Reposted from Dr. Judith Curry’s Climate Etc.
June 21, 2020 by niclewis |
By Nic Lewis
Key points about the recent Nature paper by Flaxman and other Imperial College modellers
1) The transition from rising to declining recorded COVID-19 deaths in the in 11 European countries that they studied imply that transmission of COVID-19 must have reduced substantially.
The study was bound to find that together the five government non-pharmaceutical interventions (NPI) they considered contributed essentially 100% of the reduction in COVID-19 transmission, since in their model there is nothing else that could cause it.
2) The prior distribution they used for the effects of NPIs on transmission in their subjective Bayesian statistical method hugely favours finding that almost all the reduction in transmission is due to one, or possibly two, NPIs with all the others having a negligible effect.
The probability density of the prior distribution at their median estimates of the effect on transmission of each type of NPI, which allocate essentially all the reduction in transmission to lockdowns, was many billion times greater than it would have been if the same total estimated reduction had been spread evenly across the types of NPI.
3) Which intervention(s) is/are found to be important depends critically on the assumptions regarding the delay from infection to death. When using their probabilistic assumptions regarding the delay from infection to death, a huge (and highly improbable given other assumptions they made) country-specific effect is required to explain the reduction in transmission in Sweden, where no lockdown occurred. If delays from infection to death are increased by just three days, their model no longer finds lockdowns to have the largest effect, and a more moderate country-specific effect is required to explain the reduction in transmission in Sweden.
4)The estimated relative strengths of different NPIs are also considerably affected by the use of an alternative prior distribution for their effects on transmission that does not strongly bias the estimation of most of them towards a negligible level. They are also considerably affected by phasing in over a few days the effects of the two NPIs that seem unlikely to have had their full effect on their date of implementation.
5) It follows from the above that that study provides no information whatsoever as to the actual contribution from all NPI combined to the reduction in transmission, and nor does it provide robust estimates of relative effects of different NPI.
Introduction
On 8 June 2020, Nature published a paper (Flaxman et al. 2020[1]) by modellers in the Imperial College OCIVD-19 response team. Its abstract ends with:
Our results show that major non-pharmaceutical interventions and lockdown in particular have had a large effect on reducing transmission. Continued intervention should be considered to keep transmission of SARS-CoV-2 under control.
Using a counterfactual model, the paper also estimated the impact of interventions on deaths from COVID-19 in the 11 European countries studied, saying:
We find that, across 11 countries, since the beginning of the epidemic, 3,100,000 [2,800,000 – 3,500,000] deaths have been averted due to interventions.
The mainstream media publicised the ‘3 million deaths saved’ claim, without critically appraising the paper or, generally, mentioning the relevant caveat in the paper:
The counterfactual model without interventions is illustrative only and reflects our model assumptions.
In Imperial College’s press release Dr Flaxman ignored his own caveat, saying
Using a model based on data from the number of deaths in 11 European countries, it is clear to us that non-pharmaceutical interventions– such as lockdown and school closures, have saved about 3.1 million lives in these countries
In this article I examine the main claim – that major non-pharmaceutical interventions (NPI) have had a large effect on reducing transmission of COVID-19, to which the inferred reduction in deaths is attributable, with almost all the reduction due to lockdowns. I show that this claim is strongly dependent on the assumptions made and is highly dubious.
The case of Sweden, where the authors find the reduction in transmission to have been only moderately weaker than in other countries despite no lockdown having occurred, is prima facie evidence against the paper’s main claim.
How the effects of lockdowns and other interventions were estimated
Flaxman et al. employ a ‘hierarchical Bayesian’ statistical model. It uses data on daily deaths (up to 5 May 2020, when two countries relaxed their lockdowns), the dates of imposition of five types of NPI (school or university closure, case-based self isolation, public events banned, lockdown ordered and social distancing encouraged), and estimates of the infection fatality rate, for each of 11 European countries.[2] Using these data, the model infers what time profiles of the effective reproduction number (Rt, the number of people whom an infected person in turn infects) – and hence of new infections – would produce the best match between projected and recorded deaths for each country. To do so it uses a simple model of epidemic growth and probabilistic estimates, common to all countries, of the time from infection to death and of the generation time (that from a person becoming infected to them infecting others). The assumed infection fatality rate (IFR) is common between countries for each age band, but reflects the age-structure of each country’s population. It averages slightly over 1%.
A separate initial value, R0 (the basic reproduction number), of the reproduction number Rt is inferred for each country. Rt then changes from R0 in stepwise fashion at the date of each NPI, which act multiplicatively with an equally strong inferred effect for all countries. Each country’s epidemic is seeded by a series of infections starting 30 days prior to a total of 10 recorded deaths.[3]
The model is described in more detail here, and is illustrated in Figure 1, taken from Flaxman et al.Fig. 1. Reproduction of Flaxman et al. Extended Data Fig. 3: Summary of model components
The treatment of interventions
The model uses no information on NPI’s except their type and their implementation date in each country. NPI of each type are treated as having the same (multiplicative) effect on Rt in each country. Each type of NPI is treated identically. As well as the five types of actual interventions, all first interventions (whatever type) are treated as an extra type of intervention, for each country occurring on the date of implementation of its first actual NPI (almost always either self isolation or public events ban, and never lockdown). Hence there are six NPIs with shared values for all countries.
In addition, a pseudo-NPI with a strength that is estimated separately for each country is treated as taking place on the same date as the last actual NPI. These country-specific pseudo-NPIs allow for variation between countries in the effectiveness of the implementation of their NPI. They are probabilistically constrained to be relatively small, making a country-specific effect large enough to cause a halving of Rt exceedingly improbable.
In all 11 countries the exponential growth in infections and deaths experienced early in the epidemics slowed and then turned negative, with infections and deaths decreasing. This implies that in all 11 countries Rt decreased very substantially, to below one, since the start of their epidemics.
In the Flaxman et al. model the only factor that can cause Rt to decrease significantly is the effect of each NPI. Therefore, the estimated overall effect of the NPIs in reducing Rt, and hence deaths resulting from COVID-19 disease, is bound to be very strong.
