Science


In early March, when COVID-19 was starting to spread in the UK, the government announced a strategy of “herd immunity” in which they would shield vulnerable people (such as older people and people with pre-existing conditions) from the disease, and aim to slowly allow the rest of the country to be infected up to some proportion of the population. This policy was based on the idea that once the disease had infected a certain proportion of the population then this would mean it had naturally been able to achieve herd immunity, and after that would die out. The basics of the strategy and its timeline are summarized here. This strategy was an incredibly dangerous, stupid and reckless strategy that was built on a fundamental failure to understand what herd immunity is, and some really bad misconceptions about the dynamics of this epidemic. Had they followed this policy the entire UK population would have been infected, and everyone in the UK would have lost at least one of their grandparents. Here I want to explain why this policy is incredibly stupid, and make a desperate plea for people to stop talking about achieving herd immunity by enabling a certain portion of the population to become infected. This idea is a terrible misunderstanding of the way infectious diseases work, and if it takes hold in the public discourse we are in big trouble next time an epidemic happens.

I will explain here what herd immunity is, and follow this with an explanation of what the UK’s “herd immunity” strategy is and why it is bad. I will call this “herd immunity” strategy “Johnson immunity”, because it is fundamentally not herd immunity. I will then present a simple model which shows how incredibly stupid this policy is. After this I will explain what other misconceptions the government had that would have made their Johnson Immunity strategy even more dangerous. Finally I will present a technical note explaining some details about reproduction numbers (the “R” being bandied about by know-nothing journalists at the moment). There is necessarily some technical detail in here but I’ll try to keep it as simple as possible.

What is herd immunity?

Herd immunity is a fundamental concept in infectious disease epidemiology that has always been applied to vaccination programs. Herd immunity occurs when so many people in the population are immune to a disease that were a case of the disease to arise in the population, it would not be able to infect anyone else and so would die out before it could become an epidemic. Herd immunity is linked to the concept of the Basic Reproduction Number, R0. R0 tells us the number of cases that will be generated from a single case of a disease, so for example if R0 is 2 then every person who has the disease will infect 2 other people. Common basic reproduction numbers range from 1.3 (influenza) to about 18 (measles). The basic reproduction number of COVID-19 is probably 4.5, and definitely above 3.

There is a simple relationship between the basic reproduction number and the proportion of the population that need to be vaccinated to ensure herd immunity. This proportion, p, is related to the basic reproduction number by the formula p=1/(1-1/R0). For smallpox (R0~5) we need 80% of the population to be vaccinated to stop it spreading; for measles (R0~18) it is safest to aim for 95%. The reason this works is because the fundamental driver of disease transmission is contact with vulnerable people. If the disease has a basic reproduction number of 5, each case would normally infect 5 people; but if 4 of every 5 people the infected person meets are immune, then the person will only likely infect 1 person before they recover or die (or get isolated). For more infectious diseases we need to massively increase the number of people who are immune in order to ensure that the infection doesn’t spread.

If we vaccinate the correct proportion of the population, then when the first case of a disease enters the population, it’s chances of meeting an infectable person will be so low that it won’t spread – effectively by vaccinating 1-1/R0 people we have reduced its effective reproduction number to 1, at which point each case will only produce 1 new case, and the virus will not spread fast enough to matter. This is the essence of herd immunity, but note that the theory applies when we vaccinate a population before a case enters the population.

What is Johnson Immunity?

There is a related concept to the basic reproduction number, the effective reproduction number Rt, which tells us how infectious the virus currently is. This is tells us how many people each case is infecting at the current state of the epidemic. Obviously as the proportion of the population who have been infected and recovered (and become immune) increases, Rt must drop, since the chance that they will have contact with an infectious person goes down. Eventually the proportion of the population infected will become so large that Rt will hit 1, meaning that now each case is only infecting another case. The idea of Johnson Immunity was that we would allow the virus to spread among only the low-risk population until it naturally reached the proportion of the population required to achieve an Rt value of 1. Then, the virus would be stifled and the epidemic would begin to die. If the required proportion to achieve Rt=1 is low enough, and we can shield vulnerable people, then we can allow the virus to spread until it burns out. This idea is related to the classic charts we see of influenza season, where the number of new infections grows to a certain point and then begins to go down again, even in the absence of a vaccine.

This idea is reckless, stupid and dangerous for several reasons. The first and most serious reason it is dangerous is that the number of daily new infections will rise as we head towards Rt=1, and by the time we reach the point where, say, 60% of the population is infected, the number of daily cases will be huge. At this point Rt=1, so each case is only infecting 1 other case. But if we have 100,000 daily new cases at this point, then the following generation of infections will spawn 100,000 new infections, and so on. If, for example, the virus has an R0 of 2, and takes 5 days to infect the next generation, then the number of new cases doubles every 5 days. After a month we have 64 cases, after two months we have 4100 cases, and so on. By the time we get to 30 million cases, we’ll likely be seeing 100,000 cases in one generation. So yes, now the virus is going to start to slow its spread, but the following generation will still generate 100,000 cases, and the generation after that 90,000, and so on. This is an incredible burden on the health system, and even if death rates are very low – say 0.01% – we are still going to be seeing a huge mortality rate.

The second reason this idea is reckless and stupid is that it is basically allowing the disease to follow its natural course, and for any disease with an R0 above about 1.5, this means it will infect the entire population even after it has achieved its Rt of 1. This happens because the number of daily cases at this point is so large that even if each case only infects 1 additional case, the disease will still spread at a horrific rate. There is an equation, called the final size equation, which links R0 to the proportion of the population that will be infected by the disease by the time it has run its course, and basically for any R0 above 2 the final size equation tells us it will infect the entire population (100% of people) if left unchecked. In practice this means that yes, after a certain period of time the number of new cases will reach a peak and begin to go down, but by the time it finishes its downward path it will have infected the entire population.

A simple model of Johnson Immunity

I built a very simple model in Excel to show how this works. I imagined a disease that lasts two days. People are infected from the previous generation on day 1, infect the next generation and then recover by the end of day 2. This means that if I introduce 1 case on day 1, it will infect R0 cases on day 2, R0*R0 cases on day 3, and so on. This is easy to model in Excel, which is why I did it. Most actual diseases have incubation periods and delayed infection, but modeling these requires more than 2 minutes work in a real stats program, and this is a blog post, so I didn’t bother with such nuance. Nonetheless, my simple disease shows the dynamics of infection. I reclaculated Rt each day for the disease, so that it was reduced by the proportion currently infected or immune, so that for example once 100,000 people are infected and recovered, in a population of 1 million people, the value of Rt becomes 90% of the value of R0. This means that when it reaches its Johnson Immunity threshold the value of Rt will go below 1 and the number of cases will begin to decline. This enables us to see how the disease will look when it reaches the Johnson Immunity threshold, so we can see what horrors we are facing. I assumed no deaths and no births, so I ran the model in a closed population of 1 million people. I ran it for a disease with an R0 of 1.3, 1.7, and 2.5, to show some common possible scenarios. Figure 1 shows the results. Here the x-axis is the number of days since the first case was introduced, and the y-axis is the number of daily new cases. The vertical lines show the day at which the proportion of the population infected, Pi, crosses the threshold 1-1/R0. I put this in on the assumption that the Johnson Immunity threshold will be close to the classical herd immunity threshold (it turns out it’s off by a day or two). The number above the line shows the final proportion of the population that will be infected for this particular value of R0.

Figure 1: Epidemic paths for three different reproduction numbers, with Johnson Immunity threshold

As you can see, when R0 is 1.3 (approximately seasonal influenza), we cross the approximate Johnson Immunity threshold at 44 days after the first case, and at this point we have a daily number of cases of about 40,000 people. This disease will ultimately infect 49% of the population. Note how slowly it goes down – for about a week after we hit the Johnson Immunity threshold we are seeing 40,000 or so cases a day.

For a virus with an R0 of 1.7 the situation is drastically worse. We hit the Johnson Immunity threshold after 23 days, and at this point about 140,000 cases a day are being infected. Three days later the peak is achieved, with nearly 200,000 cases a day being infected, before the disease begins a rapid crash. It dies out within a week of hitting the Johnson immunity threshold, but by the time it disappears it has infected 94.6% of the population. That means most of our grandparents!

For a disease with an R0 of 2.5 we hit the Johnson Immunity threshold at day 13, with about 140,000 cases a day, and the disease peaks two days later with 450,000 cases a day. It crashes after that, hitting 0 a day later because it has infected everyone in the population and has no one left to infect.

This shows that for any kind of R0 bigger than influenza, when you reach the Johnson Immunity threshold your disease is infecting a huge number of people every day and is completely out of control. We have shown this for a disease with an R0 of 2.5. The R0 of COVID-19 is probably bigger than 4. In a population of 60 million where we are aiming for a herd immunity threshold of 36 million we should expect to be seeing a million new cases a a week at the point where we hit the Johnson Immunity threshold.

This is an incredibly stupid policy!

Other misconceptions in the policy

The government stated that its Johnson Immunity threshold was about 60% of the population. From this we can infer that they thought the R0 of this disease was about 2.5. However, the actual R0 of this disease is probably bigger than 4. This means that the government was working from some very optimistic – and ultimately wrong – assumptions about the virus, which would have been catastrophic had they seen this policy through.

Another terrible mistake the government made was to assume that rates of hospitalization for this disease would be the same as for standard pneumonia, a mistake that was apparently made by the Imperial College modeling team whose work they seem to primarily rely upon. This mistake was tragic, because there was lots of evidence coming out of China that this disease did not behave like classic pneumonia, but for some reason the British ignored Chinese data. They only changed their modeling when they were presented with Italian data on the proportion of serious cases. This is an incredibly bad mistake, and I can only see one reason for it – they either didn’t know, or didn’t care about, the situation in China. Given how bad this disease is, this is an incredible dereliction of duty. I think this may have happened because the Imperial College team have no Chinese members or connections to China, which is really a very good example of how important diversity is when you’re doing policy.

Conclusion

The government’s “herd immunity” strategy was based on a terrible misunderstanding of how infectious disease dynamics work, and was compounded by significantly underestimating the virulence and deadliness of the disease. Had they pursued the “herd immunity” strategy they would have reached a point where millions of people were being infected daily, because the point in an epidemic’s growth where it reaches Rt=1 is usually the point where it is at its most rapidly spreading, and also its most dangerous. It was an incredibly reckless and stupid policy and it is amazing to me that anyone with any scientific background supported it, let alone the chief scientific adviser. Britain is facing its biggest crisis in generations, and is being led by people who are simply not competent to manage it in any way.

Sadly, this language of “herd immunity” has begun to spread through the pundit class and is now used routinely by people talking about the potential peak of the epidemic. It is not true herd immunity, and there is no sense in which getting to the peak of the epidemic to “immunize” the population is a good idea, because getting to the peak of the epidemic means getting to a situation where hundreds of thousands or millions of people are being infected every week.

The only solution we have for this virus is to lockdown communities, test widely, and isolate anyone who tests positive. This is being done successfully in China, Vietnam, Japan, Australia and New Zealand. Any strategy based on controlled spread will be a disaster, and anyone recommending it should be removed from any decision-making position immediately.

Appendix: Brief technical note

R0 (and Rt) are very important numerical qualities of an infectious disease but they are not easily calculated. They are numbers that emerge from the differential equations we use to describe the disease, and not something we know in advance. There are two ways to calculate them: Empirically from data on the course of disease in individuals, or through dynamic analysis of disease models.

To estimate R0 empirically we obtain data on individuals infected with the disease, so we know when they were infected and when they recovered down to the narrowest possible time point. We then use some statistical techniques related to survival analysis to assess the rate of transmission and obtain statistical estimates for R0.

To estimate R0 from the equations describing the disease, we first establish a set of ordinary differential equations that describe the rates of change of uninfected, infected, and recovered populations. From this system of equations we can obtain a matrix called the Next Generation Matrix, which describes all the flows in and out of the disease states, and from this we can obtain the value of R0 through a method called spectral analysis (basically it is the dominant eigenvalue of this matrix). In this case we will have an equation which describes R0 in terms of the primary parameters in the differential equations, and in particular in terms of the number of daily contacts, the specific infectiousness of the disease when a contact occurs, and the recovery time. We can use this equation to fiddle with some parameters to see how R0 will change. For example, if we reduce the recovery time through treatment, will R0 drop? If we reduce the infectiousness by mask wearing, how will R0 drop? Or if we reduce the number of contacts by lockdowns, how will R0 drop? This gives us tools to assess the impact of various policies.

