What is the UK government trying to do with COVID-19?

It would be a drastic understatement to say that people are confused by the official advice coming with respect to social-distancing measures to prevent the spread of SARS-CoV-2. Some are angry. Some are appalled. And that includes some very smart people who understand the relevant science better than I do, and probably at least as well as the experts who are advising the government. Why are they not closing schools and restaurants, or banning sporting events — until the Football Association decided to ban themselves — while at the same time signalling that they will be taking such measures in the future? I’m inclined to start from the presumption that there’s a coherent and sensible — though possibly ultimately misguided (or well guided but to-be-proved-retrospectively wrong) — strategy, and I find it hard to piece together what they’re talking about with “herd immunity” and “nudge theory”.

Why, in particular, are they talking about holding the extreme social-distancing measures in reserve until later? Intuitively you would think that slowing the progress of the epidemic can be done at any stage, and the sooner you start the more effective it will be.

Here’s my best guess about what’s behind it, which has the advantage of also providing an explanation why the government’s communication has been so ineffective: Unlike most other countries, which are taking the general approach that the goal is to slow the spread of the virus as much as possible (though they may disagree about what is possible), the UK government wants to slow the virus, but not too much.

The simplest model for the evolution of the number of infected individuals (x) is a differential equation

Here A is the fraction immune at which R0 (the number that each infected person infects) reaches 1, so growth enters a slower phase. The solution is

Basically, if you control the level of social interaction, you change k, slowing the growth of the cumulative rate parameter K(t). There’s a path that you can run through, at varying rates, until you reach the target level A. So, assuming the government can steer k as they like, they can stretch out the process as they like, but they can’t change the ultimate destination. The corresponding rate of new infections — the key thing that they need to hold down, to prevent collapse of the NHS — is kx(Ax). (It’s more complicated because of the time delay between infection, symptoms, and recovery, raising the question of whether such a strategy based on determining the timing of epidemic spread is feasible in practice. A more careful analysis would use the three-variable SIR model.)

Suppose now you think that you can reduce k by a certain amount for a certain amount of time. You want to concentrate your effort in the time period where x is around A/2. But you don’t want to push k too far down, because that slows the whole process down, and uses up the influence. The basic idea is, there’s nothing we can do to change the endpoint (x=A); all you can do is steer the rate so that

  1. The maximum rate of new infections (or rather, of total cases in need of hospitalisation) is as low as possible;
  2. The peak is not happening next winter, when the NHS is in its annual flu-season near-collapse;
  3. The fraction A of the population that is ultimately infected — generally taken to be about 60% in most renditions — includes as few as possible of the most at-risk members of the public. That also requires that k not be too small, because keeping the old and the infirm segregated from the young and the healthy can only be done for a limited time. (This isn’t Florida!)

Hence the messaging problem: It’s hard to say, we want to reduce the rate of spread of the infection, but not too much, without it sounding like “We want some people to die.”

There’s no politic way to say, we’re intentionally letting some people get sick, because only their immunity will stop the infection. Imagine the strategy were: Rather than close the schools, we will send the children off to a fun camp where they will be encouraged to practice bad hygiene for a few weeks until they’ve all had CoViD-19. A crude version of school-based vaccination. If it were presented that way, parents would pull their children out in horror.

It’s hard enough getting across the message that people need to take efforts to remain healthy to protect others. You can appeal to their sense of solidarity. Telling people they need to get sick so that other people can remain healthy is another order of bewildering, and people are going to rebel against being instrumentalised.

Of course, if this virus doesn’t produce long-term immunity — and there’s no reason necessarily to expect that it will — then this strategy will fail. As will every other strategy.

Putting Covid-19 mortality into context

[Cross-posted with Statistics and Biodemography Research Group blog.]