The only non-NPI factor that affects Rt in the Flaxman et al. model is the reduction arising from the proportion of the population susceptible to infection (set at 100% initially) gradually diminishing over time due to individuals already infected by COVID-19 becoming immune to it. This reduction is very small in their model, for two reasons:
- they make the very unrealistic assumption that all individuals in a country are equally susceptible to COVID-19 and, if infected, are equally likely to infect others.
- the relatively high infection fatality rates they assume result in only very small proportions of countries’ populations becoming infected in their model.
Therefore, their model has to attribute almost all the overall reduction in Rt to government interventions.
Factors not considered by Flaxman et al., all of which are highly likely to have caused some reduction in COVID-19 transmission, and which between them may well have caused substantial reductions in Rt in all 11 countries, include:
- population heterogeneity in social connectivity – which generates highly correlated heterogeneity in both susceptibility and infectivity – and in other factors determining susceptibility to COVID-19
- unforced changes in the behaviour of individuals as they adjust it to reflect COVID-19 risk
- seasonal factors: infections by common coronaviruses peak in the winter and diminish greatly as spring progresses.
As is well known by competent epidemiologists, the first of the above-mentioned factors causes Rt to diminish faster, potentially much faster, with the number of people who have been infected than if it were proportional to the number of people remaining uninfected, as assumed by Flaxman et al. The other factors directly reduce Rt.
If follows that Flaxman et al.’s counterfactual case, which predicts ~3,200,000 deaths in the absence of any NPIs (their ‘counterfactual model’), is completely unrealistic, as therefore is their estimate of 3,100,000 lives saved by interventions.
It also follows that Flaxman et al.’s claim:
Our estimates imply that the populations in Europe are not close to herd immunity (~70% if R0 is 3.8)
may be invalid. As shown here, due to population heterogeneity in susceptibility and infectivity the herd immunity threshold it is bound to be lower – quite possibly very substantially so – than if, as required for it to be ~70% at an R0 of 3.8, populations are homogeneous.
Flaxman et al.’s assertion that all the reduction in transmission (i.e., the reduction in Rt) was due to NPIs, other than very small reduction as more people have been infected and become immune, is unsound. Nevertheless, it seems quite likely that NPIs have had a significant, perhaps substantial, effect on Rt. However, given the confounding effects of the other factors mentioned it is impossible reliably to estimate the total effect of NPIs on Rt and hence on deaths.
Even when making the unrealistic assumption that almost all the reduction in Rt was due to interventions, any allocation of that reduction between the NPIs is very fragile. Flaxman et al. accept this in relation to NPIs other than lockdown, writing:
Most interventions were implemented in rapid succession in many countries, and as such it is difficult to disentangle individual effect sizes of each intervention. In our analysis we find that only the effect of lockdown is identifiable, …
On their median estimates, lockdown caused an 82% reduction in Rt, whereas no other NPI caused as much as a 1% reduction in Rt. While it would not be particularly surprising if such a drastic intervention as lockdown had had stronger effects than other NPIs, even if lockdown had a strong effect one would expect some other NPIs to have had a significant effect. So how did Flaxman et al. find that, remarkably, almost the entire effect of interventions was due to lockdown? The answer, which turns out to be two-fold, shows that their finding is not credible.
Why Flaxman et al. found almost all reduction in COVID-19 transmission to be attributable to a single intervention
Flaxman et al. use a subjective Bayesian statistical method. I have repeatedly criticised this type of Bayesian method in the climate science field, but – probably due to its ease of use – it remains standard practice there and in many other fields.
A subjective Bayesian method requires prior probability distributions to be assigned for each unknown parameter whose value is to be inferred. These prior distributions are then modified by the likelihood function, which reflects how well the modelled deaths fit the daily deaths data at varying values of the parameters, in order to arrive at a ‘posterior’ probability distribution for the parameter values. They use a common method of achieving this that results in a large number of quasi-random draws (‘posterior draws’) from the derived posterior probability distribution.
They represent the strength of interventions by a six dimensional parameter alpha (five actual NPIs plus the synthetic first intervention NPI), with the corresponding effect of intervention i (i being 1, 2,3, 4, 5 or 6)[4] on Rt being to multiply it by exp(-alpha[i]).
The combined effect of all interventions is then to multiply Rt by exp[-(alpha[1] + alpha[2] + alpha[3] + alpha[4] + alpha[5] + alpha[6])][5], which depends only on the sum of the individual alpha values. Their own posterior draws show a median value of the sum of the alphas of 1.75, which corresponds to an 83% reduction in transmission (1 – e−1.75 = 0.83).
The prior distribution assigned by the authors to the strength of the reduction in Rt caused by each intervention is of particular concern. Each of the six alpha values is assigned a gamma-distributed prior probability distribution; a small offset is applied, so that the gamma-distributed values inferred initially are marginally higher, but that is a cosmetic feature.[6] The authors write:
The intuition behind this prior is that it encodes our null belief that interventions could equally increase or decrease Rt, and the data should inform which.
That is not in fact true. As the left hand panel of Figure 2 shows, their prior allows each intervention to decrease Rt by up to 100%, but only to increase it by less than 1%. And the combined effect on transmission of all interventions (right hand panel) can only vary between –100% and + 5%. However, since the trajectory of the deaths data is, on their assumptions, bound to result in all interventions combined being found to strongly reduce transmission, the +5% limit is of no real consequence.
Fig. 2. Reproduction of the upper panels of Flaxman et al. Supplementary Fig. 3: Cumulative distribution function F(x) of the prior for one intervention’s multiplicative effect x (= e–α) on transmission (left) or for the effect of all interventions combined (= e–Σα) (right).
On the face of it, the combined effect of the six-dimensional joint alpha prior distribution looks fairly uniform over the range in which the estimated reduction in Rt could fall; it assigns a similar probability to a reduction in the range 40% to 50% and in the range 80% to 90%, for example. However, that only looks at one aspect of the six-dimensional prior distribution.
If I take the sum of the six alphas to be 1.75 (the median sum from their posterior draws) and set them to be all equal, at 1.75/6, their joint prior probability density is 0.0023. But if I set one of the alpha values to 1.70 and the remaining five to 0.01, giving the same overall reduction in transmission, the prior probability density is 64.3. That means their prior distribution assigns a 28,000 times higher prior probability assumption to this case, where one type of intervention has a completely dominating effect relative to all the others, than to a case where the same overall reduction in transmission is caused equally by all types of intervention. The reason is that the offset-gamma distribution used assigns a strongly increasing probability density as an alpha value decreases towards −0.008, its lowest permitted level, favouring cases where the effect of all but one or two NPIs is estimated to be almost zero.
