The unexpected epidemic: A political paradox

An epidemiologist says, “A new pandemic will definitely sweep the world some time this century. But you won’t know until the day it starts when it will be. So you’d better start preparing now.”

The president is downcast. He doesn’t like preparing, but he also doesn’t like when the stock-market falls and people on TV blame him for millions of deaths and blah blah blah. What can he do?

His son-in-law comes to him and says, “I read a book on this. This prediction of an unexpected epidemic can’t happen. Imagine it’s 2099 and there hasn’t been a pandemic yet. Then people would know it has to happen in 2099. So it has to happen earlier. But now, suppose we get to 2098 without a pandemic. We know it can’t happen in 2099, so we would know for sure it must be 2098, which would contradict what the so-called expert told us.” And so, step by step, he shows that the unexpected pandemic can never happen.

You know the rest: The president disbands the National Security Council pandemic preparedness team and writes a celebratory tweet. And then in 2020 a pandemic arrives, and the president announces that “this is something that you can never really think is going to happen.”

(For the original version see Quine’s “On a so-called paradox“. For an account of some of the many times experts warned that a pandemic was coming and would be disastrous, see here.)

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:

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.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:

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.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.

The coronavirus spectre

This article about the effect of the coronavirus pandemic on air travel mentions social-media criticism of millennials (of course!) for ignoring public health advice by taking advantage of lowered airfares for inessential travel. It occurred to me, though, that the well-publicised observation that the virus seems hardly to affect children and young people at all may create different incentives for different age groups.

And that reminded me of The Subtle Knife, book 2 of Phillip Pullman’s fantasy trilogy His Dark Materials about Oxford scholars (and children) exploring the multiverse. A significant portion of that book is set in a parallel world that has been overtaken by “spectres” that attack and devour the minds of adults, but leave children unharmed. So children run wild and the few remaining adults are in hiding.

No further comment…

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%.

Medical hype and under-hype

New heart treatment is biggest breakthrough since statins, scientists say

I just came across this breathless headline published in the Guardian from last year. On the one hand, this is just one study, the effect was barely statistically significant, and experience suggests a fairly high likelihood that this will ultimately have no effect on general medical practice or on human health and mortality rates. I understand the exigencies of the daily newspaper publishing model, but it’s problematic that the “new research study” has been defined as the event on which to hang a headline. The only people who need that level of up-to-the-minute detail are those professionally involved in winnowing out the new ideas and turning them into clinical practice. We would all be better served if newspapers instead reported on what new treatments have actually had an effect over the last five years. That would be just as novel to the general readership, and far less erratic.

On the other hand, I want to comment on one point of what I see as exaggerated skepticism: The paragraph that summarises the study results says

For patients who received the canakinumab injections the team reported a 15% reduction in the risk of a cardiovascular event, including fatal and non-fatal heart attacks and strokes. Also, the need for expensive interventional procedures, such as bypass surgery and inserting stents, was cut by more than 30%. There was no overall difference in death rates between patients on canakinumab and those given placebo injections, and the drug did not change cholesterol levels.

There is then a quote:

Prof Martin Bennett, a cardiologist from Cambridge who was not involved in the study, said the trial results were an important advance in understanding why heart attacks happen. But, he said, he had concerns about the side effects, the high cost of the drug and the fact that death rates were not better in those given the drug.

In principle, I think this is a good thing. There are far too many studies that show a treatment scraping out a barely significant reduction in mortality due to one cause, which is highlighted, but a countervailing mortality increase due to other causes, netting out to essentially no improvement. Then you have to say, we really should be aiming to reduce mortality, not to reduce a cause of mortality. (I remember many years ago, a few years after the US started raising the age for purchasing alcohol to 21, reading of a study that was heralded as showing the success of this approach, having found that the number of traffic fatalities attributed to alcohol had decreased substantially. Unfortunately, the number of fatalities not attributed to alcohol had increased by a similar amount, suggesting that some amount of recategorisation was going on.) Sometimes researchers will try to distract attention from a null result for mortality by pointing to a secondary endpoint — improved results on a blood test linked to mortality, for instance — which needs to be viewed with some suspicion.

In this case, though, I think the skepticism is unwarranted. There is no doubt that before the study the researchers would have predicted reduction in mortality from cardiovascular causes, no reduction due to any other cause, and likely an increase due to infection. The worry would be that the increase due to infection — or to some unanticipated side effect — would outweigh the benefits.

