Simpson’s paradox is a specific case of a wider class of problem known as the “ecological fallacy”, which says that you can’t always draw conclusions about individuals by looking at group data. A topical example: local authorities with above-average numbers of over-65s actually have a lower rate of death from Covid-19 than those with below-average numbers. But we know that older people are individually at greater risk. What’s going on seems to be that younger areas tend also to be denser, poorer, and more ethnically diverse, all of which drive risk up.
The apparent rise of the R value seems to be something like that. According to Edmunds, the rise is not because lockdown isn’t working (“it’s not that people are going about and mixing more”), but that it is working. There are, he says, separate epidemics in the community, and in care homes and hospitals.
“We had a very wide-scale community epidemic,” he told the committee, “and when we measured the R it was primarily the community epidemic. But that’s been brought down: the lockdown has worked, breaking chains of transmission in the community … now if you measure the R it’s being dominated by care homes and hospitals.”
Let’s imagine that we had two epidemics, of equal size, one in the community and one in care homes. Say 1,000 people are infected in each, and in the community each person on average infects two people, while in the care homes on average each person infects three. The total R is 2.5[1].
But now imagine you lock down and reduce both the R and the number of people infected, but by more in the community than in the care homes. Say that now there are 100 people infected in the community, and they each pass it on to an average of one person; and there are 900 people infected in the care homes, and they pass it on to an average of 2.8 people.
Now your average R is 2.62[2]; it’s gone up! But — just as with the Berkeley graduate students above — when you divide up the data into its constituent parts, it’s actually gone down in each category.
I don’t know the numbers, but according to Edmunds something like this has gone on in the real world. The collapse in the number of people with and passing on the disease in the community means that now the epidemic in care homes is a much greater share of the average. And that means, even though the R in care homes hasn’t gone up, the average R in total has, because the average in care homes was higher to start with.
To be clear: this doesn’t mean that everything is fine, or that we’ve won, or anything. “The thing that worries me is that it might be the overall R that matters,” says Kevin McConway, an emeritus professor of statistics at the Open University, who helped me understand these numbers. It’s not that the epidemics in the community and in care homes and hospitals are truly separate, islands cut off from each other — they’re interlinked, so if the disease spreads in care homes it can reinfect those of us outside it.
Edmunds said as much to the Science and Technology Committee: “Strictly speaking you have one R: there’s one epidemic and linked sub-epidemics; the epidemic in hospitals is not completely separate from the one in the community.” But to understand how it works, you need to look in this more granular fashion: the overall R is not much use on its own.
And while it doesn’t mean that we’ve won, it certainly shouldn’t be taken to mean that the British population has been lax in its approach to lockdown. Compliance has been very high, much higher than modellers anticipated.
But it does show that simple numbers can hide more complex stories. They feed, for instance, into modelling. One simple model is the SIR (susceptible, infected, recovered) model, where you assume everyone just interacts at random, mixing uniformly like molecules in a gas; but if the epidemics in care homes and the community behave very differently, then those models might give out very misleading numbers.
That’s why models such as the Imperial one try to simulate human behaviour to some degree; the extent to which it got that right is far from clear, but it was at least trying. Some more simple models that went around the internet did not. McConway, a statistician not a modeller, is profoundly wary of those: “I know enough [about modelling] to say I wouldn’t touch it because I’m not an expert; I see people getting it wrong in ways that I can recognise, whereas I’d get it wrong in ways I don’t recognise.” These subtle misunderstandings can drive major errors.
We’ve seen examples of this throughout the crisis. Early on, people (Donald Trump, notably) paid an awful lot of attention to the case numbers; but the case numbers didn’t really tell us how many people had the disease, just how many of them had been tested. And people have tried to place countries in a league table of death rates, but that’s not particularly informative either (although that’s not to say comparisons are entirely useless). Trying to boil down this messy, complicated situation to single numbers and saying whether they’re good or bad is rarely a good idea.