So it is unsurprising that they found a single intervention to be totally dominant.
The median individual alpha values in their 2,000 archived posterior draws are −0.007, −0.007, −0.007, −0.007, 1.699 and −0.006. So all interventions except lockdown were estimated to have a completely negligible effect.
The median ratio, across their own posterior draws for alpha, of the actual prior probability to what it would have been if in each draw the total effect of the intervention had been spread evenly across them, was in fact 392 billion to one!
It is not clear that the authors realised that the prior distribution they used very strongly favoured finding that most interventions had a negligible effect, and I very much doubt that any of the peer reviewers appreciated that this was the case.
The Sweden problem
Using the code and data accompanying the Nature paper as is, except with the 8,000 draws split between 4 not 5 chains to better match my computer, I can accurately replicate Flaxman et al.’s findings, with lockdown accounting for almost the entire reduction in Rt (Figure 3).
Fig. 3. Effect of interventions on Rt in the base case, with all aspects of the model as per the original version (that archived for the Nature paper). The red First intervention estimate includes the effect of the synthetic first intervention NPI and so only applies for countries where the NPI concerned was the first to be implemented; it should be ignored in all other cases. Mean relative percentage reduction in Rt is shown for each NPI (filled circle) together with the 95% posterior credible intervals (line). If 100% reduction is achieved, Rt = 0 and there is no more transmission of COVID-19.
Sweden did not have a lockdown, but it still had a large reduction in Rt, albeit one not quite as large as the average for other countries. So how did the model account for that? This is where the country specific factors, which are treated as occurring on the date of the last actual intervention and in effect are an addition to its alpha, come in.
The country specific factors are given an apparently small influence, being zero-mean normally distributed with a standard deviation that is itself zero mean normal+ distributed[7] with a standard deviation of 0.2. But for Sweden a value of 1.27, in the far tail of the resulting distribution, was inferred. The probability of such a large country factor arising by chance appears to be about 1 in 2,000. That in itself implies that their model does not adequately represent reality.
Using a less informative prior
I investigated use of a prior distribution for the six alpha parameters that was essentially flat over the alpha parameter range relevant for NPI, both for each parameter separately and for the six-dimensional joint alpha parameter. For technical reasons, rather than using a uniform distribution I chose an independent zero mean normal distribution with a standard deviation of 10 as the prior distribution for each parameter. I hereafter refer to this as the ‘flat prior distribution’, even though it is not quite flat over the parameter range of interest (approximately 0 to 2).
I then ran the model using the same assumptions, but using the flat prior distribution rather than the original offset-gamma prior distribution. Doing so should eliminate the previous strong bias towards finding that most interventions had almost no effect.
The resulting estimates of the effect of each intervention were as shown in Figure 4. The estimated effects of NPI other than lockdown all increase markedly from their near zero values when using the original prior, but the contribution of lockdown remains dominant.
Fig. 4. Effect of interventions on Rt : as in Fig. 3, but with the flat prior distribution for alpha substituted for the offset-gamma prior distribution in the original model..
The country specific factor for Sweden was slightly less high than before, at 1.12. The probability of such a large country factor arising by chance appears to be about 1 in 900; still minute.
So, even when using the flat prior, the Flaxman et al. model does not adequately fit reality. The problem is that, as it still estimates lockdown to account for the vast bulk of the total reduction in Rt, it cannot adequately account for the reduction in Rt that occurred in Sweden, where there was no lockdown.
Why Flaxman et al. found lockdown was the intervention that dominated the reduction in COVID-19 transmission
I have explained why it to be expected, given Flaxman et al.’s choice of prior distribution for the effect of interventions on the transmission of COVID-19, that a single type of intervention (or at most two types) would account for the vast bulk of the reduction in Rt. But why lockdown?
The key here seems to be that lockdown was, other than in Sweden, on average imposed at a point in time that, allowing for the assumed probabilistic delay between infection and death, would result in deaths peaking at about the time that they actually peaked. Also, the timing of lockdown, relative to the peak in recorded deaths, differed slightly less between countries that locked-down than was the case for most other interventions.
Flaxman et al. took probabilistic estimates of the delay from infection to symptoms appearing and from symptoms appearing until death, with assumed mean values of 5.1 and 17.8 days respectively, and added them to obtain the infection to death delay values. The 5.1 day delay from infection to onset of symptoms seems reasonable. But the 17.8 days mean from onset of symptoms until death looks as if it may be on the short side for European countries. Ideally, a separate onset of symptoms to death delay distribution would have been estimated for each country. However, the authors may well have been unable to find suitable European data. They actually used a value estimated by Verity et al.[8] (also members of the Imperial College COVID-19 modelling team) from just 24 cases in mainland China.
One of the peer reviewers suggested that the value Flaxman et al. were using for the delay from onset of symptoms until death of (in the originally-submitted manuscript[9] being reviewed)18.8 days, not 17.8 days, was rather short, writing:
it is smaller than preliminary estimates available from hospitalization data in Europe (about 5-6 days from onset to hospitalization, at least 2 weeks in the hospital)
I therefore increased the average delay from onset of symptoms to death slightly.
I also took the opportunity to correct the dates used in the model inputs for school/university closure in Sweden and for self-isolation in Spain to those given in Flaxman et al. Extended Data Figure 4, which agree to those in their Supplementary Table 2.
I found that adding 3 days to the infection to death delay, bringing the average onset of symptoms to death delay to ~21 days (median 19.6 days) – which is fully consistent with the peer reviewer’s comment – was adequate to reduce the problem of Sweden needing a very large country-specific factor. That factor was then estimated at ~0.4, to match the reduction in transmission in Sweden – still over twice as large as for any other country, but no longer statistically-inconsistent with their assumptions.
The resulting estimated effectiveness of the various interventions, using the authors’ original prior distribution for alpha, is shown in Figure 5.
Fig. 5. Effect of interventions on Rt : as in Fig. 3 (original prior) but with the infection to death delay increased by 3 days, and one intervention date corrected for each of Spain and Sweden (see text).