The results confirmed the best-case predictions. Cardiovascular mortality was reduced — possibly a lot, possibly only slightly. Deaths due to infections increased significantly in percentage terms, but the numbers were small relative to the cardiovascular improvements. The one big surprise was a very substantial reduction in cancer mortality. The researchers are open about not having predicted this, and not having a clear explanation. In such a case, it would be wrong to put much weight on the statistical “significance”, because it is impossible to quantify the class of hypotheses that are implicitly being ignored. The proper thing is to highlight this observation for further research, as they have properly done.

When you deduct these three groups of causes — cardiovascular, infections, cancer — you are left with approximately equal mortality rates in the placebo and treatment groups, as expected. So there is no reason to be “concerned” that overall mortality was not improved in those receiving the drug. First of all, overall mortality was better in the treatment group. It’s just that the improvement in CV mortality — as predicted — while large enough to be clearly not random when compared with the overall number of CV deaths, it was not large compared with the much larger total number of deaths. This is no more “concerning” than it would be, when reviewing a programme for improving airline safety, to discover that it did not appreciably change the total number of transportation-related fatalities.

Obesity and cancer

The Guardian has prominently posted a report by Cancer Research UK with a frightening headline:

Obesity to eclipse smoking as biggest cause of cancer in UK women by 2043

That’s pretty sensational. I was intrigued, because the mortality effects of obesity have long intrigued me. It seems like I’ve been hearing claims for decades, loudly trumpeted in the press, that obesity is turning into a health crisis, with the mortality crisis just around the corner. It seems plausible, and yet every time I try to dig into one of these reports, to find out what the estimates are based on, I come up empty. Looking at the data naively, it seems that the shift from BMI 20 to BMI 25 — the threshold of official “overweight” designation — has been associated in the past with a reduction in all-cause mortality. Passing through overweight to “obesity” at BMI 30 raises mortality rates only very slightly. Major increases in mortality seem to be associated with BMI over 35 or 40, but even under current projections those levels remain rare in nearly all populations.

There is a chain of reasoning that goes from obesity to morbid symptoms like high blood pressure and diabetes, to mortality, but this is fairly indirect, and ignores the rapid improvement in treatments for these secondary symptoms, as well as the clear historical association between increasing childhood nutrition and improved longevity. Concerned experts often attribute the reduction in mortality at low levels of “overweight” to errors in study design — such as confusing weight loss due to illness with healthy low weight — which has indeed been a problem and negative health consequences attributable to weight-loss diets tend to be ignored. All in all, it has always seemed to be a murky question, leaving me genuinely puzzled by the quantitative certainty with which catastrophe is predicted. Clearly increasing obesity isn’t helping people’s health — the associated morbidity is a real thing, even if it isn’t shortening people’s lives much — but I’m perplexed by the quantitative claims about mortality.

So, I thought, if obesity is causing cancer, as much as tobacco is, that’s a pretty convincing piece of the mortality story. And then I followed up the citations, and the sand ran through my fingers. Here are some problems:

  1. Just to begin with, the convergence of cancers attributable to smoking with cancers attributable to obesity is almost entirely attributable to the reduction in smoking. “By 2043 smoking may have been reduced to the point that it is no longer the leading cause of cancer in women” seems like a less alarming possible headline. Here’s the plot from the CRUK report:
    Screenshot 2018-09-24 11.48.43
  2. The report entirely conflates the categories “overweight” and “obese”. The formula they cite refers to different levels of exposure, so it is likely they have separated them out in their calculations, but it is not made clear.
  3. The relative risk numbers seem to derive primarily from this paper. There we see a lot of other causes of cancer, such as occupation, alcohol consumption, and exposure to UV radiation, all of which are of similar magnitude to weight. Occupational exposure is about as significant for men as obesity, and more amenable to political control, but is ignored in this report. Again, the real story is that the number of cancers attributable to smoking may be expected to decline over the next quarter century, to something more like the number caused by multiple existing moderate causes.
  4.  Breast cancer makes up a huge part of women’s cancer risk, hence a huge part of the additional risk attributed to overweight, hence presumably makes up the main explanation for why women’s additional risk due to overweight is so much higher than men’s. The study seems to estimate the additional breast cancer risk due to smoking at 0. This seems implausible. No papers are cited on breast cancer risk and smoking, possibly because of the focus on British statistics, but here is a very recent study finding a very substantial increase. And here is a meta-analysis.
  5. The two most common cancers attributable to obesity in women — cancer of the breast and uterus — are among the most survivable, with ten-year survival above 75%. (Survival rates here.) The next two on the list would be bowel and bladder cancer, with ten-year survival above 50%. The cancer caused by smoking, on the other hand, is primarily lung cancer, with ten-year survival around 7%, followed by oesophageal (13%), pancreatic (1%), bowel and bladder. Combining all of these different neoplasms into a risk of “cancer”, and then comparing the risk due to obesity with that due to smoking, is deeply misleading.

