COVID-19 projections and reality

On 27th April, I posted some short-run projections of COVID-19 cases and deaths. The plots below show how the daily new cases per million population and deaths per million population compare with reality (at least the confirmed case rates and death rates up to 4th May according to Johns Hopkins CSSEGIS Data.

Its a mixed bag. The projections match reasonably well for a few countries and are very different for others. I’ve revised the smoothing algorithm I used, and that may result in improved projections. But overall, I think I’m not doing much better than IHME, and should probably leave it to those with better models that use SEIR (susceptible-exposed-infected-recovered modeling) or computer simulations of case transmission.

Vox recently published an excellent article on the problems with the IHME modelling of COVID-19. The article also gives a link to a site which has been set up so that you can look at the US predictions made by old versions of the IHME model (and another model). The IHME models are frequently fairly far off. Here is the comparison for the USA as a whole (you can also examine State specific projections).

Its clear that the projection method takes the latest data point and plummets and essentially the same rate as the earlier rise. On second thoughts, I think my short-run projections are doing better than these for many countries.


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COVID-19 short-run projections

Purely statistical predictions of future trends in COVID-19 deaths or cases, even including predictive covariates, have been unable to make sensible forecasts that are not highly sensitive to slight additions of data. The only useful models have been the more traditional SIR and individual-based models of epidemic infectious disease spread in which scenarios allow some assessment of the impact of various social distancing measures.

It struck me there may be a way to make short-run projections of daily deaths, using information on recent trends in confirmed cases. I spent a couple of hours doing this yesterday, here is the result for Switzerland. I explain the simplistic modelling assumptions below, in what is intended only to be an exploratory analysis.

Reported daily new confirmed cases and deaths (dots) along with short-run projections.

A major issue is the quality of the available data on deaths and cases. Recent analysis of total mortality data for the pandemic period with similar data for previous years summarized in a recent New York Times article suggests that total deaths due to COVID-19 are around 60% higher than the reported COVID-19 deaths, which largely include only hospital deaths in many countries. These data are for countries with good death registration systems which cover 100% of deaths, albeit with some delays in registration and coding. For countries with poor or non-existent death registration, including most of Africa, the under-reporting will almost certainly be much higher. I’ve been looking at plots of daily deaths and noticed that there are occasional large increases in some countries for around 1 day in 7, and this may relate to timing of data compilation and reporting, or to “catch-up” when batches of deaths from outside the acute hospital sector are added. Additionally, the very strong age and sex dependence of fatality rates should mean that models need to take into account population age-sex structure and variation of case fatality rates and other factors by age and sex.

Confirmed case time series are also affected by the scope of testing and the extent to which the testing is restricted to specific risk groups or symptomatic people, or is extensive enough to approximate a population sampling. According to the data in, country testing rates in developed countries, excluding those for some small populations under 1 million, range from around 10 per 1,000 in the UK up to around 35 per 1000 in some smaller European countries. For developing countries, rates can be much lower, less than 1 per 1,000 in many African and Asian countries. Trends in confirmed cases may be strongly influenced by trends in testing rates, as well as changes in the populations targeted for testing.

I downloaded latest data up to 25 April (CSSEGIS COVID-19 data) yesterday, and initially did some curve smoothing to look at trends in daily confirmed cases and deaths, mostly to see whether the epidemic does seem to have peaked in countries now discussing easing social distancing. It struck me that it may be possible to make use of these smoothed series to do some short-run projections of deaths out for around a week, without making strong assumptions about the shape of the curve, as was done by IHME in its recent modelling. Here is a plot for Switzerland of daily new confirmed cases and deaths.

My key insight was that trends in mortality should reflect trends in confirmed cases around 14 days earlier (based on a quick literature review). If testing rates are stable, this should allow projection of daily deaths out up to around 10-14 days based on the confirmed case time series. Furthermore, it should be possible to assess and project the trend in apparent case fatality rate (deaths divided by cases 14 days earlier) which should reflect the trend in testing rates and regime. So I spent a couple of hours yesterday having a go at doing this. This is not intended to be a serious attempt at prediction of short-run trends, as I’ve made some simplifying assumptions and picked a curve smoothing technique that was to hand, but not probably ideal. But I will compare reality in a week’s time with my projections, just for the heck of it.