School closure is now found to have a slightly stronger effect on transmission than lockdown. This may seem rather unlikely in reality, but the model has no information to go on regarding the likely relative strengths of each type of intervention – it just knows when they were implemented in each country. Other interventions are found to have almost zero mean effect, as is to be expected given the nature of the original prior distribution.
Using instead the flat prior gives slightly different estimates of the effectiveness of the various interventions (Figure 6), with school closure not having quite as strong an effect as when using the original prior. The effects of social distancing, and to a slightly lesser extent public events ban and self isolation (one of which is generally the first intervention, so the red line applies to it), all cease to be negligible.
Fig. 6. Effect of interventions on Rt : as in Fig. 5, with the infection to death delay increased by 3 days, but using the flat prior distribution instead of the original prior distribution.
If the infection to death delay is increased by 5 rather than 3 days from Flaxman et al.’s assumed probabilistic magnitude – arguably still as reasonable as Flaxman et al.’s assumption – and the original prior used, the changes in the relative effectiveness of different interventions become even more marked (Figure 7). Lockdown is now estimated to have far less effect than school closure, while social distancing now has a significant effect. The country-specific factor for Sweden becomes small.
Fig. 7. Effect of interventions on Rt : as in Fig. 5 (original prior) but with the infection to death delay increased by 5 days not 3 days.
When the flat prior is used instead, the estimated effect of school closure reduces while that of all other interventions increases (Figure 8).
Fig. 8. Effect of interventions on Rt : as in Fig. 6 (flat prior) but with the infection to death delay increased by 5 days not 3 days.
Finally, I investigated the effects of phasing in certain of the interventions. Flaxman et al.’s assumption that all interventions immediately have their full effect on their date of implementation is questionable. It may not be too unrealistic for closing schools, banning public events and decreeing a lockdown, all of which it is feasible to enforce. However, responses to self isolation advice and social distancing encouragement (which both generally preceded a lockdown) are more within the discretion of the individuals concerned, and very arguably would take a little time to reach their final strength.
I examined phasing in over four days the effects of just those two NPIs, with their strength increasing evenly from 25% on the date of implementation to 100% three days later. The result, using the original prior distribution for alpha and making a ~3 day increase in the delay from symptoms to death, is shown in Figure 9. The strength of the reduction in transmission attributed to lockdown reduces slightly compared with the no phase-in case, while than attributed to social distancing increases.
Fig. 9. Effect of interventions on Rt : as in Fig. 5 (original prior), but with the effects of self isolation and social distancing phased in over 4 days and the infection to death delay increased by 3.2 days.
Finally, I repeated this experiment using the flat prior (Figure 10). The strength of the reduction in transmission attributed to lockdown reduces noticeably compared with the no phase-in case, although it is still larger than that of school closure (the estimated effect of which reduces only marginally), while the estimated effects of banning public events and (particularly) social distancing increase markedly.
Fig.10. Effect of interventions on Rt : as in Fig. 6 (flat prior), but with the effects of self isolation and social distancing phased in over 4 days and the infection to death delay increased by 3.2 days.
Conclusions
First and foremost, the failure of Flaxman et al.’s model to consider other possible causes apart from NPI of the large reductions in COVID-19 transmission that have occurred makes it conclusions as to the overall effect of NPI unscientific and unsupportable. That is because the model is bound to find that NPI together account for the entire reduction in transmission that has evidently occurred.
Secondly, their finding that almost all the large reductions in transmission that the model infers occurred were due to lockdowns, with other interventions having almost no effect, has been shown to be unsupportable, for two reasons:
- the prior distribution that they used for the strength of NPI effects is hugely biased towards finding that most interventions had essentially zero effect on transmission, with almost the entire reduction being caused by just one or two NPI.
- the relative strength of different interventions inferred by the model is extremely sensitive to the assumptions made regarding the average delay from infection to death, and to a lesser extent to whether self isolation and social distancing are taken to exert their full strength immediately upon implementation or are phased in over a few days.
It seems likely that the inferred relative strengths of the various NPIs are also highly sensitive to other assumptions made by Flaxman et al., and to structural features of their model. For instance, their assumption that the effect of different interventions on transmission is multiplicative rather than additive will have affected the estimated relative strengths of different types of NPI, maybe substantially so. The basic problem is that simply knowing the dates of implementation of the various NPI in each country does not provide sufficient information to enable robust estimation of their relative effects on transmission, given the many sources of uncertainty and the differences in multiple regards between the various countries.
Nicholas Lewis
[1] Flaxman, S., Mishra, S., Gandy, A. et al. Estimating the effects of non-pharmaceutical interventions on COVID-19 in Europe. Nature (2020). https://doi.org/10.1038/s41586-020-2405-7
[2] Denmark, Italy, Germany, Spain, United Kingdom, France, Norway, Belgium, Austria, Sweden and Switzerland.
[3] The seeding continues for 6 days, with the average number of seed infections per day being inferred by the model.
[4] The numbering of interventions used in their code is 1. school (and/or university) closure ordered; 2. case-based self isolation mandated; 3. public events banned; 4. first intervention; 5. lockdown ordered; and 6. social distancing encouraged.
[5] In mathematical notation, exp[-(alpha[1] + alpha[2] + alpha[3] + alpha[4] + alpha[5] + alpha[6])] is written e–Σα.
[6] The alpha distributions are defined by αi ~ Gamma( shape=1/6, scale=1) − loge(1.05)/6. Hence alpha can range between −loge(1.05)/6 (approximately −0.008) and plus infinity.
[7] “Normal+” means a normal distribution with the negative part of the distribution excluded.
[8] Verity R, Okell LC, Dorigatti I, et al. Estimates of the severity of COVID-19 disease. medRxiv 13 March 2020; https://www.medrxiv.org/content/10.1101/2020.03.09.20033357v1.
[9] The original Flaxman et al. manuscript was submitted on 30 March 2020, the same date as Imperial College published “Report 13: Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries.”, by the same (or almost the same) authors: https://spiral.imperial.ac.uk/bitstream/10044/1/77731/9/2020-03-30-COVID19-Report-13.pdf . From the referencing of comments in the Nature peer review file, it appears that the original Flaxman et al. manuscript was almost identical to Report 13.
Originally posted here, where a pdf copy is also available
My statistics is a bit rusty, but I believe I understand one term quite clearly: “posterior draws.” This appears to indicate the source of the subject paper’s results.