The age-specific estimates of fatality rates for Covid-19 produced by Riou et al. in Bern have gotten a lot of attention:

0-910-1920-2930-3940-4950-5960-6970-7980+Total
.094.22.911.84.013469818016
Estimated fatality in deaths per thousand cases (symptomatic and asymptomatic)

These numbers looked somewhat familiar to me, having just lectured a course on life tables and survival analysis. Recent one-year mortality rates in the UK are in the table below:

0-910-1920-2930-3940-4950-5960-6970-7980-89
.012.17.43.801.84.2102885
One-year mortality probabilities in the UK, in deaths per thousand population. Neonatal mortality has been excluded from the 0-9 class, and the over-80 class has been cut off at 89.

Depending on how you look at it, the Covid-19 mortality is shifted by a decade, or about double the usual one-year mortality probability for an average UK resident (corresponding to the fact that mortality rates double about every 9 years). If you accept the estimates that around half of the population in most of the world will eventually be infected, and if these mortality rates remain unchanged, this means that effectively everyone will get a double dose of mortality risk this year. Somewhat lower (as may be seen in the plots below) for the younger folk, whereas the over-50s get more like a triple dose.

Do billionaire mayors make you live longer?

In trying to compose an argument for why Democrats’ best hope for defeating the incompetent septuagenarian autocratic billionaire Republican in the White House is to nominate a highly competent septuagenarian autocratic billionaire (former) Republican of their own, Emily Stewart at Vox — jumping in to extend Vox’s series on the leading candidates in the Democratic presidential primary with the case for late entrant Mike Bloomberg — has some reasonable points, mixed in with one very odd accolade:

Under Bloomberg, New Yorkers’ life expectancy increased by about three years.

Not that this is false, but we must recall that Bloomberg was mayor of New York for 12 years. As pointed out by Oeppen and Vaupel in a Science article that appeared in 2002 (the first year of Bloomberg’s mayoralty), life expectancy at birth in the most economically advanced countries of the world has been increasing at an astonishingly steady 2.5 years per decade since around 1840. If we had then predicted how much increase we should expect over 12 years, we should have said… three years. Indeed, looking at a few comparably wealthy countries chosen more or less at random over the same period we see life expectancy at birth as follows:

Country20022014Increase
Australia80.0782.592.52
UK78.2481.162.92
Japan81.8383.731.90
Canada79.5781.942.37
Netherlands78.4181.653.24

Mike got it done!

To be fair there are two exceptions to this trend: Japan, which had the highest life expectancy in the world in 2002 still had the highest in 2014, but it had gained only two years.

The USA, which had the lowest life expectancy at the start (among large wealthy countries), at 77.03, fell further behind, to 79.06, and has since actually decreased. So I guess you might say that Bloomberg has shown his ability to thwart the destructive trends in the US, and make it, as he made New York, as successful as an average West European country. Which doesn’t sound like the worst campaign platform.

Trump supporters are ignoring the base (rate) — Or, Ich möcht’ so gerne wissen, ob Trumps erpressen

One of the key insights from research on decision-making — from Tversky and Kahneman, Gigerenzer, and others — is the “base rate fallacy”: in judging new evidence people tend to ignore the underlying (prior) likelihood of various outcomes. A famous example, beloved of probability texts and lectures, is the reasonably accurate — 99% chance of a correct result — test for a rare disease (1 in 10,000 in the population). A randomly selected person with a positive test has a 99% chance of not having the disease, since correct positive tests on the 1 in 10,000 infected individuals are far less common than false positive tests on the other 9,999.

This seems to fit into a more general pattern of prioritising new and/or private information over public information that may be more informative, or at least more accessible. Journalists are conspicuously prone to this bias. For instance, as Brexit blogger Richard North has lamented repeatedly, UK journalists would breathlessly hype the latest leaks of government planning documents revealing the extent of adjustments that would be needed for phytosanitary checks at the border, for instance, or aviation, where the same information had been available for a year in official planning documents on the European Commission website. This psychological bias was famously exploited by WWII British intelligence operatives in Operation Mincemeat, where they dropped a corpse stuffed with fake plans for an invasion at Calais into the sea, where they knew it would wind up on the shore in Spain. They knew that the Germans would take the information much more seriously if they thought they had found it covertly. In my own experience of undergraduate admissions at Oxford I have found it striking the extent to which people consider what they have seen in a half-hour interview to be the deep truth about a candidate, outweighing the evidence of examinations and teacher evaluations.