In the early period of a new infectious disease people try to do rough and ready calculations of R0 based on the data series of infection numbers in the first few weeks of the disease. During this period the disease is still very vulnerable to random fluctuation, and is best described as a stochastic process. It is my opinion that in this early stage all diseases look like they have an R0 of 1.5 or 2, even if they are ultimately going to explode into something far bigger. In this outbreak, I think a lot of early estimates fell into this problem, and multiple papers were published showing that R0 was 2 or so, because the disease was still in its stochastic stage. But once it breaks out and begins infecting people with its full force, it becomes deterministic and only then can we truly understand its infectious potential. I think this means that early estimates of R0 are unreliable, and the UK government was relying on these early estimates. I think Asian governments were more sensible, possibly because they were in closer contact with China or possibly because they had experience with SARS, and were much more wary about under-estimating R0. I think this epidemic shows that it is wise to err on the side of over-estimation, because once the outbreak hits its stride any policies built on low R0 estimates will be either ineffective or, as we saw here, catastrophic.

But whatever the estimate of R0, any assumption that herd immunity can be achieved by allowing controlled infection of the population is an incredibly stupid, reckless, dangerous policy, and anyone advocating it should not be allowed near government!

Since just over a week ago we have begun to see reports of changes to figures on deaths due to COVID-19 in many countries. The changes typically lead to upward revision of the death figures, and usually this seems to occur either because the daily reporting of deaths has not incorporated deaths occurring outside of hospitals, or because national organizations are catching up on deaths that are not due to COVID-19 and discovering large changes in non-COVID death patterns. For example, on 17th April we started to see reports that Wuhan city had increased its death count by about 50%, and today we find the BMJ reporting that deaths in care homes in the UK have increased rapidly. Of course as soon as China revises its figures we see accusations of cover-ups, and no doubt people are also wondering if the institutions in some hard-affected countries are competent enough to accurately report death figures. So in this post I want to explain a little about how these mortality data are collected, how deaths are reported, why figures can be suddenly revised, and what some of the data we’re seeing means, using British data revisions as an example.

How death data is collected

For people living in high-income countries it may come as something of a surprise to learn that vital registration systems – the systems that record births and deaths – are not actually very sophisticated or high-tech, and that for many countries they do not exist at all. In high-income countries these systems are often legacy systems, based on a network of paper-based reporting that is still quite far behind the needs of modern information-hungry media, and many countries have no such systems in place: the WHO estimates that 2/3 of all deaths that occur every year are not recorded in any registration system. In a pandemic like this, where media organizations want to report daily death numbers, the traditional systems in place to register deaths often cannot keep up.

Typically a vital registration system takes some time to update. After someone dies a doctor has to assign a cause of death, which in many cases will be recorded on a piece of paper that has to then be input into a computer system and slowly passed up a chain to a central authority, where it will be checked and certain data cleaning activities undertaken. In many cases the doctor’s original cause of death recording doesn’t make sense, so some checks have to be conducted to make sure that things are working. Then whatever the doctor wrote down has to be converted into a standardized cause of death (under the International Classification of Diseases) and entered into a database by its code, along with whatever local codings (for place of death, geocoding, etc) that the national jurisdiction calls for. Figure 1 (taken from the UN Stats handbook) shows the stages of the flow of vital registration.

Figure 1: Flow of data through the vital registration system

Many countries lack some or all stages of this process: for example, China still does not have a complete vital registration system, and mortality estimates are based on sample surveys outside of major cities[1]. In many countries deaths occurring in different locations may be processed at very different speeds, with death in prison, homes or elderly care facilities being reported much more slowly than in hospitals, and rural hospitals or smaller clinics reporting more slowly than major regional or teaching hospitals. When people want to know rapidly how many people are dying in a fast-evolving situation it is unlikely that we will get complete mortality estimates, and usually the only data that the health service can aggregate quickly is data on in-hospital deaths. It can take weeks, months or even a full year to obtain a full, accurate snapshot of mortality figures across the entire community. As an example, this Kaiser Foundation report on care-home deaths due to COVID-19 in the USA makes clear that there are very large differences in how completely death data is collected between states in the US, and differences in how rapidly that data is reported. Oregon, for example, presents fairly comprehensive data on cases and mortality in residents and staff, but only on a weekly basis. But 55% of deaths reported in Oregon occurred in care facilities, which likely means that the death data in Oregon is delayed by a week and there will likely be revisions to earlier totals that slip by in the rush to report information.

When media report daily deaths, what they are really doing is taking data in a relatively raw form from the first orange box (“Health services”) in figure 1, before a proper civil registration and vital statistics quality control process has been implemented. Then, subsequently, national statistical authorities release the actual figures, which can be much larger than those initial estimates, and require some large and rather embarrassing changes to the numbers. This is particularly likely if – as in the UK – care homes are understaffed and use primarily unskilled labour. During a pandemic that targets elderly people, those facilities are likely to be way too busy to process mortality data in the timely fashion the media demand!

How deaths are recorded

Another important part of the puzzle is how deaths are actually recorded. Death statistics are recorded in three different forms: the direct cause of death, which actually made the person die; contributing causes of death, which may have helped them along the line; and the underlying cause of death, which is the real reason they died. This is a matter of medicine and biology, not always easily determined: for example diabetes might be the underlying cause of death, there may have been a contributing factor from pneumonia, and the direct cause may have been some kind of organ failure. You can see this process in action in the example blue forms provided by the CDC. When a death is finally reported by the government the underlying cause will be reported, not the contributing cause; but in the case of a major pandemic we may have good reason to think that the death would not have happened without the contribution of COVID-19. Furthermore, deaths are certified by doctors, and there is not necessarily a common agreement on when something is underlying, direct or contributing, and death certificates can be notoriously low quality. This creates problems for assessments of mortality patterns generally, but it is particularly important when giving rapid assessments of mortality due to a disease that we still don’t properly understand, since a judgment about whether something contributed to or was the underlying cause of death requires a basic understanding of how that cause works. This can lead to repeated reassessments of numbers of deaths, as doctors change their understanding of how the disease kills and what comorbidities might be vulnerable to the disease.

When you see a change in mortality figures it will be because of either or both of these problems. It could arise because a new source of causes of death has finally been cleaned and added to the data; it could be that a computer system had to be updated to allow daily death records to include COVID-19; or it could be because experts decided that certain events that had previously seemed independent of COVID-19 were actually related; or it could be because the government decided to include (or exclude!) deaths where COVID-19 was a contributing (rather than underlying) cause of death.

Another possible reason for changes in death figures, and a very serious one, is that the daily figures media received were those on deaths due to confirmed COVID-19, which are accurate and precise, but that after a few weeks the statutory authorities realized that there had been a huge increase in non-COVID deaths due to pressure on the health system, and started recording those too. This is what has started to happen in Europe, and this is what we will examine using the UK as our base.

Sudden huge increase in mortality in the UK

The Office of National Statistics has finally been able to compile, clean and release the data on all causes of death in the UK over the past few weeks, and the findings are stark. In week 16 of this year (11-17 April) there were 22,351 deaths in the UK. This is 11,854 more deaths than the five year average for that week. Basically, the number of deaths in the UK in that week doubled. There were 8,756 deaths due to COVID-19 in that week, which suggests about 3,000 deaths occurred due to non-COVID causes, an excess mortality rate of about 30%. So in one week in April, the number of deaths in the UK doubled, and only 70% of those excess deaths were due to COVID-19: the other 30% were other causes which, I think it’s safe to assume, occurred because of pressure on the health system.

This ONS report also notes that for the whole year so far there have been 22,000 or so excess deaths compared to the five year average, an increase of about 10%. COVID-19 has been in full force in the UK for just 3-4 weeks, and it has already increased the year-to-date mortality rate by 10%. That was based on figures that are already basically two weeks old, so we can expect that with 3-4 more weeks of deaths still to come, the year-to-date mortality rate will increase even more – but we won’t know for a few more weeks because of the delay in reporting at-home deaths. Figure 2 (taken from the ONS report) shows this in stark relief.

Figure 2: Weekly mortality figures for the UK

 

I hope those lines in Figure 2 make very clear that COVID-19 is not “just flu” and that its impact on the UK population has been staggering. Had the government pursued its foolish “herd immunity” strategy things would have been much, much worse.

I hope this two-week-after-the-fact revision will help my reader(s) to understand that the adjustments that were made to Wuhan’s mortality figures 10 days ago are not unusual or evidence of any kind of cover up: it’s natural that a health system that is struggling to deal with a sudden massive surge in hospitalizations and deaths, and which already does not have a well-functioning mortality registration system, is going to miss some deaths on the initial pass, and is going to need a bit of time to collect all the data and make it available in a comprehensive format. Over the next few weeks we will see this happening in a lot of health systems, and additional components of COVID-19 mortality will become clearer as time passes. This does not reflect incompetence or dishonesty, just the efforts of a system that was designed for slow, annual stocktake-type processes to adapt to a rapidly-changing pandemic situation.

This also means that we should expect that the figures we see now are not the final toll of this virus. Whatever numbers we’re seeing now from the USA, for example, we should expect to grow considerably once the CDC has had the chance to compile all the separate, confusing sources of data and put together a comprehensive report.

And when they do that, it’s going to be bad. Very, very bad. This disease is very dangerous, and without major action on the part of every country it is going to exact a terrible toll.

Stay home and stay safe, people!


fn1: Like all things in China, this is changing rapidly, and the quality of mortality statistics regularly improving. The linked article is from 2015 and is probably already out of date.

There is a lot of pressure at present for the expansion of testing for COVID-19 to enable better understanding of the spread of the virus and possibly to help with reopening of the economy. Random population surveys have also been conducted in many countries, with a recent antibody survey in California, for example, finding 50 times more people infected than official estimates report. The WHO recognizes testing as a key part of the coronavirus response, and some countries are beginning to discuss the idea of “immunity passports”, in which people are given an antibody test and enabled to return to work if they test positive to antibodies and are well (since this indicates that they have been infected and gained immunity). The WHO advises against this approach because there is no evidence yet that people who have experienced COVID-19 and recovered are actually immune. But in addition to this virological concern, there is a larger, statistical concern about COVID-19 tests (especially antibody tests) and the consequence of widespread use of these tests as a policy guide: how reliable are they, and what are the consequences of deploying poor-quality tests?

My reader(s) may be familiar with my post on the use of Bayesian statistics to assess the impact of anti-trans bathroom laws on natal women. This study found that, since being transgender is a very low prevalence phenomenon, if we tried to actually enforce birth-gender bathroom laws almost everyone we kicked out of a woman’s toilet would actually be a cis woman. This is a consequence of Bayes’ Law, which basically tells us that when a condition has very low prevalence, any attempt to test for that condition will largely produce false positives unless the test is a very very accurate test. This applies to any attempt to discriminate between two classes of things (e.g. trans women vs. natal women, or coronavirus vs. no coronavirus). It is a universal mathematical theory, and there is no escaping it.

So what happens with testing for coronavirus. There are a couple of possible policies that can be enacted based on the result of testing:

  1. People testing positive are isolated from the rest of the community in special hospitals or accommodation, to be treated and managed until they recover
  2. People testing positive self-isolated and all their potential contacts are traced and tested, self-isolating as necessary
  3. People testing negative are allowed to return to ordinary life, working and traveling as normal
  4. People testing positive to antibodies with no illness are issued an “immunity passport” and allowed to take up essential work
  5. Health workers testing negative are allowed to return to hospital

Obviously, depending on the policy, mistakes in testing can have significant consequences. This is why the WHO has quite strict diagnostic criteria for the use of testing, which requires multiple tests at different specified time points with rules about test comparison and cautionary notes about low-prevalence areas[1]. Now that some antibody tests have achieved marketing status, I thought I would do a few brief calculations using Bayes’ rule to see how good they are and what the consequences will be. In particular let’s consider policy options 1, 3 and 4. I found a list of antibody tests currently being marketed or used in the USA here, and information on one PCR test, from Quantivirus. I assumed a testing program applied to a million people, and for each test under this program I calculated the following information:

  • The number of people testing positive and the number who are actually negative
  • The proportion of positive tests that are actually positive
  • The number of people testing negative and the number who are actually positive
  • The estimated prevalence of COVID-19 obtained from each of these tests

I used the current number of cases in the USA on 24th April (870,000), multiplied by 10 to include asymptomatic/untested cases and a US population of 330 million to estimate the true prevalence of coronavirus in USA at 2.6%.  Note that with 2.6% prevalence the true situation is 26,000 cases of COVID-19 and 974,000 people negative. I then compared the estimated prevalence for each test against this. Here are the results

Beckton-Dickinson/Biomedomics Covid-19 IgM/IgG Rapid Test

This test has 88.7% sensitivity and 90.6% specificity, and has been given emergency use authorization by the FDA. If used to test a million people in the context of disease prevalence of 2.6%, we would find the following results:

  • 114,906 people testing positive of whom 91,521 are actually negative
  • Only 20.4% of tests positive
  • 885,903 people testing negative, of whom 2,979 are positive
  • An estimated coronavirus prevalence of 11.4%

This would mean that under policy 1 (isolation of all positive cases) we would probably increase prevalence by a factor of 5, since 80% of the people we put into isolation with positive cases would be negative (and would then be infected). If we followed policy 3 or 4, we would be releasing 2,979 people into the community to work, get on trains etc., and infect others. We would also recalculate the case fatality rate of the virus to be 50 times lower than the actual observed estimate, because we had observed deaths among 870,000 cases (prevalence 0.26%) but were now dividing the confirmed deaths by a prevalence of 11.4%. This would make us think the disease is not much worse than influenza, while we were spreading it to five times as many people. Not good! Curing that epidemic is going to need a lot of bleach injections.