In order to calculate the denominator (confirmed cases) for estimating apparent case fatality rates acfr, I assumed that the days d from diagnosis to death ranged from 8 to 21 days with a lognormal distribution with a mean of 14.1 days. In the limit where there was high levels of testing, I next assumed that the acfr should approach that observed for confirmed cases in Wuhan (2.2%) but adjusted for the age distribution of the country. So the long-term acfr, lacfr, will be higher for developed countries with older population distribution, such as Italy (4.3%) and lower for developing countries such as South Africa (1.2%).

I projected recent trend in ln(acfr-lacfr) using simple regression against time with an exponential weight, giving weight of 1 to the observation for the most recent day, and weights decreasing by factor 0.85 each day into the past. If the recent observed acfr was already lower than my estimated lacfr, I left it constant at its current value. For countries with recently declining acfr, the projection asymptotes at lacfr. For countries with increasing acfr, that increase is projected to continue. Only in a handful of countries does that projection result in dramatically increasing acfr. I’m not sure what that says about the data series, but there is clearly some issue with the data.

The following plots show two typical examples of the projection of apparent case fatality rates in which it starts very high (when deaths have started to occur but there is still very limited testing) and declines in a reasonably regular manner. The third example, for Sweden, is a country in which there is much more variability in the apparent case fatality rate, perhaps reflecting low numbers of cases and deaths, and also likely variations in data quality or scope.

Next, I did a similar short run projection of ln(smoothed daily confirmed cases) out 7 days into the future, and then calculated the denominators associated with smoothed daily deaths out 10 days into the future. This denominator projection actually uses only the first two days of the cases projection for the small fraction of the denominator associated with early deaths. I mostly did the projection of cases to see what a slightly longer projection of deaths looked like, but don’t present that here.

The plots below show examples of these projections for a few selected countries. I’ve added some comments in the captions.

Australia has a low case fatality rate, and appears to have indeed done extremely well in containing the epidemic, as is being claimed.

Switzerland shows clear evidence that the epidemic peaked in late March to early April and is in decline.

The US projections are for continuing increasing daily cases, and for slight decline in daily deaths, probably partly reflecting increasing levels of testing. These projections are probably not that meaningful, as the US has epidemics occurring with different timing in various States, and State level modelling would probably give more nuanced results.

Its unclear from this graph whether daily cases have plateaued, but a projected declining case fatality rate associated with increasing levels of testing has resulted in a projected decline in daily deaths. It will be interesting to see whether reality does better than this.

Clearly a continuing decline for Italy, though projected deaths are nearly flat. Again, reality will hopefully do better.

A rising apparent case fatality rate has resulted in a projected continuing increase in deaths. However, Germany has concluded that daily deaths are declining and it is time to relax social restrictions. Unclear from this data, but the death rate is much lower than for most other European countries.

France also show a peak followed by decline which is projected to continue.

The Netherlands has a death rate 40% higher than Switzerland, though the confirmed case rate is only 70% that of Switzerland. But both appear to be declining.

Larger variability in daily cases and deaths make it difficult to know whether these projected rising numbers are plausible. But there does not seem to be any good evidence the epidemic has peaked in Sweden.

These projections are simplistic, and really mainly to explore the data and the possibility of dealing with changing testing rates in doing projections.  A genuinely useful projection model of this type would not only need to have better evidence-based inputs but also ideally data disaggregated by age and sex, and for larger countries with epidemics in various population centres with different timing, to model at regional rather than national level. The likelihood of “later” epidemics starting in care home or other special population and either spreading into the community or causing later epidemic waves may also need to be taken into account. To a limited extent, it may be possible to treat the data on confirmed cases and hospital deaths as “indicators” of the epidemic and its dynamics, even though large numbers of cases and deaths are not included in such statistics. But large untested populations in institutions such as care homes or prisons could make a huge difference in some countries with relatively large institutionalized populations.

Still I conclude that there may be some value in using case data to make very short-run projections of deaths. Or perhaps to test the usefulness of such an approach using scenario results from one of the SIR or individual-based models.