The really key thing, which I keep coming back to, is just how much uncertainty there is. “Modelling is bloody hard,” says McConway. “Prediction is bloody hard. The map is not the territory. We’ll know what’s happened when it’s happened.” Even something as apparently simple as the R value has to be treated with immense caution.
[1] ((1,000*2)+(1,000*3))/2000=2.5
[2] ((100*1)+(900*2.8))/1000=2.62
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SubscribeI share the article author’s doubts here about being ruled by the R value.
And indeed for the general reliance on statistics and models.
For example here is David Spiegelhalter (that is, Professor Sir David John Spiegelhalter OBE FRS, Fellow at Churchill College, Cambridge sometime consultant to pharmaceutical giants GlaxoSmithKline and Novartis, etc, etc.) admitting covid-19 fatality figures aren’t reliable.
https://www.theguardian.com…
But he goes way beyond that, which as presumably true given his status, is an absolutely staggering confession of how the UK for example gets its annual flu fatality figures – I quote verbatim:
“But these are still deeply unreliable numbers, as it is not clear if we should just be looking at Covid-19-labelled deaths anyway. The effects of seasonal flu are not based on tests or death certificates, but at looking at the total number of deaths over the winter, seeing how many extra there are than a baseline, allowing for climate, and assuming these excess deaths were linked to flu.”
And there was I, and millions of others I am sure, all assuming these “annual flu death” figures came from old fashioned commonsense things like testing.
But it now appears likely that has never much been possible, due to the time and expense on an already overburdened NHS, and my guess is that’s even far less likely to be happening right now reliably during this current covid-19 pandemic.
Which appears to make nearly all the figures we are using about as reliable as efforts to make a recognisable sculpture out of sand during a dust storm.
But nevertheless, if we do try to distill this situation to a recognisable essence, we are left with the apparently undeniable figures of the dead, which as far as we know at least tested positive for the presence of covid-19.
And that currently says 32,137 dead in the UK, population 65m = 1 in 2023; and then in Sweden, with no proper lockdown: 3,313 dead, population 10.2 million = 1 in 3079.
So Sweden with its no proper lockdown has a death rate far less than ourselves (so far admittedly, and pandemics tend to decline over the summer we are now nearly in).
Though my guess is that ours is worse probably due to being far more overcrowded per square mile/km, as England (not the UK, England) is between 2 and 4 times as densely crowded per square mile/km as France and Germany.
And the overcrowding in England is even worse in fact, as unlike Holland that has a similar population density, a lot of it is hilly (like Peak/Lake district) and mostly uninhabitable therefore – you can’t build a block of flats on Scafell Pike.
So then we are left with what the purpose was of the lockdown – and we’ve heard claims it was to “save lives”, “save the NHS”, etc, etc. but now all we are hearing about is the R rate.
Assuming that still implies we are trying to save either lives or the NHS, as the Swedish example has shown that the lockdown didn’t make any or hardly any difference, then what is the purpose of it now, and what was the cause for it in the first place?
Bearing in mind also, amidst this fanatical craze for virus spread models and obsession with R rates, we don’t seem to be hearing any similar fanaticism for modelling (and then shocking us with propaganda based on results from) the number of additional deaths caused by the lockdown.
Which could be huge, being in mind numerous thousands/millions of people are not treated, tested, operated upon, and too scared to go to the hospital because of covid-19 fears, etc.
And a clue as to why the lockdown was imposed, but nobody bothered to model the disastrous consequences of it, lies not only in the 2011 Contagion movie (inspired by the 2009 SARS epidemic), but this equally or even more misleading 2018 Contagion! – the BBC Four Pandemic documentary – note you see, how very, very close that is to this lockdown.
Of course even the BBC could not infect people with a real virus (though one wonders if the Chinese authorities or others might, which has serious biological war implications).
So in fact, not only did the BBC base their “Contagion” on a virtual virus on an app they could use to “contact trace” “virtual infections”, they took all sorts of other liberties, such as zero immunity and an R rate high enough to spur rapid exponential growth, with the result that within a short time there were about 43 million in the UK infected.