There’s one aspect of all this which appears to have been missed (or maybe it wasn’t and I missed it): When it first hits, the virus spreads relatively quickly, so without intervention a chart of infections would show a rapid increase followed by a less rapid decline with a long tail (maybe an infinite tail, like flu). The higher the chart rises, the more likely a government is to be pressured into introducing protective measures. Because the initial upsurge is rapid, the probability is that the strongest protective measures will be introduced near the peak of the natural curve. That means that the protective measures are very likely to be followed by a drop in infections, regardless of whether the measures are effective.
Now I’m not saying that the measures were ineffective, and in fact I think it’s very clear (eg. Aus, NZ) that they can be very effective, but it is incredibly easy to misread the statistics (especially when the stats are atrociously unreliable as they are with this virus). I find Nic Lewis’ analysis very interesting and pretty convincing. I suspect that Sweden is one of the key countries in unravelling the issue.
Good points, Mike.
It is amazing to me that people are analyzing this pandemic as if it were over. If the “herd immunity” concept has any validity, we have just barely begun. I have seen percentages for herd immunity from about 20% (which if I remember correctly, was from Nic Lewis) to 80%. Let’s assume Nic’s 20% is correct. That means we need 200,000 cases per million population to reach herd immunity.
Looking at the worldometer data, Qatar, with a population of 2.8 million, leads all nations in cases/million with 31,904. Only a few other countries have 5 digit cases/million. The US? 7,320. The UK? 4,511. This pandemic
has barely begun!
SARS-CoV (aka SARS) only registered about 8000 cases and 800 deaths globally in 02/03. SARS-CoV-2 is obviously more infectious, but the point is that these diseases die out naturally and don’t necessary infect everyone they could for a variety of reasons.
Something like 80% of people exposed to SARS-CoV-2 never develop any symptoms, perhaps because of immunity gained from exposure to other corona viruses. We still do not know a lot.
The biggest problem with models is people believing in them without realising what has been left out. In the COVID-19 case, the predator-prey relationship has been ignored. The people killed by the virus mostly are elderly with end of life conditions. Allowing the virus to spread too quickly would have overloaded health systems with adverse effects when the right equipment and protective measures were not in place. Allowing the virus to spread after that amongst the younger generations while isolating the vulnerable would have provided herd immunity and much better outcomes. We must not forget that applying the precautionary principle is for the benefit of those making that decision, not for the benefit of the people affected by it.
The same has happened with the ‘climate change’ idea. Modellers going off half-cocked about things they don’t understand. We could call it bureaucratic bungling based on ‘expert advice’ that is seriously flawed but presented and relied on as gospel. Who is to blame for accepting and implementing it?
How many people did the Lockdown kill? We know how many people COVID-19 kills because we can test for it. We will have to wait and see the Excess Death Count to determine how many people the Lockdown killed. We must subtract the scientifically verified Coronavirus deaths from the Excess Death Count, (it’s not a Coronavirus death unless it can be scientifically verified), and we’ll know how many people died from complications arising from the Lockdown. The Excess Death count is the key to understanding Lockdown Deaths. In the end, I wonder which will be higher.
Am I joking or am I being serious? The answer is YES.
Many people who die from the lockdown will be dying a year or even two from now due to delayed cancer diagnosis and interventions. It will be impossible to filter out.
The trouble is many deaths have been attributed to COVID-19 even though the cause was very likely something else (Comorbidity issues but not recorded). A death of a young man here in Australia a few weeks back, in his 30’s IIRC, was attributed to COVID-19, announced in the media but when it was discovered it wasn’t the cause there was very little coverage and retraction. The scare continued. His death will still be attributed to COVID-19. So the data are already contaminated with bad information.
IMO, knowing all the predictions and computer models, Bayesian modelling and statistics and processes we will never know the real truth. Draconian laws will still remain however.
Canada even forbid autopsies of Covid deaths and even suspect deaths!
This is really middle age medical thinking. We aren’t in the era of enlightenment anymore.
A point that (at least to me) seems to be missed, is that all projections are based on all viruses acting the same.
According to Medical News Today, COVID-19 is a variant of the Southeast Asia Respiratory Syndrome, or SARS-CoV-2, which visited us in 2002 and was either “contained” or mysteriously disappeared before a vaccine could be developed. Although its reproductive rate was apparently around 1, I have trouble believing that the world was able to contain a virus that visited over 30 countries.
I am reading more reports that COVID-19 seems to be mutating to a less infectious and less deadly form of the virus. Too early to tell but worth noting.
On April 18, Professor Yitzhak Ben Israel of Tel Aviv University put out a paper that forecast COVID-19 would be self limiting.
https://www.medvin.me/wp-content/uploads/2020/04/Corona-declinedocx1904.pdf
My city just instituted mandatory face masks (of the woven-fabric sort) for all residents in public, within the city limits, and further requires all businesses to enforce the rule, in order to stay open.
I’m thinking of making a mask out of one of those mesh fruit bags in which lemons are packaged at grocery stores.
In the UK most public malls etc are installing one-way paths for people to follow along with distance markers. These malls are equiped with hand sanitisers, wardens to instruct people where to go and count numbers. Seats are being removed. Plastic barriers are setup at all PoS terminals. Operators have to wear masks and gloves. The UK is considering dropping their social distance from 2m to 1m. That’s what I can recall off the top of my head. But what is even more draconian, pubs will open from July 4th but for anyone to go in for a drink you will have to register with authorities first.
The figure of 3 million seems plausible given the size of the population involved and fatality rate of
COVID-19. The 11 countries looked at have a combined population of about 200 million and the current fatality rate of COVID-19 is around 5% so even if you assume that 50% of the population were to catch it
and the final fatality rate was 2.5% then that would be about 2.5 million. A 2.5% fatality rate would make
COVID-19 about as lethal as the Spanish Flu, while for comparison the black death killed between 30 and 50% of Europe’s population and measles had about a 90% fatality rate when introduced into the New World.
But we are arguing about counter-factuals here. So I suspect that any attempt to be more precise is not really worth the effort. The estimate of Flaxman et al. seem to be in the right ballpark even if you want to quibble about the precise details. At the end of the day even a small fraction of a large number (e.g. the population of Europe) is still a big number (i.e. over one million).