UPDATE: My letter to the editor appeared in The Guardian.

Male nurses and politically incorrect comments on gender

I was just reading this article by journalist Conor Friedersdorf, complaining about how Canadian psychologist Jordan Peterson is being unfairly treated by journalists, who try to twist his subtle anti-feminist arguments into crude anti-feminist slurs. He certainly has a point. But then one comes to comments like this

[Interviewer]: Is gender equality desirable?

Peterson: If it means equality of outcome then it is almost certainly undesirable. That’s already been demonstrated in Scandinavia. Men and women won’t sort themselves into the same categories if you leave them to do it of their own accord. It’s 20 to 1 female nurses to male, something like that. And approximately the same male engineers to female engineers. That’s a consequence of the free choice of men and women in the societies that have gone farther than any other societies to make gender equality the purpose of the law. Those are ineradicable differences––you can eradicate them with tremendous social pressure, and tyranny, but if you leave men and women to make their own choices you will not get equal outcomes.

20 to 1? That seems really high. For nurses and for engineers. So I decided to do something rude, and check the numbers. For nurses, I found these statistics. There’s a lot of variation in Scandinavia. In Denmark it seems like about 20:1 female to male. But in Norway it’s 9:1. In Iceland it’s 100:1. Looking further afield, in Israel and Italy 20% of nurses are male. And in the Netherlands nearly 25%. This does not look like an ineradicable difference to me. It looks like path dependence and social context.

What about engineers? Here Peterson is, to use the technical term, talking out of his ass. There is no country in the EU with such an extreme gender imbalance for engineers: The most extreme is the UK, with about a 10:1 male to female ratio. In Sweden it’s 3:1, in Norway 4:1, and in Denmark 5:1. In Latvia the fraction of female engineers is up to 30%.

I think, if you want to make provocative “I’m just trying to be rational here” public arguments, you kind of have an obligation not to make up your supporting facts.

Overt public blackmail?

Just when you thought you’d reached the bottom of the we’re-being-governed-by-toddlers-who-missed-a-nap slough of despond, they manage to surprise you again. This time, it’s the Chancellor of the Exchequer  Philip Hammond, who decided to punish the NHS (and, by proxy, the entire English public) for the brazenness of its chief, Simon Stevens. Stevens gave a speech two weeks ago, saying the NHS is on the verge of financial collapse, and since the one thing that’s clear about the result of the Brexit referendum is that the public likes the idea of giving £350 million a week more to the NHS, maybe the government should just go ahead and do that. Instead,

Philip Hammond backtracked on plans to give the NHS more money than it eventually got in the budget after reacting with “fury” to its boss Simon Stevens’s public demand for an extra £4bn next year.

Since I am always particularly intrigued by political semantics, I was struck by this line:

Hammond and Treasury officials felt that the NHS England chief executive’s move meant that the chancellor could not be seen to be acceding to what they saw as “overt public blackmail”

What I wonder is, is there such a thing as “overt public blackmail”? Blackmail is when you make secret demands, with the threat to publicly embarrass the target by revealing hidden information. It’s not even any kind of extortion, which would mean issuing threats to force someone into a desired course of action. The only threat Stevens made is that without more money the NHS faces collapse. Warning someone of the potential consequences of their actions is neither extortion nor blackmail. And saying, we agree with the analysis, but since we don’t want to look like we’re agreeing with you, we’re going to do the opposite, is something so stupid that I don’t think  there is a specific name for it. (Maybe the Piranha Brothers used that technique?)

Now, what would be blackmail? How about telling the head of an independent government agency in private talks that his agency and the whole population are being throttled for his presumptuous public speech, not needing to say explicitly that a deferential turn might prevent future punishment — well, I guess that’s extortion.

Maybe someone should give him a cookie?

NHS hit by unforeseen Earth tilt

A critical government service has to be prepared for all foreseeable contingencies. But sometimes the unpredictable occurs, and bureaucrats can fall into panic.

A tilt in the Earth’s axis that no one could have foreseen is apparently causing daylight to grow shorter in northern latitudes and temperatures to drop, leading to an increase in communicable diseases and accidents that threatens to overwhelm NHS emergency services. Or, in other words,

Disclosure of NHS England’s attempt to impose a detailed series of duties on hospitals comes amid claims by senior insiders that its leadership is in a state of panic over winter.