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Critics agree that IHME COVID-19 projection model is flawed

I downloaded the latest IHME update of its COVID-19 projections yesterday to do another evaluation. Their projections still look very problematic. Other disease modellers and epidemiologists are coming to the same conclusion. An article just published in Statnews was much less polite than I was in my previous post. This article quoted epidemiologist Ruth Etzioni as saying “That it is being used for policy decisions and its results interpreted wrongly is a travesty unfolding before our eyes.”

The Statnews article claims that the IHME model may have influenced Trump’s thinking on when to re-open the country, and that IHME’s early very high projections for the USA are likely to be used by Trump to claim the government response has prevented a great catastrophe.

An article in the Washington Post is also highly critical of IHME and reviews the various other models in use which enable the impacts of social isolation to be better taken into account along with the epidemiological characteristics of the epidemics. A critique from researchers at Imperial College and LSHTM was also published this week in Annals of Internal Medicine and stated that the IHME projections are based “on a statistical model with no epidemiologic basis.”

These articles also note the volatility of the projections to updates of a few extra days data and like me see this as evidence of a very poor predictive model. The main impact of a model like this where the results vary wildly from one update to the next (as opposed to from one scenario to another) are very likely to reduce public/political confidence in all modelling. And this could lead to more deaths.

Having read these various other critiques, I don’t think I will bother to do a second evaluation of IHME’s latest updated projections now.

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How useful are IHME projections of the coronavirus pandemic?

The Institute for Health Metrics and Evaluation (IHME), based at the University of Washington in Seattle, caused considerable alarm on 7 April when it released projections of Covid-19 deaths which predicted total deaths for the UK would be the highest in Europe at 66,314, and higher than their projected total deaths of 60,415 for the USA. According to the results on their webpage at, daily deaths for USA would peak at 2200 in the next few days and start declining from 12 April. In contrast, the UK daily deaths continue to rise almost linearly for the next 12 days from 623 per day to 2900 per day. The curve then flattens at around 3000 deaths per day for a while before declining back to zero in June, giving total deaths of 66,314.

According to the Guardian newspaper: “The 66,000 figure was disputed by scientists whose modelling of the likely shape of the UK epidemic is relied on by the government. Prof Neil Ferguson, of Imperial College London, said last week when the prediction was published that the IHME figures were twice as high as they should have been.”

Three days later, IHME revised the UK projection downwards to around 37,000 deaths by end of July. Despite this lower figure, the UK would still have the highest death toll in Europe. The IHME website says this revision is due to the inclusion of four more days of data as input to their projection model. However, the very different projections for the UK from those for the USA and other European countries did not seem plausible to me, or explicable as due to different social distancing policies (the only predictive variable included in the IHME model).

So I have tested their projections over a short time period of days against subsequent reality. On April 11 I recorded their projections from the last data point for 9 April through to April 18. And today, I downloaded cumulative deaths from the  Johns Hopkins Covid-19 site and calculated deaths per day for Italy, Switzerland, UK and USA. The graph below shows the reported deaths for these countries as solid lines, and the IHME projected deaths from 9 April as dashed lines. I have to conclude their projection model is producing seriously bizarre results.

Reported deaths to 13 April are shown as solid curves. The IHME projected deaths from 9 April to 18 April are shown as dotted curves.

Today I also took another look at their latest projections on their website and they have changed quite substantially again. Now the UK deaths peak yesterday 13 April and start declining from now on, leading to an eventual total deaths of 23,791. The Swiss deaths per day, which have been plateaued for about a week with some signs they may be starting to decline, are projected to start rising to more than double the current number and then start declining from May 7. This is despite Switzerland implementing social distancing rules earlier than the UK and USA.

The following plot compares the government policy responses to COVID-19 for these four countries using the OxCGRT Stringency Index. The IHME also uses an index based on four policy indicators as a predictive variable in its model, and assumes that all countries reach maximum stringency one week after the last input data point. So I can’t see how this variable would create such large differences in projections.

The OxCGRT Stringency Index combines information of nine indicators of government response (school closures, travel bans, shop closures, etc) into a single index on a scale of 0 to 100 (maximum stringency).