Sweden and Japan should have been MULTIPLES of the top four:
Statista: Covid deaths per million
#1 Belgium: 848.88
#2 UK: 641.41
#3 Spain: 606.20
#4 Italy: 573.49
#5 Sweden: 502.99
#84 Japan: 7.55
https://www.statista.com/statistics/1104709/coronavirus-deaths-worldwide-per-million-inhabitants/
Wikipedia: COVID-19 pandemic in Sweden
Sweden has not imposed a lockdown, unlike many other countries, and kept large parts of its society open…
The Swedish constitution prohibits ministerial rule – politicians overruling the advice from its agencies is extremely unusual in Sweden – and mandates that the relevant government body, in this case an expert agency – the Public Health Agency – must initiate all actions to prevent the virus in accordance with Swedish law…
‘Japan model’ has beaten coronavirus, Shinzo Abe declares …
Financial Times – 25 May 2020
Japan’s constitution prohibits a compulsory lockdown…
Japan model? I don’t think that is the case based on what I know about Japanese. It’s just their culture, very clean, regimented, respectful and distant, ie, no shaking of hands, hugging and greeting in public/work places. Plenty of ideally spaced bowing. As well as wearing masks in public during times like this, same as South Korea.
Eating habits in Japan may also have an impact.
As some have pointed out, it may be important what vitamins you get on a daily bases.
Mark Twain said there are three types of Lies. “Lies, Damned lies and statistics”. Which of those this is you decide.
In the end all the number we have compiled on COVID infections and death are worthless, there was no one standard applied all over. Ad in not random testing to judge how and were the infection was and progressing all we have it to look back in the next few years and see how COVID-19 effected the overall death rate for the year. If I was a betting man it won’t show up in a five year running average since it mostly killed those soon to die anyway. That a cold way to look at it but I don’t think I will be wrong. The worse part of this whole thing in five years there a better than even chance I won’t be here. At my age you take one year at a time, the reality hit you when you spouse sibling die and when you siblings spouses die, let alone the number of dead classmate and friend start counting up.
Well done Nic.
All project should have someone of Nics calibre attached.
Since that is not going to happen anytime soon perhaps Nic and other can develop a stats checklist or flowchart. Each research project could use it, journals could use it.
It would filter out a lot of dross.
Until they explain why the flu and corona naturally stops when it’s warmer (like Trump said), they don’t have ANYTHING.
If you can’t explain the warming pre WWII, the pause, and other natural changes, you don’t have a “model”. You have a USELESS computer game.
By far and away the most effective tool was/is border controls. Taiwan proves that. The second most effective is speed and reliability of testing. Again Taiwan proves that. The third most important factor is speed and efficiency of contact tracing – again see Taiwan.
Do these three things and nothing else is needed.
The only question now is – why does the World Health Organisation still exist. They failed so miserably that they do not deserve to exist. They could have saved the world from a year or more of misery by doing the right thing but they actually opposed it.
Germany stands out in Europe – why? – border controls. Germany closed borders to neighbours mid March. The UK is only now attempting partial border controls – just hopeless. Why would Sweden’s neighbours open their borders to that plague infected state after they put in the effort to rid themselves of it.
Australian States have had border controls in place since March and are not yet open. Western Australia had internal borders to protect indigenous communities and the high value export ports in the northwest.
“Far right” Marine Le Pen was widely ridiculed for advocating for border control against the spread of that coronavirus. The sound byte was “viruses don’t have passports“; it was repeated ad nauseam in February and March in France.
But now apparently viruses have passports, or a link was found between people travelling and virus spread.
The “far right” is allegedly the party of stupid people, yet a remarkably inane slogan was used as the basis of health policy for months and defended by all the pretend “elites” and “intellectuals” like Christine Lagarde.
We really really must do something with the concept of “elites” and “intellectuals”.
Rick Will is spot on
I have just checked twenty nations-the Western lot comprising 9 in Europe and the US against the Eastern lot comprising 8 Asian plus Australia and New Zealand Running down the calendar starting 31 December 2019 to 1 Feb the Eastern lot had all implemented some form of border controls such as testing and quarantining or banning travellers from highly infected nations etc
Their mean death rate per million from Covid 19 on June 9 was 2.9
The Western nations started their border controls from 10 to 31 March
Their mean death rate was 463 per million
Yet when it came to lockdowns the Western nations acted in early March, but the eastern nations acted mostly late in Mach with three of them Taiwan, Hong Kong and South Korea having no forms of lockdown at all and Taiwan and Vietnam having only rudimentary forms
So Rick was right Quick application of border controls although certainly costly beats even far more costly lockdowns hands down
I think that the lockdown did not stop the virus in the UK. The death data indicates that there was an existing exponential decay in the rate of increase of the virus leading up to the lockdown. This trend was due to reach R=1 for people infected at the time of the lockdown.
A logarithmic graph of the number of people dying each day divided by the number of people a few days earlier gives the R number to the power of something (depending on the average time to infect people and the number of days chosen). This graph decreases as a straight line, indicating exponential decay, and it does it well before the lockdown could have an effect. It reaches 1 about the point when the people who are infected at the date of the lockdown have the highest death rate. This is just the continuation of an existing trend. 1 to the power of anything is still 1 so at this point, infections have levelled off and R=1.
If there was a step change in the number of infections due to the lockdown (going from R=3 to R= 0.8) then the graph of daily deaths would be different- it would be peakier. The graph of ratios of daily deaths, described above, would be level and then have a rapid change to a lower level. This is not what happened.
I did this with ONS death data. Sorry, I don’t know how to load up the graph.
Lockdowns. Face masks. Social distancing.
We’ve got it ALL wrong. What we should have instituted was a mandate requiring all residents of the US to carry a rabbit’s foot during the day and to hang a dream catcher in their bedrooms at night.
If we had done this from the beginning, then we would have seen a definite decline in COVID-19 cases over the months, and that would have proven the effectiveness of these measures.
What’s the source of the minimum two weeks hospital stay before death? In NYC the death curve lags the admission curve by 5 days. In England it’s 6 days. The report ‘Characteristics of COVID-19 patients dying in Italy’ https://www.epicentro.iss.it/en/coronavirus/sars-cov-2-analysis-of-deaths found average 10 days between symptoms and death. These all suggest the average hospital stay before death is 5-6 days not 17-21 days. This is a huge difference on a key data point. Why?