Cellex qSars-CoV-2 IgG/IgM Cassette Rapid Test

This test has also received emergency use authorization, and has 93.8% sensitivity and 95.6% specificity, which sounds good (very big numbers! Almost as good as Trump’s approval rating!) But if used to test 1,000,000 Americans with prevalence of 2.6% it still performs very poorly:

  • 67,569 people testing positive of whom 42840 are actually negative
  • Only 36.5% of tests positive
  • 932,430 people testing negative, of whom 1,635 are positive
  • An estimated coronavirus prevalence of 6.8%

This is still completely terrible. Isolating all the positive people (policy 1) would likely increase prevalence by a factor of 3, and we would allow 1,635 people to run around infecting others blithely assuming they were negative. Not a good outcome.

CTK Biotech OnSite Covid-19 IgG/IgM Rapid Test

This test has not yet received emergency use authorization, but has 96.9% sensitivity and 99.4% specificity. With this test:

  • 31,338 people test positive of whom 5,841 are actually negative
  • About 81% of tests are actually positive
  • 968,611 people test negative, of whom 817 are positive
  • An estimated coronavirus prevalence of 3.1%

This is much better – most people testing positive are actually positive, we aren’t releasing so many people into the wild to infect others, and our prevalence estimate is close to the true prevalence. But it still means a lot of people are being given incorrect information about their status, and are taking risks as a result.

Conclusion

Even slightly inaccurate tests have terrible consequences in epidemiology. As testing expands the ability to conduct it carefully and thoroughly – with multiple tests, sequenced tests, and clinical confirmation – drops, and the impact of even small imperfections in the testing regime grows rapidly. In the case of a highly contagious virus like COVID19 this can be catastrophic. It will expose uninfected people to increased risk of infection through hospitalization or isolation alongside positives, and if used for immunity passports significantly raises the risk of positive people returning to work in places where they can infect others. In comparison to widespread testing with low-quality tests, non-pharmaceutical interventions (e.g. lockdowns and social distancing) are far more effective, cheaper and less dangerous. It is very important that in our desire to reopen economies and restart our social lives we do not rush to use unreliable tests that will increase, rather than reduce, the risk to the community of social interactions. While testing early and often is a good, strong policy for this pandemic, this is only true when testing is conducted rigorously and using good quality tests, and not used recklessly to end social interventions that, while painful, are guaranteed to work.

 


fn1: It’s almost as if they know what they’re doing, and we should listen to them!

Tokyo Zombie Movie

The novel coronavirus (COVID-19) continues to spread globally, and at this point in its progress very few high-income countries have escaped its grip. On a per-capita basis Spain has 38 times the rate of infection of China, the US 10 times and Australia 3 times, but plucky Japan has only 0.3 times the infection rate of China. Until now the rate of growth has been low, with only tens of cases per day being recorded over much of February and March, but since last week the alarm has been sounding, and the government is beginning to worry. We had our first lockdown on the weekend, a voluntary two days of 自粛 in which everyone was supposed to stay inside, and this week discussion of lockdown began. This is because the previous week was a bright, sunny weekend with the cherry blossoms blooming, and all of Tokyo turned out to see them despite the Governor’s request for everyone to be cautious. Over the two weeks leading up to that weekend, and for perhaps two days afterwards, the train system returned to normal and Tokyo was being its normal bustling, busy uncaring self. But then on the week after that event the numbers began to climb, and now the government is worried as it begins to watch the numbers slide out of control. I am also now hearing for the first time stories of doctors having to find alternative ICU beds for COVID patients – still not a huge deal, because any one hospital does not have a large supply, but enough cases are now appearing to force doctors to seek empty hospitals elsewhere.

It is possible to see the effect of this party atmosphere in the data, and it offers a strong example of how important social distancing is. Using the data from the Johns Hopkins Coronavirus tracker (and making a few tiny adjustments for missing data in their downloadable file), I obtained and plotted the number of new cases each day, shown in Figure 1 below. Here the x axis is the number of days since the first infection was identified, and the y-axis is the number of new cases. Day 70 is the 1st April. The red line is a basic lowess smooth, not a fancy model.

Figure 1: Daily new cases by time since the first case

It is clear from this figure that things changed perhaps a week ago. New case numbers were up and down a lot but generally clustered together, representing slow growth, but since about a week ago the gaps between each dot are growing, and more dots are above than below the line. This is cause for concern.

However, it is worth remembering that each day the total number of cases is increasing, which means also that if you add the same number of new cases on any day, it will have a proportionately smaller effect on the total. We can estimate this by calculating the percentage change each day due to the new cases added on that day. So for example if there are 10 cases in total and 10 new cases are detected we see a 100% change; but 10 new cases with 100 existing cases will lead to only a 10% change. From this we can calculate the daily doubling time: the time required for the number of cases to double if we keep adding cases at the same percentage increase that we saw today. So, for example, if there are 100 cases on day 9 and on day 10 there are 10 more cases, the percentage change is 10%, and from that I can estimate that the number of cases will double after 7.2 days if that 10% daily change continues. This gives a natural estimate of the rate at which the disease is growing, adjusting for its current size. Figure 2 shows the doubling time each day for Tokyo, again with the number of days since the first infection on the x-axis. I have trimmed the doubling time at 20 days, so a few early points are missing because they had unrealistically high doubling times, and added a lowess smooth to make the overall pattern stand out. The vertical red line corresponds with Friday March 20th, a national holiday and the first day of the long weekend where everyone went cherry blossom viewing.

Figure 2: Daily time required for case numbers to double in Japan

Since the infection hit Japan the doubling time has been growing slowly, so that in February it would take almost two weeks for the number of cases to double. The doubling time dropped in March[1], which was also the time that the government began putting in its first social distancing guidelines (probably about late February); work events were being canceled or postponed by early March, probably in response to government concern about the growing number of cases, and this appears after two weeks to have worked, bringing the doubling times back up to more than two weeks. And that was when the sunny weather came and everyone went to hanami, marked on the red line, at which point the doubling time dropped like a stone. Back in the middle of March we were seeing between 10 and 40 cases a day, slow changes; but then after that weekend the number of cases exploded, to 100 or 200 a day, pretty much 4-6 days after the long weekend started. The following weekend was when the government demanded everyone stay in, and the city shut up shop; but we won’t begin to see the effect of those measures until tomorrow or this weekend, and right now the number of new cases is still hovering around 200 a day.

It’s worth noting that not all of these cases are community transmission. About 10% are without symptoms, and another 20% are having symptoms confirmed (probably because they’re very mild), which indicates the effectiveness of contact tracing in tracking down asymptomatic contacts. A lot of these cases are foreigners (something like 20-25%), and this is likely because they’re residents returning from overseas, and likely identified during quarantine/self-isolation (so not especially risky to the community). But still, even 70% of 200 is a lot of cases.

It’s instructive to compare this doubling time with some heavily-affected countries. Figure 3 shows the smoothed doubling times for Japan, the US, Italy and Australia. It has the same axes, but I have dropped the data points for clarity (I make no promises about the quality of these hideous smooths). The legend shows which country has which colour. Italy and Australia start slightly later in this data because their first imported case was not at day 0.

Figure 3: Doubling times for four affected countries

As you can see, Italy’s doubling time was almost daily in the first week of its epidemic, but has been climbing rapidly since they introduce social distancing. Australia’s doubling time was consistently a week, but began to increase in the last two weeks as people locked in. The US tracked Japan for a couple of weeks and then took a nose dive, so that at one point the daily doubling time was 3 days. Italy provides a really instructive example of the power of social distancing, which was introduced in some areas on February 28th and nationally in increasingly serious steps from 1st March to 9th March. Figure 4 shows Italy’s doubling time over the epidemic.

Figure 4: Doubling time for Italy

 

It is very clear that as measures stepped up the doubling time gradually increased. In this figure day 40 is the first of March, the first day that national measures were announced. Despite this, we can see from Figure 3 that it took Italy about a month and a half from the first case to slow the spread enough that further doubling might take a week, and early inaction meant that a month of intensely aggressive measures were needed to slow the epidemic, at huge cost.

It is my hope that Japan’s early measures, and aggressive investigation of clusters at the beginning of the outbreak, will mean that we don’t need to go into a month-long lockdown. But if Japan’s population – and especially Tokyo’s – don’t take it seriously now, this week and this weekend, Tokyo will go the same way as London and Italy. It’s time for Tokyo to make a two week sacrifice for its own good. Let’s hope we can do it!


fn1: Which the smooth doesn’t show, by the way, it’s an awful smooth and I couldn’t improve it by fiddling with the bandwidth[2]

fn2: A better model would be a slowly increasing straight line with a peak at the hanami event and then a rapid drop, but I couldn’t get that to work and gave up[3].

fn3: Shoddy jobs done fast is my motto!

Conspiracy theories about Japan’s approach to the coronavirus (COVID-19) are beginning to spread online, as people find it very difficult to believe that the country still has only 1000 cases of the virus even though it has not been testing a great deal. This has led to suggestions that Japan is covering up the true number of cases, and the epidemic is out of control in Tokyo.

This isn’t true: Japan has actually tested quite a lot of people, the epidemic is not out of control here as it is in so many other countries, there is no cover up, and what is happening in Japan is an example of what can be achieved with careful, early interventions. I will explain this here a little.

What is Japan’s epidemic situation?

According to the Ministry of Health, Labour and Welfare there were 1193 confirmed cases of COVID-19 on 25th March, of whom 272 had recovered,  43 had died and 57 required ventilator support. Japan’s first death from COVID-19 occurred on 13th February, about 41 days ago, a lot earlier than in other countries such as Germany (15 days ago), Italy (34 days ago) or the USA (25 days ago). For a disease as infectious as this one, these small differences in number of days should lead to huge differences in case numbers: Japan has had 16 days more than the USA to see this epidemic grow, but on day 9 the USA had only 645 cases – now it has 64,661 cases. It is obviously mystifying to many people that the US could see a 100-fold increase in the number of cases in the same time period that Japan saw only a two-fold increase. The obvious suspicion is that since Japan hasn’t tested that many cases, they must be hiding something. There are two reasons this theory doesn’t work: 1) Japan is actually testing more than people recognize and 2) you would definitely be able to tell if there was a 50-fold undercount of cases.

What is Japan’s testing situation?

Testing data can be obtained here. Japan has tested about 22,000 people, of whom 1193 have been confirmed positive. In contrast Germany has tested 167,000 and the UK has tested 65,000. This certainly seems like a lot of missed tests in Japan, but it is worth bearing in mind that the number of tests per positive person is actually about the same in these countries: 18.4 per positive in Japan, 19.7 per positive in the UK, and 25.5 per positive in Germany. In South Korea the number is unusual: 350,000 tests for about 9,000 cases, or 38.9 tests per positive case, but South Korea was dealing with a unique situation where a particular population group was known to be at risk (the weird religious group) and an aggressive testing policy could be targeted based on a social identity. In other countries the number of tests has approximately mapped the scale of the epidemic. This strangely stable ratio of tests to positive patients arises from the limitations on the test: it can only work on people who currently have the virus (it’s a PCR test) and it is expensive and still limited, so population-level testing cannot yet be conducted, and if done partially would miss cases. Basically every country is using passive case-finding to identify the disease, and only using the test where the symptoms suggest it, in order to conserve tests and avoid the social consequences (isolation and clinic shutdowns) associated with false positives. Japan is doing no differently here than Germany or the UK, it’s just that there are less people with symptoms, and less people to test as a result.