The IHME projection model is based on fitting a curve to the cumulative deaths time series with the form shown in the figure below, which results in a symmetrical curve for daily deaths. This means that the fitted curves will tend to have faster declines for countries with faster rising death rates. I can see no reason to think that is what happens in reality.

The IHME projection model is based on fitting a curve to the cumulative deaths time series with the form shown on the left. The daily deaths are a symmetrical curve with shape d = exp(-α*t*t), where t=0 at the peak of the curve.

I checked the projections on the website today, and indeed for three of the countries, the number of days between the peak and one third of the peak deaths is similar for before and after the peak: Switzerland (before 26 days,  after 24 day),  UK (13,13) and Italy (13, 17). The USA is quite different with 14 days to peak and 29 days to reach 1/3 of peak afterwards. I conclude that despite the sophisticated Bayesian curve fitting used, the model appears to be fundamentally inappropriate for Covid-19 projections.

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How does population age structure affect overall case fatality ratios for COVID-19?

The first graph shows coronavirus deaths in Italy up to 26 March 2020 by sex and age. The overall case fatality rate for lab confirmed cases is 11.1% and 70% of deaths are male (closer to 80% below age 80, and it drops to 63% for 80 and above, because fewer men than women survive to their 80s. This is a much higher apparent case fatality rate than other countries and it is often mentioned as an explanatory factor that Italy has the oldest population in Europe. How much do differences in age structure of populations affect overall crude case fatality rates?

A paper published 2 days ago in the Lancet used data from China to estimate infection fatality ratios by age for all COVID-19 infections after adjustments for censoring (recent cases for which there has not been enough time for deaths to occur), demography, differential testing rates by age, and underascertainment. The second graph shows the resulting infection fatality ratios (as fractions -not per cents) by age group, corresponding to an overall infection fatality ratio of 0.65%. This is much lower than the crude confirmed case fatality ratio of 2.3%.

Note: These case fatality rates relate to tested cases if all age groups had the same testing rate as 50-59 year olds (the age group with highest testing rate as proportion of population). The infection fatality ratio refers to total infections including an estimate for non-tested cases that are not diagnosed.

I did a “what if” calculation to see how the overall case fatality rate would change if the population of China (where 17% of people are aged 60 or older) had the age structure of the Italian population (where 30% of people are 60+) or that of various other countries, including Nigeria (with 4.5% aged 60+ typical of African countries).  The third graph shows the resulting overall case fatality rates.  If all else was equal, including age specific infection fatality ratios, having the Italian age distribution  would approximately double the Chinese ratio, and having that of Nigeria would halve it.

Note: these do not represent real infection fatality ratios in countries. They are predicted overall ratios for all infections if age-specific infection and fatality rates are the same as those of mainland China.

Across European countries, the variation of population age structure by itself would cause relatively small variations in overall case fatality rates. Presumably other factors such as smoking levels, cardiovascular disease prevalence, health system responsiveness, and intensive care respirator supply would be more important.  Apparent case fatality rates calculated from COVID-19 deaths divided by lab-confirmed cases are not comparable across countries for a number of reasons. In particular, overall testing rates may vary across countries, with varying proportions of community and hospital samples, and the testing rates may vary in different ways across age groups.

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COVID-19 growth rates by country

Nice new site that plots time trends in cases and deaths, total numbers and rates per million population. The time axis is days since 100+ cases/deaths or days since 1 case/death per million population. I’ve attached screenshots of cases/million and deaths/million with Switzerland highlighted. The dotted straight line on the log scale represents a daily growth rate of 1.35 (35% more cases than day before). That corresponds to a doubling time of 2.31 days. Fortunately, most curves are showing some flattening after the first 10 days to around 1.2 or lower. Australia has a curve that corresponds to a daily growth rate of 1.2. That difference is huge. At a daily growth rate of 1.35, the first case becomes 3.2 million after 50 days, whereas at 1.2 it becomes 9,100. Most of the countries that are beyond 15 days from first case/million are showing flattening of growth, and in the case of China its almost completely flat.