1. To date there are less than 10,000,000 Million Cases and less than 500,000 Deaths confirmed.
2. There are no graphs of either Deaths or Hospitalizations that show a Significant drop in the number of Cases or Deaths with the implementation of a lockdown, OR an increase after the lockdown.
3 Countries and/or states boarding each other that had a lockdown showed no significent reduction in Cases per million or Deaths per million of boarding states that had free access or limited access between states.
4. Countries that had lockdowns showed a lower peak in cases per million and deaths per million, but it appears the tail of the curve is stretching out longer.
5. The three million number seems absurd beyond all credibility. That is 1/3 of all confirmed cases, 30% the death rate per million is not even that high!
6. Ridiculous
In France, the death rate was normal until the lockdown and jumped after.
(Of course it may be that the lockdown was implemented when it became clear that the hospitalization rate was such that the death rate was going to jump.)
Some proxy evidence:
We are now in the flu and cold season in NZ. The incidence of colds and flu being reported by health centres is down around 70% from the annual average for this date. Lockdowns work in the short-term.
We had a stringent lockdown which was generally well maintained. Historically, viral infections come over the border each year. Now that lockdown is over, will our flu and colds increase? IMO, yes and covid cases too.
As for the real social cost: that’s still coming
Completely weirded out, I have no idea what else to do except link to the only data that is/are reliable (clean) so can be compared with previous years……mortality from all causes:
‘The Basic Research Question. “Did countries show an alarming excess in total deaths during the ‘Corona’ period of March to May 2020?“
The Answer: Alarming excess? No. Nowhere. Any excess? Some places. In a review of twenty-four countries in Europe, we see no mortality-excess outside the normal range in six countries; mild excess in eleven countries; and significant spikes in seven countries. In only two or three (of the latter seven) will the full magnitude of the mortality-excess double that of their own late-2010s flu spikes, with the impact softer on a longer time horizon (see the final summary section for list of countries by how much the Corona-associated excess compares to their own 2010s flu spike excesses).
Of those countries with mortality excesses, many have entered below-average mortality following the end of their spikes. I expect this will continue and will be seen in every country that showed a spike, given the age-condition profiles of those who died in this flu wave (over 80 and in poor health). I will update this post July 2 and would expect to see countries that had significant excess-mortality (especially Sweden) to show below-average mortality for June.’
‘What I want to say here is that the exhaustive data I have presented here, collected after the end of the epidemic — i.e., on the far side of the “spikes,” if any, in every country in the dataset — was already foreseeable, in outline form, in March based on the early data and epidemiological expertise, at least to those who knew what they were looking for. It was clear from observed-data by no later than April 1, and was no longer disputable by mid-April; nothing like the projections of doom by the pro-Panic side was going to happen.’
https://hailtoyou.wordpress.com/2020/06/16/against-the-corona-panic-part-xiv-total-mortality-data-in-europe-now-confirms-the-wuhan-coronavirus-was-comparable-in-magnitude-to-flu-waves-of-the-2010s-the-panic-and-lockdowns-are-fully-discredit/
The only reason that I can think of for the persistence and prevalence of wrongheadedness is political….Oh! It’s a U.S. presidential election year……You know the rest……
Here is what an experienced health professional makes of the situation in Britain:
”I would not want to be misinterpreted. Because this is a new disease and therefore could potentially affect a large number of people, I believe that it was reasonable to believe at the inception of COVID-19 in the United Kingdom that it constituted a potentially important and serious public health challenge for the Government and other institutions such as the National Health Service.
However, I do not consider, from early on in the epidemic, that it could continue reasonably or rationally to be characterised as a threat out of all proportion to other commonly experienced public health challenges, including the annual contagion of influenza. (In Germany, for example, mortality in the seasonal influenza epidemic of 2017/18 was about 21,500, while to date Covid-19 mortality is less than 9,000.) The alarm raised by the potential for a dangerous epidemic was rapidly replaced by increasing information showing, to informed and unbiased assessment, that the highly probable outcome of the epidemic was well within the envelope experienced in many years of the last quarter-century. At the same time, clear harms from the un-assessed policy of lockdown became apparent very soon after its inception.
This alternative interpretation was suppressed to the extent that the narrative concerning the disease presented on the broadcast media still maintains unchallenged belief in the disproportionate severity of the Covid-19 epidemic, long after this has been untenable in the face of accumulating evidence.
If one studies datasets published by the Office for National Statistics, and calculates all cause mortality for winter/spring for the last 27 years corrected for population for each year, 2019/2020 ranks not first, second or third, but eighth. It is also clear that for several of the last six years there has been lower than usual mortality, meaning that, in the unavoidable cycles of nature, a year of excess mortality should have been expected.
It also turns out that a key early assumption is incorrect, namely that the entire population is vulnerable to the disease. A large proportion of the population (40–60%) show immunological evidence of immune responses to this virus without ever having been exposed to it. This is because as many as one in six respiraIt seems to me that the conceptualisation and contextualisation of the disease, designed to support the official narrative established in the etory infections in a normal winter are caused by other coronaviruses, and, perhaps not entirely surprisingly, these stimulate immune responses that cross-react with the new virus. Yet even now, the broadcast media continue to repeat the initial incorrect assumption, many weeks after something that seemed highly likely from the outset, namely that many of us have some immunity to the disease, has new clear data to support it.
‘I would not want to be misinterpreted. Because this is a new disease and therefore could potentially affect a large number of people, I believe that it was reasonable to believe at the inception of COVID-19 in the United Kingdom that it constituted a potentially important and serious public health challenge for the Government and other institutions such as the National Health Service.
However, I do not consider, from early on in the epidemic, that it could continue reasonably or rationally to be characterised as a threat out of all proportion to other commonly experienced public health challenges, including the annual contagion of influenza. (In Germany, for example, mortality in the seasonal influenza epidemic of 2017/18 was about 21,500, while to date Covid-19 mortality is less than 9,000.) The alarm raised by the potential for a dangerous epidemic was rapidly replaced by increasing information showing, to informed and unbiased assessment, that the highly probable outcome of the epidemic was well within the envelope experienced in many years of the last quarter-century. At the same time, clear harms from the un-assessed policy of lockdown became apparent very soon after its inception.