It’s worth noting that Japan set up a call centre for people with COVID-19 concerns on the 28th January, and since the middle of February it has been receiving about 3000 calls a day (also, somewhat cutely, 0-2 faxes per day: don’t ever change, Japan!), so there have been about 150,000 calls over the period of testing. In a country of 120 million this doesn’t seem to be a sign of a massively out of control epidemic. I can’t find statistics on the NHS 111 line but there are many stories out there about how it is congested with calls.

Why is Japan following this policy?

There are several levels of testing that can be conducted for any disease, ranging from population screening (seen in breast cancer programs) through voluntary testing (seen in HIV prevention programs), active case finding (where community health organizations target particular groups known to be at risk of a disease, usually used for TB) to passive case finding, which is used in almost all non-fatal sexually transmitted infections, influenza, and other infectious diseases. Screening is usually only conducted if the disease course can be changed by early detection. Passive case finding is useful when there is no identifiable group to target, or the disease prevalence is low so the chance of a positive test is low, or the test is rare/expensive/invasive. In this case the test is still restricted in availability, and the disease prevalence is low so you need to use a lot of tests to find one case. This is complicated in the case of COVID-19 by the possibility that the testing process itself will infect the tester, and so it’s better not to go charging out into the community exposing testers to large amounts of potentially infected people. South Korea conducted a kind of active case finding program, but that is because they knew where to look.

In this sense Japan’s policy is really no different to that in other countries. Japan has focused its efforts up until now on finding cases through cluster investigation: a lot of cases in Japan up until recently have arisen from cluster’s connected to specific events, and finding the people connected to these clusters and isolating them is super important. A single live music event in Osaka, for example, was responsible for 48 cases (about 5% of all the cases in Japan!), and had those cases not been tracked they would have turned into a huge outbreak. You can see the effect of this cluster approach in the statistics: often new cases (particularly in rural Japan) are asymptomatic, which indicates they were caught as part of a contact tracing effort; and even today with 40 new cases in Tokyo about half have a known contact already, which suggests they were tracked down (or their contacts will be). Quite a few cases are also imported: 5 of today’s 40, for example, have an overseas travel history. Focusing on clusters means targeting testing at people who need it, which avoids clogging up testing facilities and ensures that the test follow up is good quality.

Another reason for Japan’s low number of tests is its basic advice to people with suspected COVID-19. The advice from the government to citizens and medical institutions alike is: don’t come in for a consultation unless you have a fever >37.5C and coughing/chest tightness for at least 4 days (unless you’re pregnant or otherwise at risk). Until then you should self-isolate and avoid travel. This advice is super important in Tokyo, where most people travel by public transport, and ensures sick people aren’t infecting others on the train, and it avoids over-burdening health facilities with people who just have a cold. Two of my role-playing group have gone through this process; one went to the doctor after 4 days and was diagnosed with a cold based on x-ray and influenza tests, and the other self-isolated until her symptoms faded after 3 days. We’ll never know if she is immune to the virus now, but it doesn’t matter because she wasn’t at risk and she did not infect anyone else by getting on a train. Given that a lot of cases in Italy are now being  reported as hospital-acquired, this is good advice – but it also leads to the use of less tests.

So how do we know the size of Japan’s epidemic?

If we aren’t testing, how do we know what’s happening? First, we can assume given the ratio of positive results to tests is the same as in other countries that the process is working the same way here, and less tests are needed because less people have the virus. Second, though, we can look at the state of hospital emergency and intensive care wards, and make a judgment about the epidemic from the burden those wards are facing. In New York, for example, we now have horrifying accounts of emergency wards overflowing with cases and doctors working without breaks as their hospitals become basically COVID zones. In Italy new triage guidelines are being released for rationing ventilators. I am sure that is not happening (yet) in Japan, for two reasons: I work with doctors at a major hospital, and I am regularly visiting that hospital for medical care.

I have worked in and around hospitals for my whole career, doing data management and research, including in Japan, and I am familiar with how a hospital feels when it is working well and when it isn’t. You can tell from the way the doctors and nurses are working, the state of the physical environment, and what they complain about when they talk to you during your work day, whether they are struggling. Doctors are often wrong about epidemiology but they have an eye for when things are changing in their case load, and when they talk to you about it you can tell if things are going wrong. I don’t get that impression from my day job, or from any of my research colleagues from other hospitals here. There is not yet any pressure on emergency or intensive care services. I also receive the circulars for the medical staff in my work email, and so I can see how they are preparing for a surge that has not yet happened (today for example I received reassuring news about the stockpile of emergency equipment that my hospital has, the kind of news that would probably make an American very angry at how ill-prepared their system was). It’s not complacency or a lack of care: the wave just hasn’t hit yet.

The second reason I know this is that I have had to visit a lot of different parts of this hospital for medical care for my stupid knee, which I dislocated at kickboxing four weeks ago and have subsequently discovered has been missing some major components for the past 30 years. I only discovered this through multiple x-rays, MRIs, and CT scans (which I guess Aussie doctors didn’t feel I deserved over the first 30 years of my life!) As we all know, X-rays play a very important role in COVID-19 care since they enable doctors to see what kind of damage is going on. There is no way I would have sat just 10 minutes in the x-ray queue, watching orthopaedic patients hobble in and out calmly, if my hospital were overrun with COVID patients – I would probably be sent off to an external private provider or forced to wait all day. There’s also no way the CT scanner would be available for me to use 15 minutes before my appointment.

Unless Japanese people are uniquely able to resist this virus, the surge isn’t here yet, which means the epidemic is still in its infancy here – but that may all be about to change.

Japan’s prevention policy and what is coming soon

Japan has avoided major lockdowns yet, because it acted early and sensibly in light of warnings from China. The Japanese government listened to China, sent help early on, and paid careful attention to what was happening. The first advice from the Ministry of Health, Labour and Welfare was sent early – probably in early February – and the first restrictions on public behavior were instituted probably two weeks after the first death in mid February. My work events were being canceled by the end of February, and instructions were being disseminated throughout Japan to avoid large events. New advice about self isolation was issued early, and the National Institute of Infectious Diseases began its epidemiological investigations early. Japanese companies already have seasonal flu policies in place, and it is quite common for people to self-isolate if they have influenza, and those who don’t self-isolate will wear masks and behave responsibly with their disease. Japan is also not a touchy-feely huggy kind of country, and bowing is the standard greeting. In contrast, the UK was still considering what to do about large events in early March, and hand-shaking was still being discussed. It’s incredible that the day before the UK experienced its first coronavirus death, when Italy was starting to go pear-shaped, and in light of China’s experience, the British government still had no opinion on large events or shaking hands, one of the most disgustingly unhygienic ways you can greet someone.

This early action has served Japan well – even though it at no point closed its border to China! – but it may not be enough. Yesterday there were 40 new cases in Tokyo and 95 new cases in the whole country, and the Tokyo governor asked people to stay inside all weekend and not travel at all unless it was an emergency. There has been general uproar that a large kickboxing event (K1) was held on Sunday, and also consternation at the large numbers of people still going to parks and gardens for ohanami (it’s the season). If counter-measures aren’t stepped up it’s likely that Japan will lose a grip on this. It’s my expectation that by next weekend the Ministry of Health, Labour and Welfare will announce a lockdown, at least of the major cities, and an extended closure of restaurants and bars (to be clear, I have no inside knowledge of this – it’s just my judgment). The 40 cases we saw in Tokyo today were at least partly a result of last weekend’s ohanami madness, and we won’t know the effect of a weekend shutdown until next week, so my guess is the government will increase the restrictions next weekend. Given the small number of cases at present and the slow daily growth they probably only need to maintain a couple of weeks’ shutdown, not the extended horror we have seen in some cities, but my guess it is coming. If the Japanese government does what it’s very good at and dithers, expect Tokyo to become a zombie survival game show within a month. But so far the Japanese response has been measured and careful and effective, so I hope they will continue this and will get this right.

A note on conspiracy theories and racism

It’s worth recognizing that the European and Anglosphere countries (except perhaps for New Zealand) had two months’ warning of what was coming, they watched everything that was happening in China and they basically ignored it. Even Boris Johnson’s rapid turnabout on his irresponsible and inhumane “herd immunity” policy wasn’t driven by the clear knowledge available to the whole world from China; he waited until some white dudes at the University for Killing People and Stealing their Shit had had time to update their model with the Italian experience before he realized what a disaster he was unleashing. It seems that no one in the west at any point considered Chinese experience, Chinese struggle or Chinese lives worth anything, and ignored all the warnings they were being given until it was too late. Japan, on the other hand, listened to China and bought itself a month of slow growth as a result.

The conspiracy theories you see online about China and Japan are grown in the same fertile racist soil as the European policy mistakes. There is a long-standing image of Asians as shifty, untrustworthy, authoritarian and narcissistic, and that is exactly the racist image that drives these conspiracy theories. It’s not possible for white people to imagine that Asians could be doing something better than them, so they simply imagine that Asians are lying and covering up the truth. Inscrutable, untrustworthy and impenetrable societies are hiding the numbers and pretending everything’s okay for their own nefarious ends (or to “save face”).

Needless to say, it’s all bullshit. There is no conspiracy, and nobody is covering anything up. Asia is just doing it better, and the west needs to start listening to what’s happened over here, if they want to escape this with any of their grandparents alive.

The 2019 novel coronavirus (COVID-19) has now escaped China and taken a firm grip on the rest of the world, with Italy in a complete lockdown, most of Europe shuttered and the UK and the US spaffing their response up a wall. A few weeks ago I wrote a short post assessing the case fatality rate of the disease and assessing whether it is a global threat, and I think now is time to write an update on the virus. In this post I will address the mortality rate, some ways of looking at the total disease burden, discuss its infectiousness, and talk about what might be coming if we don’t get a grip on this. In the past few weeks I have been working with Chinese collaborators on this virus so I am going to take the unusual step of referencing some of my meat life work, though as always I won’t name collaborators, so as to avoid their names being associated with a blog that sometimes involves human sacrifice.

As always, what COVID-19 is doing can be understood in terms of infectious disease epidemiology and the mathematics that underlies it, but only to the extent that we have good quality data. Fortunately we now do have some decent data, so we can begin to make some strong judgments – and the conclusions we will draw are not pretty.

How deadly is this disease?

The deadliness of an infectious disease can be assessed in terms of its case fatality ratio (CFR), which is the proportion of affected cases who die. In my last post I estimated the CFR for COVID-19 to be about 0.4% (uncertainty range 0.22 – 1.7%), and suggested it was between 2 and 10 times as deadly as influenza. The official CFR in China has hovered around 2%, but we know that many mild cases were not diagnosed, and the true CFR must be lower. Since then, however, the Diamond Princess cruise ship hove into view, was quarantined off Yokohama, and carefully monitored. This is a very serendipitous event (for those not on the ship, obviously) since it means we have a complete case record – every case on that ship was diagnosed, symptomatic or not. On that ship we saw 700 people infected and 7 deaths, so a CFR of 1%. I used a simple Bayesian method to use that confirmed mortality rate, updated by the deaths in China, to estimate the under reporting rate in China to be at least 50%, work which is currently available as a preprint at the WHO’s COVID-19 preprint archive. I think a decent estimate of the under reporting rate is 90%, indicating that there are 10 times as many cases as are being reported, and the true CFR is therefore 10 times lower. That puts the CFR in China at 0.2%, or probably twice as deadly as the seasonal flu. However, we also have data from South Korea, where an extensive testing regime was put in place, that suggests a CFR more in the range of 1%.

It’s worth noting that the CFR depends on the age distribution of affected people, and the age distribution in the cruise ship was skewed to very old. This suggests that in a younger population the CFR would be lower. There is also likely to be a differential rate of underreporting, with probably a lower percentage of children being reported than elderly people. It is noteworthy that only 1% of confirmed cases in China were children, which is very different to influenza. As quarantine measures get harsher and health systems struggle, it is likely that people will choose to risk not reporting their virus, and this will lead to over estimates of mortality and underestimates of total cases. But it certainly appears this disease is at least twice as dangerous as influenza.

CFRs also seem to be very different in the west, where testing coverage has been poor in some countries. Today California reported 675 cases and 16 deaths, 2.5 times the CFR rate on the Diamond Princess in probably a younger population. Until countries like the US and UK expand their testing, we won’t know exactly how bad it is in those countries but we should expect a large number of infected people to die.

On the internet and in some opinion pieces, and from the mouths of some conservative politicians, you will hear people say that it “only” kills 1% of people and so you don’t need to worry too much. This is highly misleading, because it does not take into account that in a normal year less than 1% of the population dies, and a disease that kills 1% of people will double your nation’s total death rate if it is allowed to spread uncontrolled. It is important to understand what the background risk is before you assess small numbers as “low risk”!