The USA is on day 20 since 100 confirmed cases (or day 18 since 1 case/million) and is following the 1.35x line very closely so far. Unlike most other countries this far into the epidemic, it is not yet showing signs of slowing down.  US total confirmed cases will overtake those of Italy and China by tomorrow or day after.

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Covid-19 update now also reports coronavirus cases and deaths as rates per million population. I’ve done some updated plots for confirmed case rates, reported death rates, and apparent case fatality rates (CFR). The latter are calculated simply as reported deaths per 100 confirmed cases using numbers on at 13.11 GMT on March 24. This may overestimate CFR for countries testing few people, or only people with symptoms (as in Switzerland), or may underestimate it when most cases are recent and deaths for those cases have not yet occurred.

The first graph shows leading countries for cases per million population. Switzerland is in second place with almost as many confirmed cases per million as Italy. I’ve excluded small countries and territories with populations of less than one million.  Otherwise, several small populations such as Iceland, Andorra and Faeroe Islands dominate the graph with rates 2- 5 times higher than Italy.

The second graph shows reported mortality per million population for the thirty leading countries. Italy and Spain have the highest rates, Switzerland is in 5th position. The third graph shows apparent case fatality rates. These may overestimate case fatality (if a lower proportion of cases are being identified through testing) or underestimate case fatality (in the early stages of the epidemic when most cases are very recent). Also, the worldometer dataset does not yet include today’s new cases and deaths for all countries.

The cross-sectional comparison at one point in time does not give any sort of correct comparison of the overall final impact of the epidemics across countries, since countries are all at different points on the epidemic curve. A number of websites are tracking trends with the time axis defined in terms of time since 10th or 100th case.

Now in 9th day of social distancing here in Switzerland. Schools and all shops apart from food, pharmacies and petrol stations are closed, gatherings of more the 5 people banned. Borders are largely closed, with only cross-border workers and others with urgent reasons allowed to cross. Papers are being checked for all except health workers (who have a fast lane) and delays of hours are being encountered. Streets are eerily quiet with little traffic.

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Looking at the COVID-19 statistics on day 3

I live just a couple of kilometres from the border of Switzerland with France, and last Monday evening the border was closed except for frontaliers (who live across the border from work) and those with urgent reasons.  We are now in day 3 of social isolation. All shops, social and fitness venues and schools are closed except for groceries, pharmacies and petrol. Gatherings of 5 or more people inside or outside are banned and everyone who can is asked to work from home. The regime in France is even more extreme, and you are required to fill out an online form to get permission for venturing outside, ie. to walk the dog.

I was looking at the Johns Hopkins website that tracks confirmed cases and reported deaths from COVID-19. It lists countries in descending order and I realized I had not seen plots of cases or deaths per capita, so I made some using the numbers there today. (i’ve not  shown San Marino separately to Italy, as it would dwarf Italy’s rates). Switzerland is the 4th highest country in terms of cases per 100,000 and 5th for deaths per 100,000 (after Italy, Spain, Iran and Netherlands).

Of course these rates are seriously influenced by rates of testing and diagnosis, and identification and reporting of deaths, and clearly some countries and regions are doing much more testing and case/death identification than others. The cross-sectional comparison at one point in time will also not give any sort of correct comparison of the overall final impact of the epidemics across countries, since countries are all at different points on the epidemic curve.

These numbers are all fast moving and the JHU website is not always as updated as the latest figures appearing in some media and government sites. But they are generally not far behind. Its interesting that the rates are much higher for Switzerland than France, but the social distancing regime in France is more draconian than here.

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Declining freedom in the world

Last week, Freedom House released its 2020 annual report on global freedom. The report documents trends in every region of the world of declining political and civil freedom: “In every region of the world, democracy is under attack by populist leaders and groups that reject pluralism and demand unchecked power to advance the particular interests of their supporters, usually at the expense of minorities and other perceived foes.”

The report compiles a freedom index for countries based on an average of two indices for political rights and civil liberties, composed of numerical ratings and descriptive texts for each country. The 2020 index adds to a time series for countries that extends back to 1972. I’ve used this time series in the past as a potential covariate for modelling or projecting causes of death such as organized conflict (see earlier post on projections). I’m also interested to see to what extent the time series upholds the view of Stephen Pinker that there has been sustained long-term improvement in both political rights and human rights globally and this will continue (Enlightenment Now, Chapters 13 and 14).