This alternative interpretation was suppressed to the extent that the narrative concerning the disease presented on the broadcast media still maintains unchallenged belief in the disproportionate severity of the Covid-19 epidemic, long after this has been untenable in the face of accumulating evidence.
If one studies datasets published by the Office for National Statistics, and calculates all cause mortality for winter/spring for the last 27 years corrected for population for each year, 2019/2020 ranks not first, second or third, but eighth. It is also clear that for several of the last six years there has been lower than usual mortality, meaning that, in the unavoidable cycles of nature, a year of excess mortality should have been expected.
It also turns out that a key early assumption is incorrect, namely that the entire population is vulnerable to the disease. A large proportion of the population (40–60%) show immunological evidence of immune responses to this virus without ever having been exposed to it. This is because as many as one in six respiratory infections in a normal winter are caused by other coronaviruses, and, perhaps not entirely surprisingly, these stimulate immune responses that cross-react with the new virus. Yet even now, the broadcast media continue to repeat the initial incorrect assumption, many weeks after something that seemed highly likely from the outset, namely that many of us have some immunity to the disease, has new clear data to support it.
It seems to me that the conceptualisation and contextualisation of the disease, designed to support the official narrative established in the earliest stages of the epidemic, has not been seriously scrutinised or challenged by the broadcast media to date. Particularly in the key months of February, March and April, I believe that this lack of challenge has been a major factor in the formulation of responses which have been inappropriate and caused major collateral damage.’
Dr John Lee, Retired National Health Service Consultant Pathologist
‘It seems to me that the conceptualisation and contextualisation of the disease, designed to support the official narrative established in the earliest stages of the epidemic, has not been seriously scrutinised or challenged by the broadcast media to date.’ Hmmmm…..Oh! It’s a U.S. Presidential election year…….you know the rest……
My apologies for the echo but the overflow hospital here is completely empty….
Ah yes, all-cause mortality — a potential subject for a separate WUWT post. (^_^)
The costs of the lockdowns is much higher in terms of lives lost than the WuFlu. In the video below, a public health doc discusses the known stats for the effects of unemployment in the US. The problem running through this thread is that those who were scared enough to support the lockdown are almost exclusively those whose paycheque was not affected. Now they spend a great deal of time self justifying, and self justifying harder when the data starts to suggest lockdowns were not the best answer. This unfortunately includes a large number of low income workers who are now into the 4th month of government handouts – $2000/month (ie, what they could get working 4 x 35 hour weeks on minimum wage – whats not to like).
Confinement is an arithmetically doomed strategy that, at best, can buy you a handful of days of respite.
Confinement is not meant to eradicate the virus. Confinement is merely meant to slow down the progression of the infection; to “flatten” the curve.
Once you have an infection rate of, say, 2.5 and you know it takes 2 days for an infected individual to infect others, you can work out a progression that gives you 83 million infected in 31 days.
If we assume that we have ordered the population to confine the day we realised we had 1000 individuals infected with a new virus, this means that we sheltered in place around day 12 of the spread of the infection.
Let us now assume that confinement reduces the infection rate from 2.5 to 1.4.
So now, we order the population to shelter in place around day 12 of the spread of the infection. By day 31 therefore, in terms of infections, we will find ourselves where we would have been on day 26 if we did not order the population to confine.
The rationale for confinement was to mitigate the potential medical surge this virus could occasion. As you know, other than in Bergamo, hospital capacity was never strained anywhere in the West. Even in New York where the governor was clamoring for more ventilators and where a military field hospital and a hospital ship were sent to boost bed capacity, the effort went wasted. Ventilators were eventually shipped to other states and the field and ship hospitals were withdrawn.
The fact that surge capacity went unused however, cannot be attributed to confinement.
There are a number of empirical and scientific data that show that confinement was not useful in slowing the contagion.
In a first instance.
As a virus, Covid19 would have been spreading in the population months before anyone noticed we had a new virus on our hands. Thus, the idea that we were able to confine the population on day 12 of the spread is highly improbable.
In a second instance.
Isaac Ben Israel, military scientist, general and ex-politician. He currently serves as the chairman of the Israeli Space Agency and the National Council for Research and Development under the auspices of the Ministry of Science, Technology and Space of Israel – Michael Levitt, biophysicist and a professor of structural biology at Stanford University (Nobel) – John Ioannidis, physician-scientist and writer who has made contributions to evidence-based medicine, epidemiology, and clinical research. Ioannidis studies scientific research itself, meta-research primarily in clinical medicine and the social sciences.
These scientists and others, have cast doubt on the purported infectiousness and mortality rates thus on the usefulness of blanket quarantines.
Also, recent studies in France and Norway lead scientists, researchers and politicians to question the benefit of blanket quarantines.
https://www.revuepolitique.fr/covid-19-ce-que-nous-apprennent-les-statistiques-hospitalieres/
https://www.revuepolitique.fr/covid-19-premier-bilan-de-lepidemie/
https://www.spectator.co.uk/article/norway-health-chief-lockdown-was-not-needed-to-tame-covid
Then we have Sweden of course, where fatalities per 10 million population puts it in 4th or 5th place behind a bunch of other developed countries.
In a third instance.
The progression of the infection and the mortality rate aboard the cruise ships and the war ships, buttress the notion that this virus is not as infectious as previously thought.
There are other things to consider. For example. The vast majority of deaths occurred in nursing homes. Incidentally, this would be a much more worthy debate to be had. Specifically:
1 – Knowing what we know of Corona viruses and knowing what we knew from the experience in China, on what grounds did some politicians take the decision to park Covid19 patients in nursing homes?
2 – Why till today, knowing what we know, there are no official guidelines to quarantine nursing homes and the staff working there?
Covid19 is a real virus.
Take the political context out of it however, and the reality is not as dramatic as it is purported to be.
Blanket quarantines were never a rational response, neither at the medical level nor at the economic level.
Just a note about vaccines.
We have been working on Corona virus vaccines for the best part of 30 years. To date, we have nothing to show for it. Not even at the veterinary level.
For some people to claim that they are 18 months away from producing a vaccine should be treated with great suspicion.
Similarly, for someone to claim that life cannot return to normal till a cure or a vaccine is found, should elicit the same degree of scepticism.