Rainbows of COVID-19

Most posts on this blog contain many numbers, but not this one. Here I wish to bring out a point made in the last post but do it by telling a story. This analogy may feel unnecessary to some but it did help me think of the issue from another perspective and it helps explain it to those that prefer stories and images to numbers and graphs.

Imagine at the start of the lock-down in March you went out for a walk each evening. And with each evening you noticed more rainbows appearing in windows. Now it’s certainly true that back in January you’d have found next to none, so it’s obvious that the rainbows were appearing in windows as people became increasingly concerned about how the NHS staff and other carers would cope with the looming threat.

But let’s say, perhaps out of lack of other things to occupy you in the lock-down, you decided to note down how many rainbows you saw on each evening’s walk and you found that the number of rainbows was still increasing.

But then it occurred to you that the weather had improved since March, evenings were lighter and your walks were getting longer and you were visiting new streets each evening. Were people still putting up new rainbows or was it just that you were viewing more houses and able to see more?

And at this point you can perhaps see the analogy. Viewing a house is like a COVID-19 test and seeing a rainbow in its window is like a test being positive. The number of positive tests you discover reflects both the number of tests that you do and the number of people infected.

But the analogy has a bit more to give.

It’s quite possible that you may view a house and fail to see the rainbow. A tree might block your view, or it may be on a window that doesn’t face onto the street you are stood on or the Sun might have melted the adhesive and the rainbow fell off (I was putting our one up two or three times a day during the heatwave). In short, you’ll miss some rainbows. It’s plausible that for every ten houses you view that does actually have a rainbow on display, you only spot it in seven of them. Conversely, you also reason that it’s next to impossible that you see a rainbow when there isn’t one there.

Seven out of ten or 70% is the typical rate of false negatives in COVID-19 swab tests. A false negative is where the person has the virus but the test comes back negative. Again, like the analogy, false positives are rare: it hardly ever happens that a test comes back as positive when the person does not have the virus.

And there’s one final point we can draw from this analogy.

In your notebook you record the date, the number of houses viewed and the addresses of houses where you saw a rainbow. This will allow you to assess, in time, whether rainbows are still going up or whether you are just going on longer walks or becoming a legendary rainbow spotter.

But you notice that some rainbows are now absent where you had seen them before. You record this on your notebook. But you realise that your method does not allow you to record all of the rainbows that have come down simply because you do not have a complete record of all rainbows that were put up.

In the analogy you can think of a rainbow coming down as being a death from COVID-19 (although in reality it symbolised a feeling that the virus was held at bay). The key point here is that in the headline figures that are published there has to be positive test prior to death for it to be recorded in the COVID-19 deaths total. There is some variation here, Public Health Scotland state the test has to be within 28 days of death, and although Public Health England and Wales don’t specify a time limit, in Wales a clinician needs to confirm COVID-19 was a factor in a death. As explained in the last post, looking at the number of deaths where COVID-19 was mentioned as cause on the death certificate avoids this problem.

Analogies are very useful but should not be taken too far and although they can help explain some aspects of an issue more clearly they can easily mislead and even generate pure nonsense (what does putting a rainbow back up represent?). Hopefully this analogy is of some use in helping people understand the COVID-19 situation.

COVID-19 headline numbers

Information on the COVID-19 pandemic has been hard to digest for a great many reasons but now that the (first) hump is behind us, it is possible to take stock using various totals of cases and deaths that are now, thankfully, increasing more slowly with each week. Here I take a look at two distinct ways to measure deaths due to COVID-19 and why there is a significant difference between them in Scotland.

As of 3 July 2020, the Scottish government reports that 18,287 people have tested positive for the virus and of those 2488 have died. Of the Scottish population, these equate to about 1 in 300 (0.33%) having tested positive and 1 in 2200 people having died (0.05%).

In the whole UK, as of 2 July 2020, the UK government reports that 284,900 people have tested positive and of them 44,198 have died. As a proportion of the UK population this is about 1 in 230 (0.43%) and 1 in 1500 (0.07%).

These fractions may be small but the impact of this virus on those that have lost loved ones and the wider effects on society are anything but.

These headline figures show that 5.6% of COVID-19 deaths in the UK occurred in Scotland, and given that it has 8.2% of the UK’s population, it does seem that Scotland has not suffered quite as much as other parts of the UK.

But these headline figures paint an incomplete picture. If we look at deaths where COVID-19 was mentioned on the death certificate then we find a figure of 4120 for Scotland (as of 21 June) which is two-thirds higher than the 2488 mentioned above.

What explains the difference in these two totals? In the 2488 total, a death is counted only if the person tested positive for the virus while they were alive. This means that some COVID-19 related deaths could well be missing because some people were not tested. In contrast, a doctor can use their professional judgement to record COVID-19 on the death certificate without any test being performed if that person had shown relevant symptoms and if they were known to be close to others who had COVID-19, such as in a care home that suffered an outbreak.