The graph below shows time trends for the number of countries falling into three broad categories of the freedom index, labelled as Free (green shades), Partly free (orange shades) and Not free (purple shades). The graph includes 185 countries. 11 very small countries with populations less than 90,000 in 2015 are not included.

Trends in numbers of countries by broad freedom category

The report’s methodology is derived in large measure from the Universal Declaration of Human Rights, adopted by the UN General Assembly in 1948. The index is based on the premise that these standards apply to all countries and territories, and operates from the assumption that freedom for all people is best achieved in liberal democratic societies. I list the components of the index below in this post.

The Political Rights index:

  • Electoral process (free and fair elections)
  • Political pluralism and participation
  • Functioning of government (policy determination, lack of corruption, openness and transparency)

Civil liberties:

  • Freedom of expression and belief
  • Freedom of association and organization
  • Freedom for trade unions and other professional or labour organizations
  • Rule of law
  • Personal autonomy and individual rights
  • Equality of opportunity and freedom from economic exploitation

Recent reports use numerical indices with range 0-40 for political rights and 0-60 for civil liberties. I’ve used the mapping of these to seven point rating scales (1-7) for consistency with indices for earlier years.  The categories Free, Partly Free and Not Free are based on the combined average of the PR and CL  ratings as follows:

     Freedom Index       Category                Upper subgroup     Lower subgroup

            1.0 to 2.5            Free                         1.0                              1.5 – 2.5

            3.0 to 5.0            Partly Free            3.0 – 3.5                   4.0  – 5.0

            5.5 to 7.0            Not Free                 5.5 – 6.0                  6.5 – 7.0

The graph above shows numbers of countries by these three categories (and also distinguishing two levels within each category defined as show in the third column above. The following graph shows the proportion of the global population in each category, by weighting each country score by its total population.

Trends in proportions of global population by freedom category

Over the last 14 years, 25 of the 41 established democracies have experienced declines in their freedom indices. This can be see in the diminishing width of the green zone from around 2006. Though there is a long-term trend of increasing global freedom until around 2005-2010, this trend has ceased and there are declining levels of freedom in the last decade. Comparing changes in the freedom index between 2015 and 2020, the gap between setbacks and gains widened compared with 2018, as individuals in 44 countries experienced deterioration in their political rights and civil liberties while those in just 24 experienced improvements. The negative pattern affected all regime types, but the impact was more visible near the top and the bottom of the freedom scale.

At the bottom of the scale, large countries like Russia and China are intensifying their suppression of domestic dissent and at the top of the scale many freely elected leaders are also taking steps to reduce existing human or political rughts. The Global Freedom Report notes that “such leaders—including the chief executives of the United States and India, the world’s two largest democracies—are increasingly willing to break down institutional safeguards and disregard the rights of critics and minorities as they pursue their populist agendas.”- The Freedom House Report goes into more detail about the trends and changes for individual countries in each region.

In the following graphs, I have plotted trends in the proportions of regional populations falling into each of the freedom categories. Because large populations dominate, and crossing one of the freedom thresholds will shift that entire population to another area, these graphs are more spikey than if I had plotted numbers of countries rather than people. For example, the large discontinuity in the purple sub-areas for East Asia and Pacific from 1977 to 1988 reflects the freedom score for China decreasing from 6.5 to 6 in that period. Similarly, the graph for North America shows the decrease in freedom from 2016 onwards in the USA with the index increasing one step from 1 to 1.5.

Finally, I also calculated a population-weighted average freedom score for regions and the world, shown in the following graph.  This also highlights the recent declines in freedom in most regions in recent years, but perhaps in a more comparative way than the regional plots above (where the population proportions relate only to the categories relevant to each region).

Is Pinker right that freedom is increasing and will continue to increase?  Maybe, he is taking a longer view than the last decade, and in the big picture there has been an overall increase in global freedom. But the reversal is worrying and may continue if populist responses continue to attack political and human rights, and humans increasingly turn away from evidence-based approaches to global issues such as pandemics, refugees, overpopulation, and the climate crisis.