What is the burden of the disease?

The CFR tells you how likely an affected person is to die, but an important question is what is the burden of the disease? Burden means the total number of patients who need to be hospitalized, and the final mortality rate as a proportion of the population. While the CFR tells us what to expect for those infected, estimates of burden tell us what society can expect this disease to do.

First, let us establish a simple baseline: Japan, with 120 million people, experiences 1 million deaths a year. This is the burden of mortality in a peaceful, well-functioning society with a standard pattern of infectious disease and an elderly population. We can apply this approximately to other countries to see what is going on, on the safe assumption that any estimates we get will be conservative estimates because Japan has one of the highest mortality rates in the world[1]. Consider Wuhan, population 12 million. It should expect 100,000 deaths a year, or about 8,000 a month. Over two months it experienced about 3000 COVID-19 deaths, when it should have seen about 15,000 deaths normally. So the virus caused about 20% excess mortality. This is a very large excess mortality. Now consider Italy, which has seen 3500 deaths in about one month. Italy has a population of 60 million so should see 500,000 deaths a year, or about 40,000 a month. So it has seen about 10% excess mortality. However, those 3500 deaths have been clustered in just the Northern region, which likely only has a population similar to Wuhan – so more likely it has seen 40% excess mortality. That is a very high burden, which is reflected in obituaries in the affected towns.

Reports are also beginning to spread on both social media and in the news about the impact on hospitals in Italy and the US. In particular in Northern Italy, doctors are having to make very hard decisions about access to equipment, with new guidance likening the situation to medical decisions made after disasters. Something like 5% of affected people in Wuhan needed to be admitted to intensive care, and it appears that the symptoms of COVID-19 last longer than influenza. It also appears that mortality rates are high, and there are already predictions that Italy will run out of intensive care facilities rapidly. The situation in northern Italy is probably exacerbated by the age of the population and the rapid growth of the disease there, but it shows that there is a lot of potential for this virus to rapidly overwhelm health systems, and when it does you can expect mortality rates to sky-rocket.

This is why the UK government talked about “flattening the curve”, because even if the same total number of people are affected, the more slowly they are affected the less risk that the care system breaks down. This is particularly true in systems like the US, where hospitals maintain lean operating structures, or the UK where the health system has been stripped of all its resources by years of Tory mismanagement.

Who does it affect?

The first Chinese study of the epidemiology of this disease suggested that the mortality rate increases steeply, from 0% in children to 15% in the very elderly. It also suggested that only a very small number of confirmed cases are young people, but this is likely due to underreporting. This excellent medium post uses data from an Italian media report to compare the age distribution of cases in Italy with those in South Korea, and shows that in South Korea 30% of cases were in people aged 20-29, versus just 4% in Italy. This discrepancy arises because South Korea did extensive population-level testing, while Italy is just doing testing in severe cases (or was, at the time the report was written). Most of those young people will experience COVID-19 as a simple influenza-like illness, rather than the devastating respiratory disease that affects elderly people, and if we standardize the Chinese CFR to this Korean population we would likely see it drop from 2% to 1%, as the Koreans are experiencing. This South Korean age distribution contains some important information:

  • The disease does not seem to affect children much, and doesn’t harm them, which is good
  • Young people aged 20-39 are likely to be very efficient carriers and spreaders of the disease
  • Elderly people are at lower risk of getting the disease than younger people but for them it is very dangerous

This makes very clear the importance of social distancing and lockdowns for preventing the spread of the disease. Those young people will be spreading it to each other and their family members, while not feeling that it is very bad. If you saturate that young population with messages that people are overreacting and that there is not a serious risk and that “only” the elderly and the sick will die, you will spread this disease very effectively to their parents and grandparents – who will die.

It’s worth noting that a small proportion of those young people do experience severe symptoms and require hospitalization and ventilation. In health workers in China there was a death rate among health workers of about 0.2%, and we could probably take that as the likely CFR in young people with good access to care. If the disease spreads fast enough and overwhelms health systems, we can expect to see not insignificant mortality in people aged 20-39, as their access to intensive care breaks down. This is especially likely in populations with high prevalence of asthma (Australia) or diabetes (the US and the UK) or smoking (Italy, and some parts of eastern Europe). So it is not at this stage a good idea for young people to be complacent about their own risk, and if you have any sense of social solidarity you should be being very careful about the risk you pose to others.

How fast does it spread?

The speed at which an infectious disease spreads can be summarized by two numbers: the generation time and the basic reproduction number (R0). Generation time is the time it takes for symptoms to appear in a second case after infection by the first case, and the basic reproduction number is the number of additional cases that will be caused by one infection. For influenza the generation time is typically 2-4 days, while for COVID-19 it is probably 4-6 days. The basic reproduction number of influenza is between 1.3 – 1.5, while the initial estimates for COVID-19 were 2.5, meaning that each case of COVID-19 will affect 2.5 people. Unfortunately I think these early estimates were very wrong, and my own research suggests the number is more likely between 4 and 5. This means that each case will infect 4-5 other cases before it resolves. This is a very fast-spreading disease, much more effective at spreading than influenza, and this high R0 explains why it was able to suddenly explode in Italy and the US. A disease with an R0 over 2 is scary and requires special efforts to control.

Those early estimates of R0 at 2 to 2.5 had a significant negative impact on assessment of the global threat of this disease. I believe they led the scientific community to be slightly complacent, and to think that the disease would be relatively easy to contain and would not be as destructive as it has become. In my research our figures for projected infection numbers show clearly that these models with lower R0 simply cannot predict the future trend of the virus – they undershoot it significantly and fit the epidemic curve poorly. Sadly governments are still acting on the basis of these estimates: the UK government’s estimate that the disease will stop spreading once 60% of people are affected is based on an R0 of 2.5, when an R0 of 4 suggests 75% of people need to be infected. An early R0 estimate of 4 would have rung alarm bells throughout the world, and would have been much more consistent with the disaster we saw unfolding in Hubei. Fortunately the Chinese medical establishment were not so complacent, and worked hard to buy the world time to prepare for this virus’s escape. Sadly many western countries did not take advantage of that extra month, and are paying the price now as they see what this disease really is like.

Because this disease is so highly infectious, special measures are needed to contain it. For a mildly dangerous disease with an R0 of 1.3 (like influenza), vaccination of the very vulnerable and sensible social distancing among infected people is sufficient to contain it without major economic disruption. Above 2, however, things get dicey, and at 4 we need to consider major measures – social distancing, canceling mass gatherings, quarantining affected individuals and cities, and travel restrictions. This is everything that China did in the second month of the outbreak once they understood what they were dealing with, and is also the key to South Korea, Japan and Singapore’s success. Because some western governments did not take this seriously, they are now going to have to take extreme measures to stop this.

How many people will be infected?

The total proportion of the population that will be affected is called the final size of the epidemic, and there is an equation linking the final size to the basic reproduction number. This equation tells us that for influenza probably 40% of the population will be affected, but it also tells us that for epidemics with basic reproduction number over 2 basically the entire population will be affected. In the case of Japan that will mean 120 million people affected with a mortality rate of probably 0.4% (assuming the health care system handles such a ridiculous scenario), or about 500,000 deaths – 50% of the total number of deaths that occur in one year. The Great East Japan Earthquake and tsunami killed 16,000 people and was considered a major disaster. It’s also worth considering that those 500,000 deaths would probably occur over 3-4 months, so over the time period they would be equivalent to probably doubling or tripling the normal mortality rate. That is a catastrophe by any measure, and although at the end of the epidemic “only” half a percent of the population will be dead, the entire population will be traumatized by it.

For a virus of this epidemicity with this kind of fatality rate, we need to take extreme measures to control it, and we need to take it very seriously as soon as it arrives in our communities. This virus cannot be contained by business as usual.

Essential supplies ready

What’s going on in Japan?

The number of cases and deaths in Japan remains quite small, and there has been some discussion overseas that Japan’s response has been poor and it is hiding the true extent of the problem. I don’t think this is entirely correct. Japan introduced basic counter-measures early on, when China was struggling and well before other countries, including cancelling events, delaying the start of the school year, introducing screening at airports and testing at designated facilities, working from home and staggering commuter trips to reduce crowding on trains. For example, work events I was planning to attend were cancelled 2-3 weeks ago, and many meetings moved online back then. Japan has a long history of hygiene measures during winter, and influenza strategies are in place at most major companies to reduce infection risk. Most museums, aquariums and shopping malls have always had hand sanitizer at the entrance, and Japan has an excellent network of public toilets that make hand washing easy. Many Japanese have always maintained a practice of hand-washing and gargling upon returning home from any outside trip, and mask wearing is quite common. Japan’s health system also has a fair amount of excess capacity, so it is in a position to handle the initial cases, isolate them and manage them. This has meant that the growth of the epidemic was slow here and well contained, although it was a little out of control in Hokkaido, where the governor declared a state of emergency (now ended). It is true that many cases are not being tested – hospitals do not recommend mild cases to attend for treatment, but to stay home and self isolate, and it is likely that mild cases will not be tested – but this is not a cover-up situation, rather an attempt to ration tests (which are not being fully utilized at the moment). There are not yet reports of emergency rooms or hospitals being overwhelmed, and things are going quite smoothly. I expect at some point the government will need to introduce stricter laws, but because of that early intervention with basic measures the epidemic appears to be under control here.

My self-isolation plan was kind of forced on me at the end of February, because I dislocated my kneecap at kickboxing in a sadly age-related way, will probably require reconstruction surgery, and am spending a lot of time trapped at home as a result. Actually that was the day that everyone else was panic buying toilet paper and so I was stuck at home with a dwindling supply of the stuff until my friends stepped up. I think most people in Japan have reduced their social activities (probably not as much as me!), and are spending less time in gatherings and events (almost of all which are canceled now), and so through that reduction in contacts plus aggressive contact tracing, the disease is largely controlled here.

Is the world over-reacting?

No. You will have heard no doubt various conservatives on Fox news and in some print outlets complaining about how the world has over-reacted and we should all be just going to the pub, perhaps you’ve seen some Twitter bullshit where a MAGA person proudly declares that they ate out in a crowded restaurant and they’ll do whatever they want because Freedumb. Those people are stupid and you shouldn’t trust them. This virus spreads easily and kills easily, and if it gets a stranglehold on your health system it will be an order of magnitude more deadly than it is right now. If you live in a sensible country (i.e. not the UK or the USA) your government will have consulted with experts and developed a plan and you should follow their recommendations and guidelines, because they have a sense of what is coming down the pipeline and what you need to do to stop it. Do the minimum you are asked to do, and perhaps prepare for being asked to do more. Don’t panic buy, but if you feel like strict isolation is coming you should start laying in supplies. Trust your friends and neighbours to help you, and don’t assume your government is bullshitting you (unless you’re in the UK or the USA, obviously). This is serious, and needs to be taken seriously.

When HIV hit the world our need to wear a condom was presented to us as a self-preserving mechanism. If you choose to circumcise your baby boy you’re probably doing so as a service to future him, not to all the women or men he might spread STIs to. But this virus isn’t like HIV. Your responsibility here isn’t to yourself, it’s to the older, frailer and less healthy members of your community who are going to die – and die horribly, I might add, suffocating with a tube in their throat after days of awful, stifled struggle – if this disease is allowed to spread. We all need to work together to protect the more vulnerable members of our community, and if we don’t react now we will lose a lot of the older people we grew up with and love.

So let’s all hunker down and get rid of this virus together!


fn1: This is a weird and counter-intuitive aspect of demography. Japan has the longest life expectancy in the world’s healthiest population, and one of the world’s highest mortality rates. Iraq, in contrast, would see half as many deaths in a normal year (without American, ah, visitors). This is because healthy populations grow old, and then die in huge numbers.

My recent post on the case fatality ratio of the new Wuhan Coronavirus sparked a long discussion about the role of European epidemics in the colonization of the new world. There is a theory that after Europeans came to the new world (the Americas, Australia, etc) they brought with them diseases that went through the local populations like wildfire, killing huge proportions of the local populations because they were not previously exposed to these diseases, and so lethality was much higher and even simple diseases that Europeans were used to (like influenza) were highly destructive in these naive populations.

This theory sparked my statistician’s skepticism, and also my cynicism about colonial narratives. Europeans arrived in the Americas in 1492, an era not known for its highly advanced demography, and when they arrived counting the locals wasn’t their primary priority. Epidemiology wasn’t particularly advanced at that time either, and medicine incredibly poor quality, not to mention the difficulty of preserving accounts from that time. Furthermore, I don’t see any evidence that the mortality rates due to diseases like smallpox and plague have changed over time in western populations, and because our recent encounters (in the past 500 years) with immunologically naive populations have been very hostile it’s hard to believe that people bothered to adequately (let alone accurately) record what happened in that time, and it’s hard to imagine that there have been any actual, valid studies of immunologically naive populations in modern times.