Which brings us to Donald Trump, who has been accused of colluding with foreign governments to defame his political opponents. He has done his collusion both in private and in public. He famously announced in a speech during the 2016 election campaign, “Russia, if you’re listening, I hope you’re able to find the 30,000 emails that are missing. I think you will probably be rewarded mightily by our press.” And just the other day he said “I would think that if [the Ukrainean government] were honest about it, they’d start a major investigation into the Bidens. It’s a very simple answer. They should investigate the Bidens because how does a company that’s newly formed—and all these companies—and by the way, likewise, China should start an investigation into the Bidens because what happened in China is just about as bad as what happened with Ukraine.”

It seems pretty obvious. But no, that’s public information. Trump has dismissed his appeal to Russia as “a joke”, and just yesterday Senator Marco Rubio contended that the fact that the appeal to China was so blatant and public shows that it probably wasn’t “real”, that Trump was “just needling the press knowing that you guys are going to get outraged by it.” The private information is, of course, being kept private, and there seems to be a process by which formerly shocking secrets are moved into the public sphere gradually, so that they slide imperceptibly from being “shocking if true” to “well-known, hence uninteresting”.

I am reminded of the epistemological conundrum posed by the Weimar-era German cabaret song, “Ich möcht’ so gern wissen, ob sich die Fische küssen”:

Ich möcht’ so gerne wissen
Ob sich die Fische küssen –
Unterm Wasser sieht man’s nicht
Na, und überm Wasser tun sie’s nicht!

I would so like to know
if fish sometimes kiss.
Underwater we can’t see it.
And out of the water they never do it.

The power of baselines

From today’s Guardian:


It took decades to establish that smoking causes lung cancer. Heavy smoking increases the risk of lung cancer by a factor of about 11, the largest risk ratio for any common risk factor for any disease. But that doesn’t make it peculiar that there should be any non-smokers with lung cancer.

As with my discussion of the horrified accounts of obesity someday overtaking smoking as a cause of cancer, the main cause is a change in the baseline level of smoking. As fewer people smoke, and as non-smokers stubbornly continue to age and die, the proportional mortality of non-smokers will inevitably increase.

It is perfectly reasonable to say we should consider diverting public-health resources from tobacco toward other causes of disease, as the fraction of disease caused by smoking declines. And it’s particularly of concern for physicians, who tend toward essentialism in their view of risk factors — “lung cancer is a smoker’s disease” — to the neglect of base rates. But the Guardian article frames the lung cancer deaths in non-smokers as a worrying “rise”:

They blame the rise on car fumes, secondhand smoke and indoor air pollution, and have urged people to stop using wood-burning stoves because the soot they generate increases risk… About 6,000 non-smoking Britons a year now die of the disease, more than lose their lives to ovarian or cervical cancer or leukaemia, according to research published on Friday in the Journal of the Royal Society of Medicine.

While the scientific article they are reporting on never explicitly says that lung cancer incidence in non-smokers [LCINS] is increasing, certainly some fault for the confusion may be found there:

the absolute numbers and rates of lung cancers in never-smokers are increasing, and this does not appear to be confounded by passive smoking or misreported smoking status.

This sounds like a serious matter. Except, the source they cite a) doesn’t provide much evidence of this and b) is itself 7 years old, and only refers to evidence that dates back well over a decade. It cites one study that found an increase in LCINS in Swedish males in the 1970s and 1980s, a much larger study that found no change over time in LCINS in the US between 1959 and 2004, and a French study that found rates increasing in women and decreasing in men, concluding finally

An increase in LCINS incidence could be real, or the result of the decrease in the proportion of ever smokers in some strata of the general population, and/or ageing within these categories.