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Climate change and the denial of reality

Greta Thunberg and Extinction Rebellion have been raising awareness of the urgent need to stop talking and start acting on global warming. The evidence that global warming is real and that it is human-caused is now overwhelming, but the public debate is regularly swamped by science deniers who in most cases clearly simply ignore or are ignorant of the evidence, and often are clearly clueless about how to assess evidence, or even what constitutes evidence.

The first illustration below, from a recent Economist issue, summarises the rise in average temperature across the earth’s surface in 2018 compared to the average for 1951-1980.

Many deniers claim that the current rising temperature is natural, resulting from ice age cycles or orbital variations of the earth. The graph below shows how current CO2 levels are dramatically higher and rising faster than in any interglacial period over the last half million years.

And our best climate models predict temperature rises associated with CO2 levels which match measured temperatures over the last 40 years. If the impact of CO2 is excluded from the models, it is not possible to explain the observed rise in temperature (see graph below).

Three recent studies published in Nature and Nature Geoscience use extensive historical data to show there has never been a period in the last 2,000 years when temperature changes have been as fast and extensive as in recent decades (1-3).

It had earlier been thought that similarly dramatic peaks and troughs might have occurred in the past, including in periods dubbed the Little Ice Age and the Medieval Climate Anomaly. But the three studies use reconstructions based on 700 proxy records of temperature change, such as trees, ice and sediment, from all continents that indicate none of these shifts took place in more than half the globe at any one time.

The Little Ice Age, for example, reached its extreme point in the 15th century in the Pacific Ocean, the 17th century in Europe and the 19th century elsewhere, says one of the studies. This localisation is markedly different from the trend since the late 20th century when records are being broken year after year over almost the entire globe, including this summer’s European heatwave. Major temperature shifts in the distant past are also most likely to have been primarily caused by volcanic eruptions, according to one of the three studies.

The oft-quoted 97% figure

In the last few days I have seen several articles quoting the claim that 97% of climate scientists accept that humans are causing global warming.  This figure actually comes from a 2013 article in Environmental Research Letters by Cook et al. titled “Quantifying the Consensus on Anthropogenic Global Warming in the Scientific Literature” (4). It actually estimated that among abstracts expressing a position on global warming, 97.1% endorsed the consensus position that humans are causing global warming”.  Not a per cent of scientists but a per cent of papers whose abstracts expressed a position. But the misquote has achieved the status of a universal factoid trotted out by those arguing that humans are causing global warming as well as climate sceptics, who point to 3% thinking it is not real means there is uncertainty.

A more recent review of abstracts from 2013 and 2014 (the_consensus_on_anthropogenic_global_warming) found that of 24,210 abstracts of papers on climate change, only five explicitly rejected human role in global warming. As two of these papers were by the same author, the final figure for scientists who publish on global warming and reject a human causative role is 1 in 17,352 or 0.006%. Almost certainly this percentage is even lower now as more evidence floods in every year. This is probably as close to unanimity as humans are capable of in areas of science that involve such massive amounts of data of different kinds.  Its probably approaching the level of unanimity among physicists and geologists about the shape of the earth. In that case, the evidence is also overwhelming but quite straightforward and accessible to anyone. I suspect the number of scientists publishing papers arguing the earth is flat is actually a real zero per cent.

The obfuscation and undermining of science

I recently commented elsewhere that the climate change denial is being fuelled by deliberate obfuscation and funding of deniers, politicians and right-wing think tanks, that is reminiscent of the way that tobacco companies set out to confuse and obfuscate the very clear scientific consensus. And I went even further to say that in both cases, the relevant industries knew the truth from quite early on but hid that.  After I posted it, I had some qualms. While I thought I was right, perhaps I was just remembering second hand comments and I should check my facts. So I did.

Cummings et al (6) have documented the evidence that the tobacco companies knew and for most part accepted the very strong evidence that cigarette smoking was a cause of cancer by the late 1950s. They and Brandt (7) also document how the tobacco companies’ response was to deliberately undermine the acceptance of the facts by funding research intended to obfuscate the debate about smoking and health and to manufacture controversy about the facts.