Furthermore, there has been a major revisionist movement in the west in the past 20 years, which has tried to deny the reality of genocide in the Americas and Australia, and to cast the white invaders as innocent of any crimes, or at worst having made a few well-meaning mistakes. In Australia this has been spear-headed by Keith Windschuttle, whose Fabrication of Australian History series explicitly attempts to deny violence towards Aborigines and recast the destruction of Australian Aborigines as a consequence of disease and demographic decline. This has been pushed by national newspapers (The Australian, of course, fulfilling their role as propagandists for Satan) and our former prime minister, and its “success” has no doubt sparked similar narratives in other countries. There is even a counter-narrative in the Spanish world of the “Black Legend“, which dismisses claims of violence by Spanish conquistadores as propaganda by England and France. It’s very convenient for these people if they can claim that immunologically naive populations are especially vulnerable, and population decline due to violence is actually the consequence of disease. They can even claim that mass movements of indigenous populations occurred due to disease, not genocide. Handy!

This led me to ask two related questions:

  1. Are immunologically naive populations actually subject to higher mortality rates when disease hits them?
  2. Did disease kill the majority of the population in the Americas, and was that disease introduced by Europeans?

The first question can be answered by looking at the history of black death in Europe, and by genetic studies. The second depends on demographic and epidemiological data, and as I will show, there is none, and all the accounts are extremely dodgy.

The history of diseases in naive populations

A population that is naive to a disease is referred to as a “virgin soil” population, although it appears that this name is never used to describe European populations affected by the plague (which was imported from Asia) – “virgin soil”, along with terra nullius, is a concept reserved for the new world. In fact Europe was virgin soil for the plague in the 14th century, and experienced repeated and horrific epidemics of this disease from the 14th century to the 16th century, with smaller plagues later on. In total the black death is estimated to have killed 30-60% of the population of Europe, and to have precipitated huge social changes across the continent. That was 700 years ago, and yet today the case fatality rate due to plague remains 60%, so 700 years of exposure to this disease hasn’t changed European susceptibility at all.

We can also see this in influenza. The H1N1 epidemic of 2009 killed only 0.01% of people who caught it, even though it was a new strain of influenza to which people could be expected not to be immune. The Spanish flu probably killed 10-20% of people it infected, but it did not do an especially greater job in isolated communities who had never experienced influenza before. For example in Samoa it probably killed about 20% of the population, having infected 90%, which suggests it did not behave particularly egregiously in an unexposed population. Smallpox, which has existed for 10,000 years in humans, had a similar mortality rate over most of its history, with variations in this mortality rate primarily driven by the number of people infected and the quality of the healthcare system. There is some evidence that the mortality rate is lower in Africans, who had been exposed to it for longer, but if so this has taken 10,000 years to manifest, which suggests that in general infectious diseases do not behave differently in “virgin soil” populations, though they can be much worse in populations with inadequate health care or infection control methods.

It’s worth noting that many estimates of the impact of these diseases rely on extremely dubious estimates of population. Putting aside demographic methods of the 14th century, Samoa in 1918 was a colony managed by New Zealand, with a colonial management so incompetent that they allowed people to disembark from a plague ship flying a yellow quarantine flag, and then mismanaged the resulting epidemic so badly that everyone on the island got infected. Did New Zealand’s colonial administration have any incentive to accurately count the population before the epidemic? Did they accurately register newborns and elderly people, or did they only record the working age population? How good were their records? If the Samoa population is underestimated by a small amount then the mortality rate plummets, and conclusions about the effectiveness of the disease in this naive population are significantly changed. And was the population even naive? Were the NZ colonial administrators previously recording every influenza epidemic on the island?

These problems are an order of magnitude worse when we try to understand what happened in native populations.

How many Spaniards went to Mexico?

Accounts of the effect of epidemics depend ultimately on our knowledge of the population affected, and population estimation is a very modern science. How was this done in 15th century America, by people who were busy slaughtering the people we now wish they were counting? What was the variation in population estimates and who was recording population, how and why? Fortunately we have a partial answer to questions about how population was recorded, because a historian called David P. Henige wrote a book called Numbers from Nowhere: The American Indian Contact Population Debate, much of which can be read on google books, that makes a lot of strong criticisms of recording of population at that time. Sadly his specific chapters on over-estimation of epidemics are not available online, but he does provide an analysis of accounts by Spanish reporters of the numbers of Spanish soldiers present at certain actions on the continent. As an example, he reports on the number of deaths recorded during the noche tristes, an uprising in the city of Tenochtitlan in which the Aztecs rose against their Spanish occupiers and slaughtered them, driving them out of the city. Spanish accounts of that event – by people who were there – record the number of deaths as between 150 and 1170, with Cortes (the general in charge) recording the lowest number. Henige also notes accounts of expeditionary forces that vary by up to 10% between reporters who were on the scene, and may not even mention Indian attachments that probably far outnumber the Spanish forces. He reports on a famous Spanish reporter on the continent (las Casas) who misreports the size of the continent itself by a huge amount, and notes that a room that was supposed to be filled with treasure as tribute was given radically different sizes by different Spanish observers, as was the amount of treasure deposited therein. He also notes huge discrepancies (up to a factor of 10) in population estimates by colonial administrations in north America. He writes

If three record books showed Ted Williams lifetime batting average as .276, .344 and .523 respectively, or if three atlases recorded the height of Mt. Everest as 23,263 feet, 29,002 feet, and 44,083 feet, or if three historical dictionaries showed King William XIV as ruling 58 years, 72 years and 109 years, their users would have every right to be thoroughly bemused and would be justified in rejecting them all, even though in each case research could show that in each case one of the figures was correct. Yet these differences are of exactly the same magnitude as those among the sources for the size of Atahulpa’s treasure room that Hemming [an author reporting this story] finds acceptable

These are all relatively trivial examples but they make the point: almost nothing reported from the colonies in the 15th century was accurate. In the absence of accurate reporting, what conclusions can we draw about the role of infectious diseases? And what scientific conclusions can we draw about their relative mortality in virgin soil populations?

Scientific estimates of epidemic mortality in Latin America

A first thing worth noting about scientific reports of epidemic mortality in the Americas is that they often use very old sources. For example, this report of the environmental impact of epidemics in the Americas  cites McNeill’s Plagues and Peoples (1977), Dobyns’s estimates of population from 1966 and 1983, Cook’s work from 1983, and so on. It also relies on some dubious sources, using references extensively from Jared Diamond’s 1997 breakout work Guns, Germs and Steel. Some of these works receive criticism in Henige’s work for their credulity, and Diamond’s work has been universally canned since it was published, though it has been very influential outside of academia. Many of these works were written long before good computational demography was well established, and though it’s hard to access them, I suspect their quality is very poor. Indeed, McNeill’s seminal work is criticized for using the Aryan population model to explain the spread of disease in India. These works are from a time before good scholarship on some of these issues was well established.

Dobyns’s work in turn shows an interesting additional problem, which is that no one knows what caused these epidemics. In his 1993 paper Disease Transfer at Contact, (pdf) Dobyns reports on many different opinions of the diseases that caused the demographic collapse in south America: it may be smallpox, or plague, or Anthrax, or typhus, or influenza, or measles. Dobyns’s accounts also often note that people survived by fleeing, but do not ever consider the possibility that they were fleeing from something other than disease. Contrast that with accounts from north America 400 years later (such as the story of the Pince Nez reported in Bury My Heart at Wounded Knee), which make clear that native Americans were fleeing violence and seeking sanctuary in Canada. There is a lot of certainty missing from these accounts, and we need to be careful before we attribute population decline to disease if we don’t know what the disease was, and are relying on accounts from people who refused to consider the possible alternative explanations for the social collapse they are witnessing.

This is particularly complicated by recent studies which suggest that the epidemic that wiped out much of the Mexican population was actually an endemic disease, that jumped from local rats to the indigenous population, spread from the mountains to the coasts (not from European coastal settlements), and had symptoms completely unrelated to European diseases. In this account, a long period of drought followed by rain triggered a swarm of a type of local rat into overcrowded settlements of native peoples, where a type of hantavirus jumped from those rats to humans and then decimated the population. The disease started inland where the drought had been worse and spread outward, and it primarily affected indigenous people because they were the ones forced to live in unsanitary conditions as a consequence of slave-like working conditions forced on them by the invaders. Note here that the western invaders, presumably completely naive to this disease, were not affected at all, because the main determinants of vulnerability to disease are not genetic.

Further problems with the epidemic explanation for native American population loss arise from the nature of the transatlantic crossing and the diseases it carried. The transatlantic crossing is long, and if anyone were carrying smallpox or influenza when a ship left port the epidemic would be burnt out by the time the ship reached the Americas. In fact it took 26 years for smallpox to reach the continent. That’s a whole generation of people slaughtering the natives before the first serious disease even arrived. During that time coastal populations would have fled inland, social collapse would have begun, crops were abandoned, and some native communities took sides with the invaders and began to work against other native communities. In 9 years of world war 2 the Germans managed to kill 50 million Europeans, several millions of these due to starvation in the East, and created a huge movement of refugee populations that completely changed European demographics and social structures. What did the Spaniards do in 26 years in central America?

It is noticeable that many of the accounts from that time seem not to account for flight and violence. Accounts at that time were highly political, and often reported only information that served whatever agenda the writer was pursuing. Las Casas, for example, whose accounts are often treated as definitive population estimates, appears not to have noticed massive epidemics happening right in front of him. Others did not notice any possible reasons why natives were abandoning their fields and farms, and didn’t seem to be able to consider the possibility that something scarier than disease was stalking the land. The accounts are an obvious mess, with no reliable witnesses and no numbers worth considering for serious study.

Conclusion

Without good quality demographic data, or at least even order of magnitude accuracy in population estimates, it is not possible to study the dynamics of population collapse. Without decent information on what diseases afflicted local populations, it is impossible to conclude that “virgin soil” populations were more vulnerable to specific diseases. There is considerable evidence that disease mortality is not different when populations are naive to the disease, drawn from European experience with plague and global experience with influenza, and there is no solid evidence of any kind to support the opposite view in indigenous populations. Historical accounts are fundamentally flawed because of their subjectivity, lack of accuracy even when their interests are not threatened, and the unscientific nature of 15th century thought. A whole generation of conquistadores acted with extreme violence before dangerous diseases arrived on the continent, so many accounts of population collapse must reflect only war, but even after the diseases arrived it is likely that they were no more dangerous in native populations than they were in Europe, which by the 16th century was experiencing endemic smallpox that regularly killed large numbers of people (in Europe in the 18th century it killed 400,000 people a year). There is no reason to think that the Americas were special, or that their local population was especially vulnerable to this or any disease.

It is important to recognize that these issues – accurate diagnosis of disease, accurate estimates of numbers who died, and accurate population numbers – are not just academic exercises. You can’t put them aside and say “well yes, we aren’t sure what disease did it, how many people died, and what the population was, but by all accounts it was bad in the colonies.” That’s not how epidemiology works. You would never, ever accept that kind of hand-waving bullshit when applied to your own community. Nobody would accept it if the Chinese government said “yeah, this coronavirus seems bad, but you know there aren’t that many people affected, the population of Wuhan is anywhere from 1 million to 20 million, and we don’t even really know it’s not seasonal influenza or smallpox.” You would rightly reject that shit out of hand. It’s no different when you’re talking about any other population. We have no reason to suspect any special impact of epidemics in the Americas or Australia, and no reason to conclude that they were especially influential in the history of those regions compared to the violence inflicted on the locals – which we know happened, and we have many accounts of. To look at the accounts we have of disease in the new world, and conclude anything about them beyond “it happened” is to put undue confidence in very, very vague and very poor reporting. There is no empirical evidence to support many of the claims that have been made in the past 40 years – and especially, by genocide deniers, in the past 20 years – about the role of disease in the destruction of indigenous populations of the new world.

This matters for two reasons. First of all, it matters because it has interesting implications for how we think about the threat of disease, and how new diseases will affect naive populations when they jump from animals to humans (which is how almost all new diseases start). These diseases can be extremely dangerous, killing 30-60% of the affected people in some cases, but the reality is that for them to become pandemics they need to mutate to facilitate human-to-human transmission, and that mutation significantly reduces their mortality rates. It is rare for a disease that transmits easily to also be dangerous, and there is very little in the history of the human race to suggest otherwise. The Spanish flu pandemic of 1918 is perhaps the sole exception, and if so it should show just how rare such events are. We should, rightly, be concerned about coronaviruses, but we should also not expect that just because we’re naive to them they’re going to be extra dangerous. Diseases do what they do, and that is all.