I won’t go into full details – the devil truly is in the details, as it’s about numerous modelling assumptions that probably need expert or commonsense hours to consider one by one.
But again, just like the Contagion movie, the idea was to firstly “scare the pants” off the viewers – e.g. undoubtedly the likes of Boris Johnson, with Brit stars in it like Oscar winner Kate Winslet – but then something far more sinister in both cases.
Which was to send the message that as horrible, terrifying and dangerous as a serious pandemic is (which the BBC “simulation” in 2018 “reassured” us was – you know, just like the government says about terrorist atrocities – not a matter of “if” but of “when”), scientists can control it, beat it even.
The Contagion movie, while by script-admitting that safe vaccines can take years to produce (or maybe never, like HIV, no vaccine yet produced since 1981), instead showed this utterly implausible but “heroic” (or in reality probably irresponsible and suicidal) act of star epidemologist Jennifer Ehle (another Brit star actress) who injects herself with a trial virus which ends up saving millions of lives.
But in the BBC documentary, science still “comes to our rescue” largely by spreading the viral idea that we can stop a deadly virus in its tracks by locating “superspreaders” (those who do a lot more “R-ing” than everybody else) and quarantining them.
Which suggests according to the BBC4 documentary, we are looking at a future if “the mad scientists” get their way in which as soon as there is any sniff of a virus, the logical corollary of the scientific consensus on epidemiology to date is we need to either lock down or dress in Hazmat suits (forcibly one presumes, as I can’t see it being effected by choice) these “superspreaders”, whose lifestyles bring them into contact with an unusually large number of people.
Such as publicans, hospitality staff, priests (spare me the communion wafer please, I don’t want to die of supercovid-219), librarians, checkout operators (soon to be automated anyway, regardless of the lost jobs) etc, etc.
Because the worrying thing that never really gets figured into these models, and appears to have happened in the case of covid-19, is that the disease was spread far and wide long before it came to national attention, which undue attention was as far as I can see mainly due to the outbreaks and deaths in Italy.
Whereas nobody much gave a damn while they thought it was mostly confined to China – a lot of China-Italy travel was unearthed of course, at least explaining why Italy got it badly first.
There’s another huge problem therefore with this R value and the associated models.
As unlike the “BBC (virtual) virus” it is not going to be possible to trace who gets and who transmits any new virus without testing (and reliably, which is also a serious problem, with only 70% accuracy claimed for the standard PCR test, and even that is doubted by many), at least for quite some time, any fast spreading virus is likely going to be all over the place before any lockdown or quarantining can be effected.
e.g. quite a few weeks ago they found in the US in the San Francisco Bay area a random sample (rarely done anywhere) tested over 25% positive for covid-19.
Which if true in the UK also would mean up to approximately 16 million could already have been infected before the lock down, which in fact would be well within the estimates of the Oxford University study, which suggested it could be up to 50%.
So if it is true that massive numbers of people in the UK already have the virus (but mostly hardly have any symptoms), then now testing is being done at a rate of 100,000 or whatever per time period – this may mean that the models then “reverse engineer” the R rate from using a totally false new infection figure, mistaking newly infected cases after partial release of the lockdown for people who have had it for a very long time, and may or may not be still infectious, causing a totally false suddenly inflated R figure.
This is my guess of what may happen next, and then the same knee-jerk response that caused the lockdown will likely reimpose it, and quite possibly even stricter than the first time.
Which then would in my view be likely to cause really serious problems between public and police (i.e. possible riots, etc.) as it’s clear a significant proportion of the public have had enough already, especially now the sunny weather is here.
While people might believe they can avoid or survive a virus, what people really are in terror of is starvation, rioting, and food motivated burglaries that could turn into mass rapes and murders, when police services are too stretched to protect the public any more (somewhat depicted in the 2011 Contagion movie).
Which has already been on the cards with various events we have witnessed, such as the bare supermarket shelves, with old people left behind in the mad stampede, turning up to find there is no food left or even toilet roll.
By initiating such globally unprecedented measures like lockdowns, the national leaders have risked the whole system, the availability of food, the ability to maintain law and order (clearly being seen in America now, with police and automatic weapon armed protesters ready to murder one another), based on an obsession with R value based models.