What proportion of lung cancers should we expect to be found in non-smokers? Taking the 11:1 risk ratio, and 15% smoking rate in the UK population, we should actually expect about 85/(15×11)≈52% of lung cancer to occur in non-smokers. Why is it only 1/6, then? The effect of smoking on lu estimated that lung cancer develops after about 30 years of smoking. If we look back at the 35% smoking incidence of the mid 1980s, we would get an estimate of about 65/(35×11)≈17%.

Achieving transparency, or, Momus among the rotifers

1561 v. Heemskerck Momus tadelt die Werke der Goetter

At the recent Evolutionary Demography meeting in Miami there were two talks on the life history of rotifers. One of the speakers praised rotifers as a model organism for their generously choosing to be transparent, facilitating study of their growth and physiological changes. I had never really thought much about transparency as a positive feature of organisms (from the perspective of those wanting to study them) — though I guess the same has also favoured the development of the C. elegans system.

I was reminded of the famous quip (reported by his son Leonard Huxley) of T H Huxley, when he asked a student at the end of a lecture whether he had understood everything:

“All but one part,” replied the student, “during which you stood between me and the blackboard.”

To which Huxley rejoined, “I did my best to make myself clear, but could not render myself transparent.”

Momus would have been pleased.

Your shadow genetic profile

So, the “Golden Gate killer” has been caught, after forty years. Good news, to be sure, and it’s exciting to hear of the police using modern data systems creatively:

Investigators used DNA from crime scenes that had been stored all these years and plugged the genetic profile of the suspected assailant into an online genealogy database. One such service, GEDmatch, said in a statement on Friday that law enforcement officials had used its database to crack the case. Officers found distant relatives of Mr. DeAngelo’s and, despite his years of eluding the authorities, traced their DNA to his front door.

And yet… This is just another example of how all traditional notions of privacy are crumbling in the face of the twin assaults from information technology and networks. We see this in the way Facebook generates shadow profiles with information provided by your friends and acquaintances, even if you’ve never had a Facebook account. It doesn’t matter how cautious you are about protecting your own data: As long as you are connected to other people, quite a lot can be inferred about you from your network connections, or assembled from bits that you share with people to whom you are connected.

Nowhere is this more true than with genetic data. When DNA identification started being used by police, civil-liberties and privacy activists in many countries forced stringent restrictions on whose DNA could be collected, and under what circumstances it could be kept and catalogued. But now, effectively, everyone’s genome is public. It was noticed a few years back that it was possible to identify (or de-anonymize) participants in the Personal Genome Project, by drawing on patterns of information in their phenotypes. Here’s a more recent discussion of the issue. But those people had knowingly allowed their genotypes to be recorded and made publicly available. In the Golden Gate Killer case we see that random samples of genetic material can be attributed to individuals purely based on their biological links to other people who volunteered to be genotyped.

The next step will be, presumably, “shadow genetic profiles”: A company like GEDmatch — or the FBI — could generate imputed genetic profiles for anyone in the population, based solely on knowledge of their relationships to other people in their database, whether voluntarily (for the private company) or compulsorily (FBI).

Natural frequencies and individual propensities

I’ve just been reading Gerd Gigerenzer’s book Reckoning with Risk, about risk communication, mainly a plaidoyer for the use of “natural frequencies” in place of probabilities: Statements in the form “In how many cases out of 100 similar cases of X would you expect Y to happen”. He cites one study forensic psychiatry experts who were presented with a case study, and asked to estimate the likelihood of the individual being violent in the next six months. Half the subjects were asked “What is the probability that this person will commit a violent act in the next six months?” The other half were asked “How many out of 100 women like this patient would commit a violent act in the next six months?” Looking at these questions, it was obvious to me that the latter question would elicit lower estimates. Which is indeed what happened: The average response to the first question was about 0.3; the average response to the second was about 20.