But more importantly, we need to reject this idea that the catastrophe that unfolded in the new world between 1492 and 1973 wasn’t the fault of its perpetrators, white Europeans, and we need to reject even partial explanations based on epidemics. It was not disease that killed the people of America and Australia. There is no evidence to suggest it was, and a lot of reasons to question the limited evidence that some people present. The epidemic explanation is a nice exculpatory narrative, which tells us that even if white Europeans had approached the people of the new world with open minds and hearts in a spirit of trade and collaboration they would still have been decimated by our diseases. In this story we may have done some bad things but it doesn’t matter, because contact was inevitably going to destroy these fragile and isolated peoples. And this story is wrong. It isn’t just uncertain, it is wrong: there is nothing in the historical record to support it. If white Europeans had approached the new world in this spirit, there would have been a generation of trade and growth on both sides before the diseases struck, and then we could have helped them to escape and overcome the diseases we were familiar with, that were no more dangerous to them than they were to us. Their communities would have been better prepared to resist the social consequences of those diseases because they would not have been at war, and would not have been experiencing social collapse, overcrowding, starvation and poverty because of western genocidal policies. They would not have been forced into overcrowded and desperate accommodation on drought-stricken plains as slaves to Spanish industry, and the homegrown epidemic of 1545-48 would not have affected them anywhere near as badly. It’s important to understand that the tragedy that befell native Americans was caused by us, not by our diseases, and our diseases were a minor, final bit of flair on a project of destruction deliberately wrought by western invaders.

This other story – of diseases we couldn’t help but strike them down with, even if we had been pure of heart – is a genocide denier’s story. It’s self-exculpatory nonsense, built on bad statistics and dubious accounts of native life presented by biased observers. It is intended to distract and to deny, to show that even if we did a few bad things the real destruction was inevitable, because these frail and noble savages were doomed from the moment they met us. It is a racist narrative, racist because of its false assumptions about native Americans and racist because of what it assumes about the balance of mortality in the continent, racist for trying to pretend that we didn’t do everything we did. It is superficially appealing, both because it adds interesting complexity to an otherwise simple story, and because it helps to explain the enormity of what Europeans did in the Americas. But it is wrong, and it is racist, and it needs to be rejected. There is no evidence that epidemics played a major role in the destruction of native American communities, no evidence that native Americans were especially vulnerable to our diseases, and nothing in the historical record that exonerates European society from what it did. White Europeans enacted genocide on native Americans, and just a few of them happened to die of some of our diseases during the process. European society needs to accept this simple, horrible fact, and stop looking for excuses for this horrible part of our history.

Since 31st December 2019 there has been an outbreak of a new coronavirus in China. It originated in the city of Wuhan, and over the past 22 days has spread rapidly, including cases in several cities outside China. Initial reports suggested it originated in a seafood market in the city, which had me hoping it was the world’s first fish-to-human infectious disease, though I think we need to wait a while before we establish exactly where it started. It appears to have achieved human-to-human transmission, which is unusual for these zoonotic (animal-origin) viruses. International media are of course reporting breathlessly on it, and you can almost feel them salivating over the possibility of another SARS-style catastrophe. But how dangerous is it?

In this blog post I would like to use some initial data and reports to make an estimate of how dangerous this disease is, for those who might be considering traveling to (or canceling travel to) China. I’d also like to make a few comments on the reporting and politics of this disease, and infectious diseases generally.

The Case Fatality Ratio

For the sake of easy writing, let’s call this new disease Dolphin Flu, since it originated in a fish market. The main measure of how deadly any infectious disease is is its case fatality ratio (CFR), which is the number of people who die divided by the number of people infected, multiplied by 100. It seems to be a natural law of infectious diseases that the more infectious a disease is the less fatal it is, and anyone who has played that excellent pandemic game on their phone will know that there is a cost associated with a disease being infectious, which is usually that – like the common cold – it spreads fast but kills no one. Understanding the CFR is important to understanding how nasty a disease is likely to be. Here are some benchmark CFRs:

  • Untreated HIV: 100% (i.e. 100% of people infected with HIV die if they aren’t treated)
  • Untreated Ebola: 80-90%
  • Malaria (Africa): 0.45%
  • Spanish influenza (1918): ~3%
  • Measles: 0.2%

Nature is pretty, isn’t she? It’s worth noting that Spanish Influenza was a global catastrophe, which had major political and economic consequences, so any disease with a CFR around the level of influenza that is similarly infectious is a very scary deal. Ebola and HIV are extremely deadly but also not very infectious (you have to have sex to get HIV, which means my reader(s) face almost zero risk). It’s the respiratory diseases (the lungers) that really worry us.

Calculating the Case Fatality Ratio for Dolphin Flu

In order to calculate the CFR we need to know how many people are infected, and how many have died. Official government data this morning (reported here) puts the death toll at 17 people, and we can be fairly sure that’s correct, so next we need to calculate the number infected. This excellent website tells us there are 555 confirmed cases, but this is not the right number to use for this calculation, because with all of these respiratory-type diseases there are many cases who never go to a doctor and/or never get confirmed. In ‘flu season we call these “influenza-like illnesses” (ILI) and they are important to understanding how dangerous the disease actually is. In fact for many of these diseases there is an asymptomatic manifestation, in which people get the disease and never really show any symptoms. So we need to have an estimate of the total number of cases including those that were not confirmed. Fortunately the excellent infectious disease team (who do a great course in infectious disease modeling if you have the money) at Imperial College have used the number of cases appearing at non-Chinese cities to estimate the total number of cases using data about travel flows from Wuhan city. Their headline estimate at this time is 4000 cases, with an uncertainty interval from 1000 to 9700.

Next we need some information on other diseases. The CDC website for seasonal flu tells us that in the 2017-2018 season in the USA there were 20,731,323 confirmed cases of influenza, 44,802,629 total cases (including unconfirmed) and 61,099 deaths. A Japanese research paper on the H1N1 pandemic tells me there were 637,598 total cases (including unconfirmed) and 85 deaths due to H1N1. The Wikipedia entry on H5N1 bird flu tells me there were 701 confirmed cases and 407 deaths (I think there were very few unconfirmed cases of bird flu because it was so nasty).

Putting this together, we can get the CFR for confirmed and unconfirmed Dolphin Flu, and compare it with these diseases, shown below.

  • Unconfirmed Dolphin Flu: 0.43%, ranging from 0.22% to 1.7%
  • Confirmed Dolphin Flu: 2.98%
  • Unconfirmed Seasonal Flu (2017-18 season, USA): 0.14%, ranging from 0.11% to 0.16%
  • Confirmed Seasonal Flu (2017-18 season, USA): 0.29%
  • Unconfirmed H1N1 (Japan): 0.01%
  • Confirmed H5N1 (Global): 58.06%

This suggests that Dolphin Flu is between 2 and 10 times as dangerous as seasonal influenza, and about as dangerous as malaria if you are infected with malaria in an African context (i.e you may not be able to afford and access treatment, and you’re so used to idiopathic fevers that you don’t bother going to the doctor until the encephalitis starts).

That may not sound dangerous but it’s worth noting that seasonal influenza is one of the most dangerous things that can happen to an adult of child-bearing age except getting in a car and childbirth. It’s also worth noting that depending on the degree to which the Imperial College team have overestimated the number of unconfirmed cases, Dolphin Flu could be heading towards half as dangerous as Spanish Influenza. We don’t yet know if it is as contagious as influenza, but if it is …

I would say at this stage that Dolphin Flu looks pretty nasty. I probably wouldn’t cancel travel, because it’s still in its early stages and the chance of actually getting it is tiny (especially if you aren’t in Wuhan). But tomorrow is Chinese New Year, the largest movement of people on the planet, so in a week I expect that it will be all over China and it may be much harder to go there without getting it. I guess in that context the decision to quarantine Wuhan makes sense – if it’s half as dangerous as Spanish Flu, it’s worth suffering the short term economic damage of shutting down one of China’s largest cities to avoid spreading a disease that could be a global catastrophe.

So, given that information, would you travel? And what decision would you make if you were an administrator of public health in China?

About Cover Ups and Authoritarianism

Media coverage of disease outbreaks almost invariably follows western stereotypes about the country where they happen. With Ebola it’s all about bushmeat-eating primitives who can’t understand modern medicine; with MERS it was secretive religious lunatics; and with anything coming from China it’s a weird mix of Sinophobia, orientalism and obsessions with China’s authoritarian government. Because China fucked up the SARS response, we can see Western media basically salivating at the chance to report on how they’re covering this up too. But it’s important to understand that unconfirmed cases are not covered up cases. With respiratory diseases there will always be unconfirmed cases and there will always be someone who slips through the net and goes traveling, spreading the disease to other cities. Indeed, with a completely new disease it’s entirely possible that there are asymptomatic cases that no health system can detect.

In fact this time around the Chinese response has been very quick, open and transparent. They notified the disease to the WHO on 31st December, probably very soon after the first cases appeared, and the WHO Director-General has been fulsome in his praise of the Chinese response. Within perhaps 10 days of notifying the disease to the WHO they had isolated the virus and developed tests, and now they have quarantined a city of 12 million people because they know that the impending Chinese New Year could cause major transmission risks. Before complete quarantine they had introduced fever checks at exit points to international destinations, another sign of taking the disease seriously. This is unlikely to be successful if the disease has an asymptomatic phase (since you get on the plane before you have a fever) but short of blood-testing everyone in the city, there is little more that anyone could expect the government to do.

How to handle western media panic

None of this will stop western media from playing to the west’s current fear of China, and once the disease is over you can bet they will start talking about how the Chinese response was too authoritarian. You can also bet that the mistakes the administration inevitably makes will be discussed as if they are hallmarks of a Chinese problem, rather than mistakes any government could be expected to make when trying to control a disease that spreads at the speed of a cough. And this will all be made worse by the way western media get into an absolute lather about infectious disease stories. So be cautious about stories about China’s cover-ups, about authoritarianism, and avoid believing disease panics. Check in with the WHO’s updates, read the Imperial College website, and be careful about the western media’s over-hyping of disease threats and Chinese collapse. For a balanced view of infectious disease issues generally (and excellent coverage of the tragic, ongoing Ebola Virus outbreak in DRC) I recommend the H5N1 blog. For understanding how to interpret risk, I recommend reading David Spiegelhalter’s twitter. And remember, when you’re balancing risks, that getting in a car, or choosing to have a child (if you’re a woman) are probably the two most dangerous things anyone in a developed nation can do in their lives. You don’t need to go to China to experience any of those risks!

Let’s hope that this disease turns out to be another fizzer, keep a level head, and don’t let western media hype scare us!


About the picture: The picture is from the Twitter thread of @CarlZha, an excellent independent Chinese voice. It’s a photo of some guys doing renovation work on a clinic somewhere in China. There isn’t actually a Zombie outbreak yet!

Australia has been burning since New Year’s Eve, with bushfires spreading across a huge area of the eastern seaboard. The entire New South Wales coastal region from the border of Victoria to north of Sydney has been affected, along with a big swathe of eastern Victoria (Australia’s most densely-populated state) and communities up and down the coast are slowly being consumed. The main highway linking Western Australia to the eastern states has been cut, and towns on the route are running out of food. As I write this 21 people are listed as missing in Victoria, and about two score people have died along with the loss of hundreds of houses. These figures are preliminary because fire experts predict the fires will burn for weeks still, and the emergency services have not yet had any chance to assess damage in many areas. The federal government has mobilized 3000 army reserve soldiers, troop transports are being used to evacuate entire towns, and in many areas the fires have been left to burn because there are insufficient resources to fight them. Today, 4th January 2020, multiple records for maximum temperatures were toppled, with Canberra setting a new record of 43.8 C, 47C in western Sydney, and all of the south east under a blanket of intense heat and strong winds. The fires may change direction later in the day as a southerly change moves in, though intense winds may spread them even then. From a personal perspective, multiple friends of mine have been marking themselves safe on Facebook, or updating social media with information about their preparations for the incoming fire fronts. Although Australia is used to bushfires, the biggest ones usually occur later in the year and they do not normally all occur at once, across the entire country. This is the effect of global warming, and there is much worse to come over the next few decades.