For which as the BBC documentary exposed, are very hard to get reliable data to work properly, even if the model is adequate, which is also doubtful.
So we are left with a PM, Boris Johnson, who has ordered a knee-jerk reaction response, based on a worst case scenario model, that may be wholly fictional, with a misguided set of scientists behind it believing they can “save us all”, forgetting the ridiculous and unrealistic way that the scientists played by Jennifer Ehle in the Contagion movie did – injecting herself with an untested and (in real life) probably lethal vaccine, which in this pure fiction of course unrealistically worked.
The message from the movie being you see, that we must do anything to stop Kate Winslet dying, and only science could (or could have) saved her.
If only we’d locked down sooner, or had implemented mass temperature testing or screening (and as the movie pointed out, for what? – when the virus was not already known).
We already know what airport security is like due to “anti-terrorism measures”, but if we allow ourselves to be ruled by basically this scientific paranoia, based on what might happen, rather than what does or has happened recently, there will be no end to it.
If this argument carries on far enough we will have to ban all risky (food especially) imports, probably shut down all Chinese restaurants and deport all Chinese (that’s just the start, if we find viruses originating elsewhere).
And force all the potential “super-spreaders” who have lots of public contact (including politicians and journalists themselves, let’s well keep in mind) to more or less permanently wear Hazmat suits.
Or frankly there’s a saner way, which will not turn us all into mummified prisoners shuffling around our everyday lives (those allowed out that is, which will be uncertain) in fear of the next “deadly virus.”
And it involves the acceptance of risk, and also unpleasant realities, which the public is normally shielded from, and in the future also should be in my view.
If the concern is a real 20%+ style untreatable virus, the most important thing is to maintain the system, and have enough body bags and means of body disposal (by cremation one assumes, as the most hygienic way).
So that the 80% who do survive it can live on, both adequately fed and without the terror and murderous and rapacious brutality which would result from the breakdown of law and order.
That’s what needs planning for, and not some kind of “heroic victory by science” over a pandemic, which the reality has been well proven (Sweden alone proves it) they cannot truly control.
The micromanagement of everybody’s lives, which is currently being enforced, is not acceptable to too many people, and not even effective, unless for example all but the tiniest amount of foreign travel is banned, and all illegal immigration is controlled, which it is not remotely the case at present.
Neither can enough of the public be relied upon to act according to instructions, when we have seen even in the case of Prof Ferguson himself, he has repeatedly defied his own lockdown, even knowing (or believing) he was an infected person, and even worse, knowing his alleged mistress had a husband and children who could then have become almost inevitably infected.
The moral there is if you don’t want to look stupid for breaking your own silly unenforceable rules, then simply don’t make them.
Our world, as even approximately as we knew it, cannot continue if we allow ourselves to be infected with this paranoia, and as is becoming obvious as the days pass currently, by trying to enforce this unworkable policy of “social distancing.”
(just try to enforce that on the millions of strangers who are gong to have intimate relations with one another in the coming summer season, rendering the whole thing ineffective and pointless)
Yes: if scientists can devise some sort of “super vaccine”, that will protect us from all such infections, and it has been tested long enough to be believed to be safe (which I’d suggest would take several years of trials, and not on humans at first), then yes, I would be in the queue to have it.
But otherwise, we have to face the reality of 600,000 a year are dying of numerous other causes in the UK annually, and a significant proportion as a result of viral infections we cannot prevent.
Including of course HIV, which according to the WHO still has 37 million people currently infected, with up to 1 million dying a year, but about which hardly a word is ever breathed by science or the media, while they assure us they are going to manage and contain and “defeat” covid 19.
Like doctors in general, it appears that the epidemiologists are going to bury their mistakes.
And indeed they are not as I said much talking about all the dead resulting from or occurred inevitably under the lockdown which we are certain have or will occur, it’s just a matter of the numbers, and which would not have occurred otherwise.
