If this has already been covered , please point me to the post. My query sits with the 2 graphs embedded into the false positive article. The upper i understand to be a calculation of community cases during the early testing , and the lower the actual cases reported then and now
Are you referring to the charts that I embedded here or something else? I don't follow what you have done.
OK, I think I see what you did, although I don't understand why - hence my confusion.
If there had been 198,797 tests on 1st April with a cases/tests ratio of 38.4%, there would have been 76,320 cases. In fact, there were 11,896 tests with 4,567 cases.
Of course, the population used for these tests was those who were presenting possible symptoms - not a typical sample of the wider population that we are tending to see today.
This cases/tests rate get curiouser and curiouser. Having been fairly flat at 0.5% for two months, it suddenly went up to about 1.5% on 6th September and remained fairly flat for two weeks. Now, it has shot up again to about 2.5% in 3 days. Whether it will flatten for a while or not, we don't know.
Does anyone else find this puzzling?
The first step in cases/tests was just before Boris announced his 500,000 tests/day target. It coincided with a sudden 3x increase in testing rate. This lasted two weeks around the same level.
The latest step (and it is not clear if it will flatten or rise) started just before Boris made his announcements yesterday.
Initially, I wondered whether shorter time for testing caused false positives to rise but, as Dave B. said (and I have since researched), this would tend to reduce them. So increasing test speed and increasing false positives are not causally related. Am I just over-thinking it, or could there be an associative relationship - such as a shared cause or purpose?
I will leave that question out there.
Yes it makes my eyes pop out of my head especially the 0.5%.
And this is a bit sensational but I keep reflecting back to the WMD thing in 2003 with all its dodgy dossiers etc.
The thing is statisticians and people who use statistical tools are creatures of habit.
And when they set Z scores for confidence limits etc they tend to always pick the same ones from a standard lists of alternative from text books tables etc.*
These are the most popular ones.
I hope this from a table goes to the forum OK but it is one of links below.
90% 0.4500 0.0500 1.645
95% 0.4750 0.0250 1.960
98% 0.4900 0.0100 2.326
99% 0.4950 0.0050 2.576
Because it is two tailed if they picked say 95% the actual false positive would be 5%/2 ; or 2.5 % ; which is what “ Area in one tail (alpha)” means
0.025 x 100 = 2.5%
Of course if they had picked 99%
[another very popular one; 95% and 99% are the ones most commonly selected I think]
before the 6th of September then
false positive would be 1%/2 ; or 0.5 % ; which is what “ Area in one tail (alpha)” means.
Of course this is a really shocking thesis even too shocking for me really it must be a remarkable coincidence.
Because that might mean that all the positive cases were false positives if they picked 99% before the 9th
And now, after they dropped it to 95%.
I have just skimmed through these two sites now and they look ok to me.
I really do have a grade A in A’level statistics from 1979 so whilst very rusty I can still remember the basic details.
https://people.richland.edu/james/lecture/m170/ch08-int.html
https://www.statisticshowto.com/probability-and-statistics/z-score/
We might have to make sure they are not turning old negatives into positives.
All the data will be in the spreadsheets and you just need to change the LOD detection threshold setting and old negative cases will automatically turn positive if you back date it.
We probably need to do screen shots of the case tables; I took one yesterday.
* Particularly if you do it in this order
Determine the mean and standard deviation on blank.
Then pick the confidence limit you might like from the standard list.
And then determine the LOD or detection threshold
which is the orthodox order of doing it.
They may have also raised the false positive rate on hospital admissions, ventilator and deaths data as well.
But it would mean that they have done it elsewhere as well like Spain?
The Swedish Wikipedia data has a rolling case/test data.
https://en.wikipedia.org/wiki/COVID-19_pandemic_in_Sweden
Although we need to take a lot of caution when comparing one countries data to another
Yes it makes my eyes pop out of my head especially the 0.5%.
Thanks Dave.
You may have seen my rebuff to Chris York's attack on the false positives on HuffPost
https://forums.lockdownsceptics.org/viewtopic.php?f=5&t=547
Of interest and use here is the BMJ online tool for calculating false positives.
https://www.bmj.com/content/369/bmj.m1808
It is useful for anyone to tinker with - and misuse, if they are not careful. One can play tunes on this to iterate to the total positives from the testing program. Unfortunately, it does not go into fractions of percent (why should it - it was never intended to use PCR this way). So I wrote one for myself. It is a Bayesian equation which you will be more familiar with than I. My maths is not what it used to be 183 years ago.
One possible problem here is the possible influence of some rubbish tests that have not produced positives when they should have done. As you say, the 0.5% total positives is unbelievable. Anyway, surprise, surprise it is also unachievable unless, say, with 0% prevalence and 99.5% specificity.
Then the 'step' at 1.5% total positives could be achieved with 0.6% prevalence and 99% specificity, both possibly unlikely.
The current 2.5% total positives could be achieved with the same 0.6% prevalence and 98% specificity.
Aha, what have we here? With the same prevalence - a bit on the high side at 0.6% - a switch of specificity from 99% to 98% would cause a jump from 1.5% to 2.5%.
I find myself getting increasingly out of my depth here and I am looking for someone else with a more agile brain to pick this up. To me, the crucial point is the sudden jumps rather than the values per se. I just wanted to get the ball rolling.
The heads rolling could come later.
We are obviously interested in 4th September to the 10th September range.
Are you quite sure about your cases/tests data of err 0.5 to 1% ?
You see ONS said that in their in the community survey seem to have a value a tenth of that?
….during the most recent week (4 to 10 September 2020), we estimate there were around 1.10 (95% credible interval: 0.77 to 1.51) new COVID-19 infections for every 10,000 people per day …..
Circa 0.1% cases/tests?
…..in the community population in England, equating to around 6,000 new cases per
day (95% credible interval: 4,200 to 8,300)…..
England at approx 3,000 cases per day , were doing really well to pick up half of that by testing less than 1% of the population per day.
Sample selection bias I suppose?
Or are they going to say 98% ? of their cases are not in the community?
https://coronavirus.data.gov.uk/cases
% testing positive
04 September 2020 0.10% 0.08% 0.12%
05 September 2020 0.10% 0.08% 0.12%
06 September 2020 0.11% 0.08% 0.13%
07 September 2020 0.11% 0.09% 0.14%
08 September 2020 0.11% 0.09% 0.15%
09 September 2020 0.12% 0.09% 0.16%
10 September 2020 0.12% 0.09% 0.17%
admittedly the ONS survey sample were ;
…..within the community population; community in this instance refers to private residential households and it excludes those in hospitals, care homes or other institutional settings……
But I thought most of these new cases were supposed to be “within the community population”
There is an excel spreadsheet in there with chronology of % testing positive from April.
They appear to have got it down to 0.03% over a prolonged period of time so I think we can give that as the maximum false positive to the ONS and the Manchester Labs [ hurrah ]they used .