What surprised me was that Gigerenzer seemed perplexed by this consistent difference in one direction (though, obviously, not by the fact that the experts were confused by the probability statement). He suggested that those answering the first question were thinking about the same patient being released multiple times, which didn’t make much sense to me.

What I think is that the experts were thinking of the individual probability as a hidden fact, not a statistical statement. Asked to estimate this unknown probability it seems natural that they would be cautious: thinking it’s somewhere between 10 and 30 percent they would not want to underestimate this individual’s probability, and so would conservatively state the upper end. This is perfectly consistent with them thinking that, averaged over 100 cases they could confidently state that about 20 would commit a violent act.

Quoth the raven, Never Trump

Carl Hempel famously crystallised an obstruction to the formalisation of inductive reasoning as the “Raven paradox”: Suppose I am an ornithologist, concerned to prove my world-shaking hypothesis, “All ravens are black”. I could go out into the field with binoculars and observe ravens. Suppose that over the course of the week I see 198 black ravens, 0 white ravens, 0 green ravens, and so on. These are strong data in favour of my hypothesis, and my publication in the Journal of Chromo-ornithology is assured. (And if they turn it down, I’ve heard there are numerous black studies journals…) But it gets cold out in the field, and sometimes damp, so I could reason as follows: “‘All ravens are black’ is equivalent to ‘all non-black objects are not ravens’.” And in my warm and dry study there may be no ravens, but there are many non-black objects. So I catalogue all the pink erasers and yellow textbooks and white mugs, and list them all as evidence for my hypothesis.

The status of this charming story as a paradox depends on the belief that no one would actually make such an inference. Behold, the president of the United States: Last week the special prosecutor for matters related to Russian interference with the 2016 US election released an indictment of 13 Russians. None of them had worked with the Trump campaign. Trump’s response:

In other words, while it is proving too difficult to collect proof of the contention “No anti-American voter fraud was performed by Trump,” he is collecting evidence that “There were actions not performed by Trump that were anti-American voter fraud.”

The EU OS

Twenty years ago I had a short visit from a college friend* who had just discovered the technical utopia. Completely enthralled. The Internet was going to upend all power relations, make all governments irrelevant, make censorship impossible. I was fascinated, but I did ask, How is The Internet going to clean the sewers?

But there was something else that intrigued me. He was very much on the nonscience side as a student, but he had just been learning some programming. And he had discovered something amazing: When your computer looks like it isn’t doing anything, it’s actually constantly active, checking whether any input has come. The user interface is a metaphorical desktop, inert and passive until you prod it, but beneath the surface a huge amount of complicated machinery is thrumming to generate this placid illusion.

I thought of this when reading The European Union: A Very Short Introduction. The European Union is complicated. For instance, in EU governance there is the European Council and the Council of the European Union, which are distinct, and neither one is the same as the Council of Europe (which is not part of the EU at all). There is a vast amount of work for lawyers, diplomats, economists, and various other specialists — “bureaucrats” in the common parlance — to give form and reality to certain comprehensible goals, the famous “four freedoms” — free movement of goods, capital, services, and labour. The four freedoms are the user interface of the EU, if you will, and the

There’s a lot of legacy code in the EU. In the absence of a further world war to flatten the institutions and allow a completely new constitution to be created, EU institutions had to be made backward compatible with existing nation states. There is a great deal of human work involved in carrying out these compatibility tasks. When people complain that the EU is “bureaucratic”, that’s more or less what they mean. And when they complain about “loss of sovereignty” what they mean is that their national operating system has been repurposed to run the EU code, so that some of the action of national parliaments has become senseless on its own terms.

Some people look at complicated but highly useful structures with a certain kind of awe. When these were social constructs, the people who advised treating them with care used to be called “conservatives”. The people who call themselves Conservative these days, faced with complicated structures that they can’t understand, feel only an irresistible urge to smash them.

* German has a word — Kommilitone — for exactly this relationship (fellow student), lacking in English. Because it’s awkward to say “former fellow student”.