We are it appears faced with a quasi-scientific and despotic (as it locks the whole population up/down at its whim) government by proxy, mostly peopled by PC EU supporting figures, like the “Scientists for EU” group Prof Ferguson’s alleged mistress is associated with.
Who having failed to remove Boris Johnson from office as they desire by electoral means, have instead used their scientific authority and his frightened relative ignorance (his education is in literature/classics) to effectively run the country.
But it’s not acceptable, as we didn’t elect them, and most of us only elected Boris Johnson because we thought he’d do Brexit properly, which is still nowhere near complete or certain, but a “paper event” only so far.
In succumbing to this course of action, Mr Johnson seems to have bought into the fiction cooked up by all of Imperial, the BBC and Hollywood.
But this is no movie, this is real life, and tens of millions are being and are going to be affected by this lockdown in awful ways, up to a hundred thousand old people already having died in fear, isolation and loneliness of all causes.
And we do not know how many yet losing their jobs and businesses, but possibly millions judging by the events in America.
Science has got a place, in that it benefits our lives; medicine has a place, in which it mainly protects us from suffering, and “saving lives” has in fact always been a secondary issue.
But we cannot allow science to wrap us in cotton wool to the extent that life no longer becomes worth living, and cannot ultimately be sustained much beyond the average span in any case, especially not while much quality of life remains.
Government must therefore in future plan for what they are very sure is going to happen, not on unreliable scientific advice about what might happen.
Especially when the consequences of taking such action, as with this lockdown, causes numerous other disasters about which there is little or no “might happen”, and which were wholly avoidable without these drastic knee-jerk measures having been taken.
The excuse that “every other nation” (which isn’t true anyway, for example Sweden) is doing it, is not valid, any more than a wise lemming would follow the rest over the cliff top, which in the final analysis seems to be what we have been doing.
Whatever the scientific arguments for or against a lockdown, politically it was inevitable. As soon as the phrase herd immunity was mentioned, the more excitable elements of the media and the Twittersphere were calling Boris a mass murderer. Now think back to early April and imagine the hysterical level of criticism that the Government would have faced with deaths climbing, seemingly inexorably, towards 1,000 per day while Boris was “sitting on his hands”. The Government would have had to have ordered a lockdown and would have had no defence to the charge of having acted too late.
In the early days, Whitty et al emphasised that this was a mild disease for the vast majority. Once lockdown started, we didn’t hear that any more. I think in the desire to ensure public compliance, the Government has overdone the “deadly disease” messaging, with the result that many people are worrying too much about the risks of returning to normal life.
“at least it was trying” is a damning indictment. If you can’t accurately model something, it’s probably better that you don’t or people will take decisions based on that model which may ultimately be completely wrong. There are whole sections in the book Black Swan on this which have been borne out by recent experience.
(Really good article, however – I always find Simpson’s paradox fascinating and usually relevant to public policy)
I spy another computer model.
One small point. Nobody knows the actual infection rate… there is no data. The problem with this mess is that disease, ie infection with symptoms or noticeable symptoms which are reported ‘cases’ is being conflated with total number of infections which being asymptomatic (not disease) or minor are not reported ‘cases’.
There is no data by which the relationship between number of infections in the population and the number of these that become cases of disease can be established.
Also we know that infection turns to serious/critical, therefore reported ‘cases’ in a limited sub-set of the population – the elderly and/or with underlying health conditions. Therefore a relationship between infection and serious disease cannot be applied for the population as a whole.
To infer that the shape of the curve showing cases of disease mirrors the infection curve, is not science it is make-believe and untrue in the absence of data. Saying the flattened curve of reported cases is the curve of flattened infection is not telling the truth. To say this shows lockdown worked is a logical fallacy and is not science which requires external corroborative data to demonstrate a causal link between two variables.
How many people were infected when the first case of disease was reported? Unknown.
What has been the daily incremental increase in the number infected since? Unknown. What is the shape of that curve – unknown, there being no data.
Herd immunity, like vaccination, does not prevent infection, it prevents infection becoming disease… like a fire extinguisher, it does not prevent fires, it puts them out before they take hold.
