'second wave' would have been much flatter.
Indeed, bearing in mind that PCR tests are more likely to pick up dead virus fragments, many of these would have been recoveries rather than actual cases.

Splatt
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Re: Help me with the maths of PCR and Cases

Post by Splatt »

jmc wrote: Wed Apr 07, 2021 9:55 am Even after all your posting here over the months you still dont seem to be able to differentiate between pure calibration test results of RT/PCR machines and actual real world testing results from large volume labs with large banks of these machines running 24 hours a day. Mass screening for a very low prevalence antigen. No matter how many times it is explained to you. And how many primary sources are linked to.
No. I fully understand it despite your incredibly disingenuous attempts to completely ignore all the supporting data along with surveillance reports after the even further firming it up.

You're making up operational error rates along with everything else that simple aren't listed in reality and using those made up figures to present false levels of tests.

You constantly ignore all the actual assessed sensitivity and specificity rates along with those measured independently outside the mass lab scenario.
You then constantly ignore the weekly and monthly surveillance data and the error bounds they place on those figures from there.

You fail to provide any verifiable data to back up any of you actual real world lab value claims (and figures which were certainly not accurate for any lab ive worked in).

You're fond of making "real world" claims which ignore (i) real world results and (ii) appear to have no peer reviewed or verifiable academic source at all.

Splatt
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Re: Help me with the maths of PCR and Cases

Post by Splatt »

MikeAustin wrote: Wed Apr 07, 2021 4:48 pm During last summer, Lighthouse Labs produced 7x the false positives that Cambridge Labs would have produced. And the so-called 'second wave' would have been much flatter.

ONS now estimate specificity of PCR to be at 99.92% in the real world.
Yes there were and remain some very odd lighthouse results for periods of time and the QA there is likely awful but an overall average appears to be that.
Indeed, bearing in mind that PCR tests are more likely to pick up dead virus fragments, many of these would have been recoveries rather than actual cases.
That is not a false positive though. Its a genuine RNA present positive result.
That's interpretation of the result which is political not scientific which is the problem.
The "science" part does it jobs but then it ends up with politicians (or worse, scientists being political) for the end result.

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