How much does herd immunity help?

I was asked in a recent email about the potential contribution of (partial) herd immunity to controlling Covid-19.  This seemed a question that many may be asking, so here is the original question and my reply (expanded slightly).

We know that the virus burns itself out if R remains < 1.

There are 2 processes that reduce R, both operating simultaneously:

1) Containment which limits the spread of the virus.

2) Inoculation due to infection which builds herd immunity.

Why do we never hear of the second process, even though we know that both processes act together? What would your estimate be of the relative contribution of each process to reduction of R at the current state of the pandemic in Wales?

One of the UK government’s early options was (2) developing herd immunity1.  That is you let the disease play out until enough people have had it.
For Covid the natural (raw) R number is about 3 without additional voluntary or mandated measures (depends on lots of factors).   However, over time as people build immunity, some of those 3 people who would have been infected already have been.  Once about 2/3 of the community are immune the effective R number drops below 1.  That corresponds to a herd immunity level (in the UK) of about 60-70% of the population having been infected.  Of course, we do not yet know how long this immunity will last, but let’s be optimistic and assume it does.
The reason this policy was (happily) dropped in the UK was the realisation that this would need about 40 million people to catch the virus, with about 4% of these needing intensive care.  That is many, many times the normal ICU capacity, leading to (on the optimistic side) around half a million deaths, but if the health service broke under the strain many times that number!
In Spain (with one of the larger per capita outbreaks) they ran an extensive antibody testing study (that is randomly testing a large number of people whether or not they had had any clear symptoms), and found only about 5% of people showed signs of having had the virus overall, with Madrid closer to 10%.  In the UK estimates are of a similar average level (but without as good data), rising to maybe as high as 17% in London.
Nationally these figures (~5%) do make it slightly easier to control, but this is far below the reduction needed for relatively unrestricted living (as possible in New Zealand, which chose a near eradication strategy)   In London the higher level may help a little more (if it proves to offer long-term protection).  However, it is still well away from the levels needed for normal day-to-day life without still being very careful (masks, social distancing, limited social gatherings), however it does offer just a little ‘headroom’ for flexibility.  In Wales the average level is not far from the UK average, albeit higher in the hardest hit areas, so again well away from anything that would make a substantial difference.
So, as you see it is not that (2) is ignored, but, until we have an artificial vaccine to boost immunity levels, relying on herd immunity is a very high risk or high cost strategy.  Even as part of a mixed strategy, it is a fairly small effect as yet.
In the UK and Wales, to obtain even partial herd immunity we would need an outbreak ten times as large as we saw in the Spring, not a scenario I would like to contemplate 🙁
This said there are two caveats that could make things (a little) easier going forward:
1)  The figures above are largely averages, so there could be sub-communities that do get to a higher level.  By definition, the communities that have been hardest hit are those with factors (crowded accommodation, high-risk jobs, etc.) that amplify spread, so it could be that these sub-groups, whilst not getting to full herd-immunity levels, do see closer to population spread rates in future hence contributing to a lower average spread rate across society as a whole.  We would still be a long way from herd immunity, but slower spread makes test, track and trace easier, reduces local demand on health service, etc.
2)  The (relatively) low rates of spread in Africa have led to speculation (still very tentative) that there may be some levels of natural immunity from those exposed to high levels of similar viruses in the past.  However, this is still very speculative and does not seem to accord with experience from other areas of the world (e.g. Brazilian favelas), so it looks as though this is at most part of a more complex picture.
I wouldn’t hold my breath for (1) or (2), but it may be that as things develop we do see different strategies in different parts of the world depending on local conditions of housing, climate, social relationships, etc.

Update

Having written the above, I’ve just heard about the following that came out end of last week in BMJ, which suggests that there could be a significant number of mild cases that are not
detected on standard blood test as having been infected.
Burgess StephenPonsford Mark JGill DipenderAre we underestimating seroprevalence of SARS-CoV-2? https://www.bmj.com/content/370/bmj.m3364
  1. I should say the UK government now say that herd immunity was never part of their planning, but for a while they kept using the term! Here’s a BBC article about the way herd immunity influenced early UK decisions, a Guardian report that summarises some of the government documents that reveal this strategy, and a Politco article that reports on the Chief Scientific Adviser Patrick Vallance ‘s statement that he never really meant this was part of government planning.  His actual words on 12th March were “Our aim is not to stop everyone getting it, you can’t do that. And it’s not desirable, because you want to get some immunity in the population. We need to have immunity to protect ourselves from this in the future.”  Feel free to decide for yourself what ‘desirable‘ might have meant.[back]

lies, damned lies and obesity

2016-07-15 11.02.43 - inews-obesityFacts are facts, but the facts you choose to tell change the story, and, in the case of perceptions of the ‘ideal body’, can fuel physical and mental health problems, with consequent costs to society and damage to individual lives.

Today’s i newspaper includes an article entitled “Overweight and obese men ‘have higher risk of premature death’“.  An online version of the same article “Obese men three times more likely to die early” appeared online yesterday on the iNews website.  A similar article “Obesity is three times as deadly for men than women” reporting the same Lancet article appeared in yesterday’s Telegraph.

The text describes how moderately obese men die up to three years earlier than those of ‘normal’ weight1; clearly a serious issue in the UK given growing levels of child obesity and the fact that the UK has the highest levels of obesity in Europe.  The i quotes professors from Oxford and the British Heart Foundation, and the Telegraph report says that the Lancet article’s authors suggest their results refute other recent research which found that being slightly heavier than ‘normal’ could be protective and extend lifespan.