In other words, a likely explanation for the difference between the 2488 and 4120 totals is that deaths are being missed in Scotland’s headline figures because in some cases there was no positive test. Although this is certainly happening elsewhere in the UK, the difference is much smaller with the UK death certificate total of 54,303 being only 23% greater than the one based on positive tests.

To gain another clue for what might explain the discrepancy between Scotland’s death totals we need to look at levels of testing.

According to the Scottish government, a total of 383,722 tests have been “carried out” as of 3 July 2020. The two governments report their numbers of tests differently and so for the UK we have the choice of either tests “processed” at 5.29 million or “made available” at 6.18 million. We have to live with the mismatch, but using these figures we can at least say that somewhere between 6% and 7% of tests in the UK have been in Scotland, a bit below its 8.2% population share.

And so it shouldn’t be too surprising that the 6.4% of positive tests in the UK that were found in Scotland (18,287 of 289,400 mentioned above) falls into this 6% to 7% range. In other words, testing per head of the population is lower in Scotland than elsewhere in the UK as is the number of positive tests.

This all suggests that Scotland’s headline COVID-19 numbers for positive tests and deaths are low not because the outbreak has been less severe in Scotland but because levels of testing have been lower. In fact, Scotland seems to have done not much better or worse than the UK as a whole if we judge it by the fact that its death certificate total of 4120 is 7.6% of the UK’s 54,303 and so close to Scotland’s share of the population.

References

References are given below if you’d like to take a look yourself. Please let me know if you see anything amiss with what I’ve said above.

The pages linked to below will be updated daily or weekly and revisions are not uncommon so don’t be surprised if some of the numbers I use above (written on Sunday 5th July) do not match what you see, but all the main conclusions I came to above have held up with changes over the last week.

Scottish government headline figures

UK government headline figures

Death certificate totals from National Records of Scotland

Death certificate totals for England & Wales

Death certificate totals for Northern Ireland

I’ve collated figures from all the above links and annotated them with more detail in this spreadsheet. It also shows how all the percentages mentioned above were calculated.

EDIT 6 July 2020 08:22 – UK figure for death certificates was corrected but this doesn’t affect any arguments made in this post.

Immigration and emigration

This is the fourth in a series of posts. So far there’s been

To complete the picture we need to look at emigration, people leaving Scotland, and immigration, people entering Scotland.

Natural change and migration in Scotland
Data here. Primary source: National Records of Scotland.

This graph shows two statistics:

  • Natural change: the number of births less deaths.
  • Net migration: the number of people coming to live in Scotland less those leaving.

For each, a negative number means a drain on the population and a positive one means a boost. So you can see that although emigration caused the population to decrease from 1956 to 1965, this was roughly balanced by a positive natural change – the baby boom.

From the mid-1960s onwards natural change falls dramatically, in part due to the availability of the contraceptive pill, and since the mid-1970s Scotland’s natural change has just wobbled around zero; in other words, the numbers of deaths and births have been roughly the same.

So since the mid-1970s, Scotland’s population change is mainly due to net migration which was negative from the mid-1970s until the late 1980s, then about zero until it went positive from 2004 due to immigration from several newly admitted EU member states. You can also see that natural change then shifted from being negative to positive. This could be due to recently arrived young adults starting families.

The historical data for Scotland in the above graph ends in the year of the brexit referendum but data from the Office for National Statistics shows that net migration into the UK remained positive after 2016.  It also shows that net migration from the EU has stayed positive but has decreased to a six year low, and that net migration from outside the EU has increased to its highest for a decade.

Public attitudes to immigration and reaction to it from politicians attained a new significance around the time of the brexit referendum, but I’ll leave that interesting and thorny topic for another blog post.

Birth, death and the bit in between

This is third post in this series about population and sheds some light in things discussed in the last two posts: Scotland’s current population and Scotland’s population – long view.

The following graph shows the number of people that were born and that died in each calendar year from 1855 to 2016.

Graph of births and deaths in Scotland.
Data here. Primary source: National Records of Scotland.

The first feature to catch the eye is that births exceeded deaths, sometimes by 2 to 1 during the late 19th century.  The number of births declined sharply during the First World War and then shot up again immediately after it. The dip in the population before the onset of war in 1914 noted in the previous post might well be related to the decreasing numbers of births apparent on this graph.

Births declined again in the inter-war years but started to climb during the late 1930s. There is a very slight dip in 1939 and 1940 but after that, quite unlike the previous war, it started to climb rapidly again from 1941. This may be related, one way or another, to the USA entering the war.

Following the spike at the end of the Second World War there is the broad baby-boomer bump that peaks in 1964. Thereafter the births fall quite rapidly so that in 1976 it actually falls below the number of deaths for the first time since 1855.