In the immediate post-war years – the dawn of the nuclear age – science was in high esteem. Scientific advances (the bomb, radar, computing) had played a major role in winning the war, and continued to transform everyday life with radio, TV, electronics and electrical labour-saving devices. The tobacco industry launched an unprecedented strategy to undermine acceptance of scientific results through funding research intended to undo and obfuscate what was known. In doing so it provided substantial funding to researchers and doctors who would work to confuse the public and more or less invented the modern conflicts of interest that are now such a source of contention in science, medicine, media and public policy. This strategy of producing apparent uncertainty in the science (which actually largely did not really exist) undercut public health efforts and regulatory responses designed to reduce the harms of smoking.

Following the publication by Sir Richard Doll and Austin Bradford Hill in 1952 of a definitive review American, German and British studies which showed smoking was an important cause of lung cancer, the major tobacco companies of the time commissioned a public relations company, Hill and Knowlton, to regain public confidence in the tobacco industry.

In 1954 the British Medical Journal published the first prospective results from the British Doctors Study set up by Doll, confirming that lung cancer rates were much higher in smokers, and increased with the amount smoked. Doll and Hill reported that smokers also had higher death rates from heart disease, chronic lung disease, and many other conditions and, in 1957, the British and Dutch were the first governments to accept officially that smoking caused lung cancer.

John W. Hill, Hill and Knowlton’s president at the time, said that denying the facts would not be enough as this would clearly be borne from self-interest. Instead, demanding more science was a better tactic. He suggested that the goal of the tobacco industry should be to build and broadcast a major scientific controversy which would convey the message that the health effects of smoking were not conclusively known. One way to achieve this end was to commission more research into the causes of illness. Hill proposed the creation of a research group which would serve a public relations purpose demonstrating the tobacco industry’s collective concern for the public. The Tobacco Industry Research Committee was founded. In an advert published in more than 400 newspapers across the United States, tobacco companies promised to explore the science of tobacco and to ensure consumer well-being.

A wide range of other industries have subsequently adopted similar strategies to invent scientific controversy to undermine public action to address known harms. While the tobacco industries have now conceded and accept that tobacco smoking causes cancer, respiratory and cardiovascular diseases, the fossil fuel industries and their supporters are doing their utmost to undermine acceptance of the evidence and consensus on global warming.

The Guardian recently documented the evidence that the fossil fuel industries’ own scientists were advising them in the 1970s that there was an “overwhelming” consensus that fossil fuels were responsible for atmospheric carbon dioxide increases (8). And a confidential report prepared for Shell found that CO2 could raise temperatures by 1C to 2C over the next 40 years with changes that may be “the greatest in recorded history”.  In 1990 Exxon funded two researchers, Dr Fred Seitz and Dr Fred Singer to dispute the mainstream consensus on climate science. Seitz and Singer were previously paid by the tobacco industry and questioned the hazards of smoking. Singer, who has denied being on the payroll of the tobacco or energy industry, has said his financial relationships do not influence his research (8).


  1. Neikom R. et al. No evidence for globally coherent warm and cold periods over the pre-industrial Common Era. Nature 2019, Vol 571, pp550-554
  2. Neikom R. et al. Consistent multidecadal variability in global temperature reconstructions and simulations over the Common Era. Nature Geoscience 2019, Vol 12, pp643-649
  3. Brönnimann S, et al. Last phase of the Little Ice Age forced by volcanic eruptions. Nature Geoscience 2019, Vol 12, pp650-656
  4. Cook J. et al. Quantifying the consensus on anthropogenic global warming in the scientific literature. Environmental Research Letters 213, Vol 8 (2), 023024
  5. Powell JR. The Consensus on Anthropogenic Global Warming. 2015, Vol 39(6). Available at
  6. Cummings KM, Brown A, O’Connor R. The Cigarette Controversy. Cance Epidemiol Biomarkers Prev 2007, Vol 16(6), June 2007.
  7. Brandt AM. Inventing conflicts of interest: a history of tobacco industry tactics. American Journal of Public Health 2012, Vol 102(1), pp63-71.
  8. Watts J, Blight G and Gutierrez. Half a century of dither and denial – a climate crisis timeline. Guardian Wed 9 Oct 2019.


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