Australia is currently labouring under a conservative government. For the past 40 years – barring a couple of years in the early 1990s – this party has refused to accept the reality of climate change, has denied its human origins, has fought tooth and nail in international forums to prevent global action against climate change, and has refused to do anything to stop climate change locally. After the past Labour government introduced real measures to begin mitigating climate change the incoming conservative government reversed them, hobbled the renewable energy industry, and used accounting tricks to meet its commitments under the Paris Agreement. Even when they admit that climate change is real they refuse to link climate change to any of the environmental challenges Australia faces, whether drought, storm, flood or fire, and they refuse to take action to mitigate global warming, insisting instead on adaptation.

Today is what adaptation looks like. Communities destroyed, tens of thousands of people evacuating from their homes, huge stretches of forest and national park burnt out, wild animals and stock burnt alive, infrastructure ruined, and the entire country brought to a standstill as it watches the fury of nature in helpless horror. There is nothing that can be done, and ultimately nowhere to run. Climate change has reached the driest, most fragile continent on earth, and its inhabitants are adapting: running, hiding, burning, gasping and hiding on beaches and boats as they watch the sky turn black with the ashes of their homes and communities.

This is what adaptation looks like. This is what the climate change deniers have been demanding of us for the past 20 years. Mitigation is too expensive or impossible, they say, it is better to adapt, to prepare ourselves for the warmer future. Instead of preventing what is coming we should build robust communities that are ready to deal with it. These communities certainly have shown how robust they are as they adapt to the coming firestorms, crouching in the midday dark on beaches or waiting hours in crawling traffic as they abandon their homes. Robust communities, fleeing for their lives from a storm they have been forced to adapt to by 40 years of inaction.

This is what adaptation looks like, and it will get worse. Not only will it get worse, but the people who refused to take any action to prevent this storm coming will also abandon you to its fiery maw. They said you should adapt, but they won’t give you any money to adapt, because when conservatives are faced with a community challenge their answer is always: there’s no money. The same people telling you it’s too expensive to prevent climate change will also tell you it’s too expensive to adapt. Don’t believe me? Look at this government’s response to requests for funding for fire prevention. For two years the fire chiefs have been pushing the government to increase funding for fire services by a mere $12 million per year, and they have refused because “there’s no money.” Today they released $20 million for emergency fire fighting planes, which will arrive two weeks too late and probably won’t help anyway. Up until yesterday they were refusing to consider funding firefighting volunteers. That’s what they think of adaptation. You can burn, for all they care. They and their rich mates will hide in the cities, pretending to be friends of the communities that are forced to adapt, while they refuse to spend a single cent of the money they have made selling coal to the world. They will let you burn before they’ll share the profits of global warming with you.

This is what adaptation looks like, for communities that in many cases were staunch supporters of these conservative governments. Many of the towns and rural areas burning this new year are in staunch Liberal/National-voting seats, people who voted for the governments that deny climate change, and are now running because those same governments won’t help them adapt. Meanwhile the rich columnists of the conservative media sneer at them for not buying insurance, or for not preparing properly, as their homes become uninsurable and undefendable in the face of global warming. Conservatives don’t care about their own rural electorates, and will throw them to the fires of their greed. Nor will they show them the respect of even pretending to care: the prime minister, who in his victory speech last year said he would “Burn every day” to make the lives of the “quiet majority” better was on holiday in Hawaii as his country burned, and hosting a party for cricket players by the Sydney harbour as the disaster escalated. These people will never burn for you, nor will they show you even a modicum of respect or compassion.

Conservatives are traitors, economic wreckers, and ecological vandals. They will destroy this country before they will admit they are wrong, they will watch it all burn down before they will give up their ill-gotten gains, and they will never ever show compassion to the people whose lives are destroyed by their policies. Conservatives are the biggest threat to industrial civilization that humanity has ever faced, and their political movement needs to be destroyed utterly before it destroys us. Wherever you are in the world, you need to get these preening, greedy cowardly traitors out of office. The only hope for the future of civilization as we know it is the destruction of conservative political parties, their expulsion from the body politic, and their complete humiliation intellectually, culturally and politically. Get rid of them, before they get rid of you.

Some commentators on Twitter and in the media are saying that Labour lost the 2019 General Election because it lost too many votes to remain parties, and that failure to retain support from remainers was the problem. Angry Labour activists on Twitter have been listing off the remain seats that were lost, and saying that a strong remain strategy would have saved the party.

This is completely wrong, and I will show this using data from the 2019 election and the 2016 referendum.

Methods

First I used the dataset of constituency-level results I assembled over the weekend, which contains results for 339 constituencies, semi-randomly sampled from the list of all constituencies on the BBC election site and linked to leave voting data from the 2016 EU referendum. The detailed methodology for assembling this dataset is given here. I then assembled a separate data set of only the seats Labour lost, using this handy (but not quite alphabetical) guide from the Metro newspaper. I merged these with EU referendum data.

Using the full constituency data set, I created a logistic regression model of probability of retaining a seat against constituency leave vote, for all the seats that were held by Labour at the 2017 election. I plotted the predicted probability of losing a seat against the proportion of the population in that seat. Then, I conducted a crosstabs and chi-squared test for the seats held by Labour in 2017, showing the probability of losing a seat in 2019 by whether or not it was a leave-voting constituency. I defined a “leave-voting constituency” as any constituency voting above the median leave vote (which was 53.55).

Next, using the data set of the 59 constituencies Labour lost, I calculated the mean vote in this set of constituencies, and the proportion of constituencies that were leave-voting constituencies. I compared this with data for all Labour held seats that were not lost in the 2019 election.

Results

In my constituency data set there were 142 seats held by Labour in the 2017 election, of which 30 (21%) were lost in the 2019 election. Figure 1 shows the cross tabulation of leave seats with seats Labour held in 2019[1].

Figure 1: (Hideously ugly) cross tabulation of Labour-held seats by whether those seats voted leave

As can be seen, 92% of remain seats were held, compared to 66% of leave seats. This is extremely statistically significant (chi-squared statistic 14.35, p<0.001). That’s a nasty sign that the main risk of losing a seat was that it was a leave seat, not a remain seat.

We can show this explicitly using logistic regression. Figure 2 shows the predicted probability of a seat being held by Labour in 2019, plotted against the proportion of the seat that voted to leave in the EU referendum. The red dots on this figure indicate whether it was held by Labour in 2019: red dots on the top of the figure are seats retained, plotted at the value of their leave vote; red dots at the bottom are seats that were lost, plotted at the value of their leave vote.

Figure 2: Probability of losing a seat in 2019 by leave vote

This model was highly significant, and showed that every 1% point in the leave vote reduced the odds of Labour holding the seat by 7%. Note that this figure includes Scotland, so the results might be slightly different if only England were considered, but even the strongest remain-voting seat that was lost – even were it in Scotland – is well above the remain vote of some seats that were held. This model shows that at the extreme end of the leave spectrum, up above 60% of the electorate voting for leave, the probability that Labour retained the seat dropped to around 50%. That’s terrible!

My constituency data set contains only 142 Labour seats, and 30 seats that were lost, but actually 59 seats were lost. Since my data set is semi-random, there is a small chance that it will misrepresent the results. So I checked with the dataset of all seats that were lost. This data set contains 59 seats. Here are some basic facts about this data set, and comparisons with the constituency data set and the full list of Labour-held seats:

  • Labour lost 14 remain-voting seats (24% of all seats lost) and 45 leave-voting seats (76%). This is very similar to my crosstabs, where 24 of 30 seats lost (80%) were leave
  • The average leave vote in the 59 seats that were lost was 57.7%, slightly above the median, ranging from 31.2 – 71.4%.
  • In contrast, the average leave vote in the 112 seats in my constituency data set that Labour held was 48.8%, ranging from 20.5 – 72.8%
  • The average leave vote in all seats held by Labour going into this election was 51.1%, ranging from 20.5 – 72.8%

This is clear statistical evidence that Labour went into this election having a slightly remain-leaning set of constituencies, primarily lost leave-voting constituencies, and emerged from the election even more remain-focused than when it went in.

Conclusion

Labour did not lose this election because of a large swing in votes to the remain parties. It did not lose a large number of remain-voting seats, but was decimated in the leave-voting areas. Labour held on to all of its most heavily remain-focused seats. In attempting to appeal to both leavers and remainers, Labour managed to retain most of the remainers and lose a lot more leavers. Labour emerged from this election even more remain-focused than it was when it went in[2]. There are some very simple reasons for this:

  • The swing to the Tories and away from Labour was much bigger in leave-voting seats
  • The Brexit party was only active in Labour-held seats, and got its largest vote share in the strongly leave seats
  • The swing to the Lib Dems was much less closely related to the leave vote than was the swing away from Labour (see my last blog post, Figure 4)
  • The intensity of the relationship between leave voting and swinging to Lib Dems was lower in Labour-held seats than Tory-held seats (see my last blog post, Figure 4)

In trying to please both sides of the Brexit divide, Labour failed to satisfy the leavers. Pro-brexit Labour voters were simply much, much more committed to Brexit than pro-remain Labour voters were to remain, and so Labour lost the leave areas. There are lots of remainers out there who want to claim that remain is wot did it, but they are simply wrong. I’m super pro-remain myself, but the data makes it very clear: British Labour voters want to leave, and they were willing to pack in their allegiance to the Labour movement to get that done. Whatever you might think of their politics, that is the simple hard fact of the electorates Labour represented.

It’s worth noting that in 2017 Corbyn campaigned on Brexit. The Labour manifesto explicitly accepted Brexit and said Labour would negotiate and leave. At that election Labour won a historically high share for a party in opposition, a higher share of the vote in fact than Blair won in 2005 (when he retained government). In that election they came within a bees’ dick of winning government, and in that period before Corbyn accepted the compromise of a second referendum two Tory PMs left, and Johnson only held onto government by the skin of his teeth (recall there was talk of a unity government). Blair and Cameron have both shown it’s possible to hold government with 35% of the vote, so it’s perfectly possible that had Corbyn gone into this election on a leave platform he would have seen a much smaller swing against him, and could have won it. We don’t know, but on the basis of all the evidence here it seems like the second referendum policy was a disaster for Labour.

This gives two clear lessons for Labour to take in over the next few years and as they choose a new leader:

  1. Labour’s policies and Corbyn were not the primary problem, and dropping them is not going to help. Obviously Corbyn is going to go, it’s traditional, but the manifesto’s policies were not the problem. The Labour right is going to push for the party to throw the Corbyn years down the memory hole (in today’s Guardian we have Suzanne Moore begging for a vet to “sedate” the Corbyn supporters!), because they are and have always been intent on fighting these genuinely left wing policies. Ignore them, and stick to the real Labour platform that will really help the country as it recovers from the horrors of this Tory leadership
  2. Labour – and the British left generally – have to get over Brexit. There is no option left to remain, and no chance it will ever happen now. The Labour right want to claim that Corbyn doesn’t understand working class voters but his original policy – of full-throated Lexit – was much more in tune with what ordinary working class Labour supporters want than anything that the Blairist rump have to say. The debate now for Labour has to be about the type of Brexit, and how to make it work. This means fighting Johnson’s bullshit deal, but on the basis that they can make a better one – obviously this doesn’t matter now but it is the job of the opposition to hold the government to account, and they should do so from the clear perspective of their voters, that Brexit has to happen. This is going to be hard for some of the urban remainers from the south and east, but that’s life if you’re a politician. Further talk of remain just has to end

For 20 years the EU was a thorn in the Tory side, constantly causing them trouble. Cameron ripped that thorn out with this referendum, and although May spent some time botching the healing process Johnson has patched up the damage and squeezed out the last remainer pus from the Tory body politic. If Labour don’t face the reality of Brexit and what it did to this party at the 2019 election, then the issue will fester for them – as it did over so many years for the Tories – and hold them back just as it did the Tories. It is time for Britain to move on from Brexit, and for the Labour movement to accept the reality of the disaster that is coming. Once people realize how Johnson’s Brexit has screwed them, they will turn to Labour – and Labour needs to be ready with a transformative, genuinely left wing agenda in order to recapture its heartland and do what is right for working people. Corbyn was right about Brexit, right about the policies Britain needs, and after he is gone he will still be right about what has to be done. Don’t repudiate those lessons, and in the process destroy the movement.


fn1: My apologies for pasting this as a picture directly copied from Stata, instead of making a nice pretty table – I hate it when people do this but it’s late and I hate making tables in html. Stata offers an option to copy as html but it doesn’t work. Sorry!

fn2: This final conclusion is shakey because it depends on my constituency data set, and I don’t know if it would still be true once all the remaining Labour-held seats are entered into the dataset. I think it will, but there’s a chance the final data set will end up the same level of leaviness as the 2017 constituencies, statistically speaking. But this conclusion is not a very important one anyway, so it doesn’t matter if it isn’t held up by the full dataset.

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