I messed up “sensitivity” and “specificity” because I am more into pure maths than applied maths and more used to the terms “true positives” and “true negatives” which are more self-explanatory. So I will redo the calculation below. My apologies for this.
“Sensitivity” and “specificity” are deliberately confusing terms meant to be memorised by medical students and then used mostly within the “profession” to exclude those who are outside the racket. (This happens in all “professions”, not just among charlatans such as NHS GPs who allow the plebs to think they have doctorates and local solicitors who “specialise” in conveyancing, “helping” senile elderly ladies manage their bequests whether in property or financial assets, and remortgaging.) “True positive rate” is a much clearer term that indicates how many % of people who test positive actually have what is supposed to be have been tested for. Nobody will confuse “true positive” with “true negative” as I unfortunately did “sensitivity” with “specificity”.
The aide memoire “I’m positive that I’m sensitive” seems a good way to remember which way round it is 🙂
The figures for 70% sensitivity (true positives) and 95% specificity (true negatives) (which I have checked) come from the “practice note” in the British Medical Journal that I linked to. The BMJ, owned by Elsevier, is a vehicle for Big Pharma propaganda – see the relevant pages of Edward Bernays’s great (absolutely must-read) book “Propaganda” on how “trade journals” create and manage “opinion” within a “trade”, and also Vance Packard’s “Hidden Persuaders” in which – going by memory – I seem to recall he talks about the marketing of librium which medics were told should be prescribed “whatever the diagnosis”. Things are done more subtly nowadays. Nowadays there is little leftwing critique of how say “flu jabs” were marketed until they became “normal”, although that would be extremely interesting knowledge to have at the present time. (Perhaps there are some loony-right articles about it, mixed up with assertions such as that the Sandy Hook massacre was fake. By such means is clear critique obstructed. This kind of method developed after Bernays wrote.) Similarly “everyone” talks of “Oxford” research, “Cambridge” research, and “Imperial College” research, rather than whichever drug companies are really calling the shots. At Oxford it’s Astra Zeneca. At Cambridge it’s Glaxo Smith Kline. I don’t know who it is at Imperial.
The BMJ article, entitled “Interpreting a covid-19 test result”, says the 70% and 95% figures are at the lower ends of reviews and that they are approximate. I am not trying to be an “expert” who produces a super-accurate estimate of how many people have had SARS-CoV2. I have no particular opinion on what the real figure is. I am just trying to pick at what a heap of flimsy rubbish the officially encouraged lines of thought are where testing is concerned.
The stuff in the block quote is just me applying Bayes’s Theorem. Feed in the rate of true positives and the rate of true negatives, and you get the “likelihood ratio” (“Bayes factor”) that tells you how to alter the whole-population incidence rate (i.e. the probability that a person chosen at random has the problem) to get the post-test probability (one figure for if it’s positive, another for if it’s negative) that the tested person has the infection. This is the principle of how you get from ANY medical test result to an estimate of the probability that the person has the infection or other problem. Of course you are right that other indicators should be accounted for, which is why I said let’s take the person at random from the population.
In the real world, testing is not done at random. Two cases in particular are interesting: first, when people who do have “the symptoms” are NOT tested, and second, when people who don’t have the symptoms (or who at least have only a high temperature or basically a cold) ARE tested. In Britain I reckon both groups include a lot of people.
“Covid-19” is a collection of flu-type symptoms. (Impairment of smell and taste also happens with the common cold which is usually a much less severe illness than flu.) Many who have had these symptoms have never been tested for SARS-CoV2. If I recall correctly, these include our host on this blog and his wife. If the ill people are in “care homes for the elderly” (mostly rented by wide boys from companies they are connected with that are registered offshore), they have usually been left without any hospital treatment. Ambulance teams have been told not to attend to them, but to spend hours cleaning and re-cleaning their ambulances instead, Nero-style. If they then die, many are recorded on their medical certificates of the cause of death (MCCDs) as having died with Covid-19 even if they were never actually tested for SARS-CoV2. (How many of the 40000+ deaths “with Covid-19” in Britain does this account for, I wonder?) I.e. they were recorded as having died with Covid-19 because they had flu symptoms, and then probably many of them died of pneumonia (another collection of symptoms that can have many causes) inside care homes, pneumonia that was brought to the care homes by patients who caught it in hospital and were then discharged back into the care homes. (If you want to murder loads of people in a care home, this is a way to do it.) The policy is one of “involuntary euthanasia”. In Germany the extermination policy did not start with Jews, gays, Jehovah’s witnesses, recidivist criminals, etc. – it started with the physically and mentally disabled. There haven’t been many press articles about how the homeless have been getting along in Britain since they were cleared off the streets in March either.