Births only just out-number deaths until 1995 when the situation reverses and deaths exceed births. This remains the case until 2006 when the situations reverses again as births increase and deaths decrease.

A notable feature, apparent from just a glance at the graph, is that the number of births shows far more rapid variation than deaths. Surprisingly, it is hard to see the enormity of the two world wars by looking at how deaths have varied, but both wars stand out clearly in the number of births. On the strength of this evidence it would seem that our geopolitical circumstances influence our desire to procreate more than they determine the timing of when we shuffle off this mortal coil.

Edit 12/12/2018: As pointed out in a comment below, the deaths time series does not include deaths that occurred outside Scotland. Only deaths that occurred in Scotland and so registered in Scotland are counted in this deaths time series. Full detail can be found in this explanatory note from the National Records of Scotland. This explains why the war does not show spikes in the numbers of deaths in these graphs. The comments in the previous post stand though as they all relate to residents of Scotland, and the population of Scotland did see a net increase over the Second World War.

Scotland’s population – long view

This is one of my favourite graphs from the book. It’s one that I can stare for a while and even still sometimes I notice something interesting about Scotland’s history just by looking at how its population has changed.

Scotland's population from 1855 to 2015
Data here. Primary source: National Records of Scotland.

The line shows Scotland’s population in each year and should be read against the left axis. As you can see, the population increased from about 3 million in 1855 to reach about 5 million by 1940, then plateaued for decades, followed by an uptick in the last decade that brought it to its present 5.4 million. For contrast, England’s population has grown more rapidly, from about 16 million to 55 million over this time with much of this growth, unlike Scotland, taking place during the 20th century.

The red bars show the annual growth rate. Through the late 1800s the growth rate varied between 0.5% to 1.0%. Although this annual growth rate may seem small, the change over several decades compounds to produce a significant 50% increase over the first 50 years of this graph.

Scotland’s population growth appears to come to an attend at the time of the First World War, but a close look at the data shows that the two negative bars indicating population decline are before the war in 1912 and 1913. Growth resumes at a muted rate from 1914. (I’m not sure what the explanation is for this oddity. If you know, please get in touch.)

After a brief spurt, the growth rate falters again in the mid to late 1920s but remains positive through much of the 1930s until the outbreak of the Second World War. From 1940 to 1944 there is the biggest historical exodus from Scotland as people leave to join the war effort, but this is reversed in the late forties as people return, at least the ones that were lucky enough to survive.

Hidden in that post-war spike in growth rates is an increase in birth rates. You can see a clue for this by looking at the population: it is higher after the war-time dip than before it. In other words, despite the deaths due to war, the net result was to increase Scotland’s population, by about 100,000 between 1939 and 1949.

The second half of the twentieth century was a period of decline with the growth rate often being negative as deaths outnumber births. Also, there was more emigration out of Scotland than immigration into it.

The next big change came in 2004 when the growth suddenly leapt to 0.3% having been zero or negative in preceding years. And the growth rate went higher still, reaching 0.7% in 2007 and 2011. Such sustained growth had not been seen in Scotland for over a century.

The explanation, of course, is that many new states joined the EU in 2004 and many people in eastern European countries such as Poland chose to exercise their new rights as EU citizens to come to Scotland to live and work. Of course, this wave of immigration was not just confined to Scotland but was present throughout the UK.

The next post will take a closer look at how and why the population has changed.

Scotland’s current population

Scotland’s population is the highest it has ever been at a little over 5.4 million people. This figure is for the middle of 2017 and was published in April 2018 by the organisation tasked with providing authoritative statistics on population, the National Records of Scotland.

They also provide this graphic which is packed with much more detail.

Statistics on Scotland's population.
Primary source: National Records of Scotland.

One striking fact is that women outnumber men in Scotland. In fact, this is true in most developed (meaning wealthier) countries. In less developed countries males slightly outnumber females and this is also true of the world’s overall population as most of the global population live in less wealthy countries.

This kind of chart is sometimes referred to as a “population pyramid” because it’s wider at the bottom than the top. Well, it used to be wider when national statistics of this kind were first published, but it is suffering from a form of middle-aged spread.

The various bulges correspond to times when the birth rate was high. There was a brief burst of baby-making immediately after the Second World War, and those babies are now around 70 years old. There was a more sustained spell of procreative hanky-panky from the late 1950s and through the 1960s resulting in a bulge of people who are now between about 45 and 60 years old. And these “baby boomers”, as they are called, went on to have babies themselves and so we see a third, smaller bulge of people in their twenties. The fourth, and smallest bulge is of children and is likely associated with the wave of immigration that followed the entry of a number of countries into the EU from 2004 to 2006.

This one graphic touches on a number of challenges facing our society, most obviously on schooling, immigration and growing health and social care needs of a growing cohort of people moving into old age. We’ll come back to all of these in future blog posts.

The next post takes a closer look at how the population has grown and shrank over the last 160 years.