It would be helpful if journalists understood ‘the science’ even if the politicians do not.
Epidemic becomes pandemic when attempts to control the spread of infection by strict quarantine fails, or the spread is too large to be contained. Believing that having failed to or been unable to control epidemic it is possible to control pandemic is the reasoning of the mad house. Saying it is so knowing it cannot be so is deceitful.
Could we just stop tte deceit. Governments made a grave error because they ignored the actual data and science, and instead chose to be panicked by non-science – a computer model from an ‘expert’ whose models (Foot & Mouth, BSE, SARS) have failed every time in the past.
We do have data. Serological studies have started to come in, including from Iceland, New York, Italy, and cruise ships.
The Imperial model has been unfairly trashed by the ignorant in social media, but the predictions seem to be correct and consistent with the serology data. A widespread study from the UK gets published this week I think, but initial estimates from it seem to be in line with current knowledge.
” Herd immunity, like vaccination, does not prevent infection, it prevents infection becoming disease… like a fire extinguisher, it does not prevent fires, it puts them out before they take hold.”
But isn’t that the point. Most of our existing Coronaviruses affect a few people here and there, but don’t cause significant problems. It seems that it because the became pandemic in the past when they first reached humans, and now we have herd immunity. Given our lack of success with vaccines in this area to date, this seems like the inevitable route we will have to take at some stage.
The subheadline is a patently false premise, dishonest or ignorant.
“A rise in the Covid-19 infection rate actually means that lockdown is working”
Working?? Do you have any clue what the purpose of the lockdown even was? It had nothing to do with R-values, nothing to do with death rates or infection rates, none whatsoever.
The only reason we agreed (however tacitly) to the suspension of our Constitutional rights with the lockdowns – the sole, solitary reason – was to prevent excess deaths that would’ve occurred had our health care system been overwhelmed, as happened in Italy. It was to spread out over a longer period of time the same deaths and infections, to keep that curve below the hospital and health care system capacity.
That was the only reason given for, the only reason used to sell to us, the lockdowns. PERIOD. In that regard, it’s #MissionAccomplished, and every lockdown should be rescinded immediately. Every lockdown now is an illegitimate expansion of power – not authority, power – by despotic governors.
To reiterate, the curve has been flattened, which was the only justification for suppressing our Constitutional rights. #EndTheLockdownsNow
So to make any reference to the infection rate as a means of defending the lockdowns is sheer dishonesty or ignorance. It makes me wonder about the author’s motivation in moving the goalposts.
Is he a wannabe-tyrant, like so many governors, drunk on his totalitarian instincts and impulses? Is he a Leftist, trying to capitalize on this crisis to re-shape the world to his tyrannical ideal?
I don’t know. You tell me.
I think I understand how the R number is calculated theoretically, but how is it calculated in practice in the UK? If we don’t know how many people in the UK are infected how can we know the R rate? Does anyone know what figures they use for the calculation?
Astute observation. No denominator for those infected as an unknown guestimate are asymptomatic and possibly a majority not antigen or antobody tested. Quite a mess linked directly to those largely anonymous individuals pushing one model after another at the poor (in the sense of unfortunate!) politicians who will ultimately be held accountable.
I take Tom’s point about the hospital, care home and community R rates not being in entirely separate islands. But surely the focus of government actions now should be to try to make these three elements as separate as possible, so people working in care homes are as isolated as possible from the wider community? To some extent, I think this is indeed happening.
But it is frustrating that there is not more of an effort by the government to publish more data and also to fine-tune the lockdown in the light of the latest data. For example, the community R figure must be well below 1, from what Tom says here and what one can glean from the data that is publicly available. If people knew this, they would perhaps be more willing to return to work, with all the social distancing etc that would come with that. As many people have said, the government’s initial policy of scaring people into the lockdown has now been too successful as we try to find a way out of it. Citing a misleadingly high R number just reinforces the problem.
Doesn’t every kid learn at school not to average averages?