One of the most important provisions in the Coronavirus Act (sections 11-13) is the provision for indemnifying designated people from liability when patients die. Now that the petty-official manager stuck-up types who infest this country have been entrained into spouting “coronavirus”-themed bullsh*t by their higher-ups and the media, bullsh*t that directly contradicts what is going on often in front of their eyes, and what they could in any case work out if they were used to applying a teensy bit of logic in a sensible way undirtied with any poncy “I’m an expert” role-playing, they basically have the taste for blood. It’s a twist on the Stanford Prison Experiment or Stanley Milgram’s electroshock experiment.
It’s very scary indeed and the prognosis doesn’t look good. The economic background is one of very heavy over-employment, as anyone who has walked past an office building can attest. We are at the early stage of a cull which is likely to exceed greatly what has happened so far.
(See the “toilet paper” story. Exciting to Daily Mail readers because it’s about bums, and also about dirt, this was deliberate misdirection by the government in order to make shortages look amusing and to direct attention to this particular commodity, a shortage of which is certainly annoying but is nowhere near as problematic as shortages of food. In March, various food items were similarly put on private-sector ration and similarly ran short on the shelves, but it was “wiping your bum” that got most of the media attention. As a piece of psychological warfare it was a bit of a practice on a shooting range. One can also remark on the functioning of the NOTION of “panic” – not actual “panic” but the notion of it.)
Now to the calculation. I am taking 6% as the incidence rate because it was mentioned here.
So we have
prior probability = incidence rate = 0.06
convert to odds: prior odds = 0.06 / 0.94 = 0.063830
true positive rate = sensitivity = 0.70
true negative rate = specificity = 0.95
false negative rate = 1 – 0.95 = 0.05
likelihood ratio = Bayes factor = true positive rate / false negative rate = 0.70 / 0.05 = 14
posterior odds = prior odds * likehihood ratio = 0.063830 * 14 = 0.893617
convert to probability: posterior probability = 0.893617 / 1.893617 = 0.471910
a positive test result from “RT-PCR” test, carried out on person chosen randomly, indicates that
the probability they are infected with SARS-CoV2 is 47%
As I said, many may have had SARS-CoV2 but were never tested. But there are also many who have been tested, and who tested positive, and who probably did not have SARS-CoV2. If these were all people who were tested only because they had the whole collection of specified symptoms, then the above figure 47% doesn’t tell us much, because it rests on an incidence figure of 6% which is (supposedly) for the whole population. However, they were NOT all people who displayed the said symptoms. Many of them were probably as fit a fiddle or at least had no more than a minor cold for a day or two. They include many who work in the NHS. The official advice is get tested if you have any one of the three famous symptoms. NHS advice:
You can get a test:
(…) if you have coronavirus symptoms now (a high temperature, a new, continuous cough, or a loss or change to your sense of smell or taste)
Note the use of “or” rather than “and”. A minor sniffle will give you the third of these symptoms.
It’s relevant that tests have been given out like smarties to NHS staff, because I would imagine that now that most hospital wards have been shut down the managers don’t want loads of nurses and other employees running around all over the place with nothing to do other than “makework”.
Last, while I’m here, going by official figures and interpretations it seems that many have caught SARS-CoV2 and successfully fought it off, in some cases without even getting symptoms. Their immune systems have defeated it, sometimes even before their antibodies have been called out! That’s good news! In many individuals, it’s been a case of Evolved Human Biology 1, The Nasty Virus 0. And not all of these people are children. Reason suggests that on average they have had a smaller viral load than those who have died from the virus, but the point is that their immune systems have fought the virus and won.
This makes it a disgrace that there has been absolutely no “public health advice” telling people how to strengthen their immune systems. (Cryzine make this point well in their footnote 7 here.) I could make a list of foods and substances but will mention only iron, zinc, and vitamin C (e.g. in orange juice) for the time being. Many middle class and lower middle class bureaucratic types assume that whatever they are not ordered to say to “the public” is material that “the public” shouldn’t hear, and doubtless they could come up with a dozen reasons why advice about “how to strengthen your immune system” would be “inappropriate” to give to people, would be misinterpreted, would cause more harm than help, would cause the sky to fall in, and so on and so forth, ad nauseam – a string of bullsh*t “reasons”.