The things in the reports are all true. However, to quote the Witness Oath of British courts, it is not sufficient to tell “the truth”, but also “the whole truth”.

The Telegraph article also helpfully includes a summary of the actual data in which the reports are based.

obesity-table

As the articles say, this does indeed show substantial risk for both men and women who are mildly obese (BMI>30) and extreme risk for those more severely obese (BMI>35). However, look to the left of the table and the column for those underweight (BMI<18.5).  The risks of being underweight exceed those of being mildly overweight, by a small amount for men and a substantial amount for women.

While obesity is major issue, so is the obsession with dieting and the ‘ideal figure’, often driven by dangerously skinny fashion models.  The resulting problems of unrealistic and unhealthy body image, especially for the young, have knock-on impacts on self-confidence and mental health. This may then lead to weight problems, paradoxically including obesity.

The original Lancet academic article is low key and balanced, but, if reported accurately, the comments of at least one of the (large number of) article co-authors less so.  However, the eventual news reports, from ‘serious’ papers at both ends of the political spectrum, while making good headlines, are not just misleading but potentially damaging to people’s lives.

 

  1. I’ve put ‘normal’ in scare quotes, as this is the term used in many medical charts and language, but means something closer to ‘medically recommended’, and is far from ‘normal’ on society today.[back]

Statistics and individuals

Ramesh Ramloll recently posted on Facebook about two apparently contradictory news reports on vitamin D, one entitled “Recommendation for vitamin D intake was miscalculated, is far too low, experts say” and the other  “High levels of vitamin D is suspected of increasing mortality rates“.

While specifically about diet and vitamin D intake, there seems to be a number of lessons from this: about communication of science (Ramesh’s original reason for posting this), widespread statistical ignorance amongst scientists (amongst others), and the fact that individuals are not averages.

Ramesh remarked:

Science reporting is broken, or science itself is broken … the masses are like deer in headlights when contradictory recommendations through titles like these appear in the mass media, one week or so apart.

I know that rickets is currently on the increase in the UK, due partly to poverty and poor diets leading to low dietary vitamin D intake, and due partly to fear of harmful UV and skin cancer leading to under-exposure of the skin to sunlight, our natural means of vitamin D production.  So these issues are very important, and as Ramesh points out, clarity in reporting is crucial.

Looking at the two articles, the ‘too low’ article came from North America, the ‘too much’ article, although reported in AAAS ‘EurekaAlert!’ news, originated in University of Copenhagen, so I thought that maybe the difference is that health conscious Danes are simply overdosing.

However, even as a scientist, making sense of the reports is complicated by the fact that they talk in different units.  The ‘too low’ one is about dietary intake of vitamin D measured in ‘IU/day’, and the Danish ‘too much’ report discusses blood levels in ‘nanomol per litre’.  Wow that makes things easy!

Furthermore the Danish study (based on 247,574 Danes, real public health ‘big data’) showed the difference between ‘too much’ and ‘too little’, was a factor of two, 50 vs 100 nanomol/litre.  It suggests, Goldilocks fashion, that 70 nanomol/liter is ‘just right’.  Note however, the ‘EurekaAlert!’ news article does NOT quantify the relative risks of over and under dosing, which does make a big difference to the way they should be read as practical advice, and does not give a link to the source article to find out (this is the AAAS!).

Digging a little deeper into the “too low” news report, it is based on an academic article in the journal ‘Nutrients’,A Statistical Error in the Estimation of the Recommended Dietary Allowance for Vitamin D“, which is re-assessing the amount of dietary vitamin D to achieve the same 50 nanomol/litre level used as the ‘low’ level by the Danish researchers.  The Nutrients article is based not on a new study, but a re-examination of the original meta-study that gave rise to the (US and Canadian) Institute of Medicines current recommendations.   The new article points out that the original analysis confused study averages and individual levels, a pretty basic statistical mistake.

nutrients-06-04472-g001-1024  nutrients-06-04472-g002-1024

 Graphs from “A Statistical Error in the Estimation of the Recommended Dietary Allowance for Vitamin D“. LHS is study averages, RHS taking not account variation within studies.

A few things I took from this:

1)  The level of statistical ignorance amongst those making major decisions (in this case at the Institute of Medicine) is frightening. This is part of a wider issue of innumeracy, which I’ve seen in business/economic news reporting on the BBC, reporting of opinion polls in the Times, academic publishing and reviewing in HCI, and the list goes on.  This is an issue that has worried me for some time (see “Cult of Ignorance“, “Basic Numeracy“).

2) Just how spread the data is for the studies. I guess this is because individual differences and random environmental factors are so great.  This really brings home the importance of replication, which is so hard to get funded or published in many areas of academia, not least in HCI where individual differences and variations within studies are also very high.  But it also emphasises the importance of making sure data is published in such a way that meta-analysis to compare and combine individual studies is possible.

3) Individual difference are large.  Based on the revised suggested limits for dietary vitamin D, designed to bring at least 39/40 people over the recommended blood lower limit of 50 nanomol/litre, half of people would end up with blood levels higher than four or five times that lower limit, that is more than twice as high as the level the other study says leads to deleterious over-consumption levels.  This really brings home that diet and metabolism vary such a lot between people and we need to start to understand individual variations for health advice, not simply averages.  This is difficult, as illustrated by the spread of studies in the ‘too low’ article, but may become possible as more mass data, as used by the Danish study, becomes available.

In short:

individuals matter in statistics

and

statistics matter for individuals