Is this just a very complicated way of saying that the more people below the age of, say, 65 become infected, the better? That has always been my belief, which is why I am always happy to see people out in the sunshine and fresh air, possibly, contracting C-19.
I think you need to revise on confirmation bias. There is nothing in the article to say the more people under 65 who get the virus, the better.
How is it possible to compare R in a care home and wider community? Care home may have R around 3 or even more however once everyone is infected and that would happen within a few days, R becomes zero when there is no more residents to infect. Similarly a more pronounced reduction in R has happened in London because disproportionately more people in London must have been infected yet elsewhere infection curves remained more flat reduction in infection rate/hospitalisation (R) was not as noticeable.
If you assume that the most socially active people living in the most dense areas start the spreading(high R0 value) and then eventually heads towards hermites living I sparsely populated areas(very low R values), how can these models assume that we all essentially live and behave the same way(R0 = 2.5)? This is the basis for calculating herd immunity level( 1-(1/R0)). Makes no sense. Why wouldn’t the 80/20 rule apply to R values? 20% of the people have 80% of the social interactions mostly contained in networks. If you then apply a marginal R value instead of an average value when calculating herd immunity, the level is much lower. I think google mathematicians and professor Tom Britton in Sweden is now revising their models and the Herd immunity levels could be between 20″“40% instead of the 60-70% touted by the feral modellers previously. How would a herd immunity level of say 30% change “Lockdown thinking”?
To me the problem doesn’t seem to be that statistical variations might give a slightly disingenuous measurement of R0, it’s that R0 is actually a snapshot of the infection rate from about 10-19 days ago.
Covid-19 has an incubation of 5-14 days and test results take an average of 5 days to be produced according to Vance in the briefing. Most people tested do so because they have symptoms, small groups such as medical professionals get tested regardless as does the small ONS sample who are tested every 7 days. This gives a best case scenario of 5 days to show symptoms & get a test done + 5 days to get the result. When this is used to calculate R0 it is for an infection acquired at least 10 days ago.
With such a lag in R0 calculation how can the government know the changes they make to the lockdown now haven’t pushed R0 above 1 thus having a disastrous effect on the numbers infected due to exponential growth from a starting number of between 136k (average) & 250k(top end) people currently infected (again from Vance in the briefing). Any form of exponential growth from these starting numbers during a grey zone of 10 days would set the NHS on a course to be overwhelmed in a very short space of time.
Interesting. Tom, you write, “… they [women] tended to apply to more competitive departments”. It could be argued that more women tend to apply to less competitive departments. This point is conceded in part by your shift towards the word popular in place of competitive when you write, “it might be, for instance, that there is a lack of investment in the popular but female-dominated classes.”
The article you cite (Bickel, et.al.) is less ambivalent, it concludes, “Women are shunted by their socialization and education toward fields of graduate study that are generally more crowded, less productive of completed degrees, and less well funded, and that frequently offer poorer professional employment prospects.” It’s hard to see how these courses could be best characterised as being “more competitive”.
This criticism is, of course, correct. It would have been more sensible of Tom not to get into the politics of the Berkeley example (or the social justice issues underlying the politics). The example would stand up, without reference to whether the arrangements were, in detail, just or unjust. The point is, simply, that the aggregate number in itself did not demonstrate injustice. Tom could have chosen another example where this problem did not arise, like the batting averages over two seasons of player A who had the highest average over the two seasons taken together and player B who had the highest average in each of them taken separately.
I don´t doubt that lock-down slows down the spread of infection, at least among people who normally move around. It might not be as protective to people in need of care in nursing homes. The problem with lock-down is how to open up. There is a obvious risk that the virus starts spereading again, reching the nursing homes, upsettning media and forcing a new lock-down.
Models seem to give very little useful guidance, rather misguidance. Predictions of Swedish death rates based on the Imperial college paper were catastophically wrong, sofar predicting twenty times more deaths than what has actually happened (https://www.medrxiv.org/con…. But it is still early in the pandemia.
Mats Adler, MD, PhD. Stockholm, Sweden
An excellent analysis – thank you.