March of this year coronavirus exploded in Europe, including in Switzerland, hit with over 16,000 cases (nearly 2,000 per million population) by month’s end. Worse yet, new cases were spreading rapidly. The disease was slower to arrive in Sweden, with fewer than 2,000 total cases by the end of March for the whole nation: a mere 190 per million population, less than one tenth the rate seen in Switzerland.
Not only did Sweden have far fewer total cases, they were seeing fewer new cases each day:
Clearly the Swedes, although victim to coronavirus like all of us, were far less stricken than the Swiss. It’s no surprise that Switzerland put serious lockdown measures in place, while the Swedes implemented social distancing but with far less severity than the Swiss. One wonders, how are they doing?
Both countries’ strategies worked; they both put a halt to the rapidly rising epidemic. But Switzerland’s stricter approach worked better. A lot better.
Sweden has managed to hold the epidemic at a steady level, a little over 50 new cases per day per million population. That’s enough to strain the health care system, but not break it. However, they remain on “the brink” at such levels, which leads me to think that recent measures in Sweden to loosen yet more, are ill advised. What they’re doing now only holds the outbreak at bay; loosening will let it escape.
Switzerland, however, have shown the world how to recover after being hard hit by this epidemic. Not only has the rate of new cases dropped as rapidly as could realistically be expected, the Swiss have shown the fortitude and courage to stick with their winning strategy, driving infection rates well below the 50 cases/day/million population level in Sweden. Roles are reversed; with only 5 cases/day/million population, now it’s Switzerland getting new cases at only 1/10th the rate of Sweden.
My conclusions: 1. Social distancing works. 2. Lockdown works better, much better. 3. Doing just enough to prevent crisis levels means the new case load remains at a sustained level which is very costly in human lives, and will not subside.
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The Swedish point of view (with which I do not agree) is that Switzerland is merely delaying the inevitable.
Here in NZ we are now down to < 5 cases per week, with 0 for the last 3 days, and have just reduced restrictions after 7 weeks of a strict lockdown. I am very pleased with the way it has been handled, given our situation in mid-March.
In the US, the state of Montana seems to be a huge success story. Using the John Hopkins data sets, their per capita case load has consitenly been well below the national average, and their new case numbers have been dropping swiftly to nearly none. I wonder if anyone has some insight into why this is? Yes, Montana is a very sparsely populated state, but that doesn’t seem to be the whole story.
I’m not so sure that its sparse population–also correlated with geographic remoteness and rural character–isn’t most of the story.
A rough-and-ready demonstration: consider major-league sports franchises as proxies for wealth, population, and degree of urbanization. Then go to the US page on the Worldometers coronavirus tracker, here:
The table is sortable, so click to sort by cases per million population. Now count how many pro franchises you can think of in the top ten and bottom ten.
Top ten: I count two states without (as far as I can recall) a pro franchise of their own–Connecticut and Rhode Island. Both are well and truly served by franchises in nearby states (notably New York and Boston). Even Maryland has the Orioles and the Ravens.
Bottom ten: Well, Oregon has the Trailblazers, and then there’s the… hmmm. (It is true that Mainers often cheer hard for the Red Sox, though.)
Cattle in Montana in a feedlot get sicker quicker than cattle on the open range, but the open range is often not a barrier forever. It’s travelers from Europe in Feb/March, and Americans forced home in mid March. Where they went is where it bloomed early. Only exception is New Orleans, which was sparked by Mardi Gras. Very little of that filtered out to Montana.
Temperature effect started in April. Much oof the leveling is simply that. We are looking at a subdued seasonal attenuation which will persist until September, and then all hell is likely to break loose. We’ll see.
“Temperature effect started in April.”
Do you think so? I haven’t been so sure, based on the fact that the epidemic seems to be expanding quite happily–though not, of course, for us–around the globe in many different climates simultaneously. Pure hot weather doesn’t seem to be much of a barrier, as far as I can tell–for instance, Saudi Arabia is growing quite rapidly just now despite 100 F highs. Of course, it’s complicated because presumably it’s not just temperature, but how humans respond to temperature.
Can you expand on why you think the temperature explains the decline in growth observed in April, and not (say) various epidemiological countermeasures, which mostly started around mid-March? Not arguing, I’d really like to know. As you point out, any seasonal effect could be quite consequential, and hence of great interest.
A fair number of the people in montana put the anit in antisocial. They live 80 miles from the nearest town and the only drive in once a month or so. Not really optimal as far as rona is concerned. Also the governor is not nearly as insane as one would expect. (As the old bumbersticker says : Montana, at least our cows are sane)
Town once a month sounds pretty optimal to me! :-)
There is far more behind the numbers than a simple examination of the bare statistics can show
What is the policy in both countrys for the treatment of the aged for instance.
If you do not admit the over 80 into ICU you save hospital capacity.
In nz we have managed to halt the virus
..at huge cost to our economy.
I have no issues with this but many do.
I would point out that even if you had done nothing there would have been a huge blow to your economy, because of supply and demand effects from other countries.
Analysis from Spanish flu pandemic seems to show that those cities in the US that came down hard and fast recovered their economic activity more quickly
I would also point to South Korea as having had the best response and would seem to be the way to go just by eyeballing the stats :)
As you say there are many things yet to be analysed
all the best
When much of the western world is crippled with persistent COVID-19, the NZ economy will humming like never before. They’ve made a fantastic investment in their future.
And the best response, and it’s not a horse race, is China’s.
Very neat. Thanks.
I posted a link to this paper preprint under the previous post. It appears to “show” that lockdowns don’t affect the downward trend significantly. If it does, I suspect that is due to the choice of countries to look at (only 4) as this post shows the opposite.
I’ve always felt Sweden’s approach was not likely to get the virus under control. That country is in the top 10 of deaths per capita now (not that deaths alone is a measure of how bad this disease is – it may do permanent damage to multiple organs). Its active case number is still rising, unlike Switzerland’s which has fallen dramatically, by comparison.
I’m generally pleased, like Mark, with the way it was handled in New Zealand though I think we were very lucky early on given the poor crowd control and no screening at the airports. The lockdown had an impact within the standard incubation period – it’s hard to imagine why a lockdown would not have an impact, given the transmission paths are much more limited. I think we are moving through the restriction levels a little too quickly but we may stay lucky. Here’s hoping.
“Inferring change points in the spread of COVID-19 reveals the effectiveness of interventions” (https://science.sciencemag.org/content/early/2020/05/14/science.abb9789)
“Effective containment explains subexponential growth in recent confirmed COVID-19 cases in China” (https://science.sciencemag.org/content/368/6492/742)
The first paper could have been stronger if they used a true counterfactuals approach to establish causation of lockdowns. As it is, they showed a coincidence between downtowns in rates of spreading and German changes.
The second paper illustrates what we can look forward to if COVID-19 finally gets contained. That is not at all the case in the USA and the UK.
Considering the difference in level of testing between countries comparing confirmed cases is nearly pointless. Sweden do far too little testing for those numbers to say much about the spread of the disease, less than half the number of Switzerland. Excess mortality is probably the best way of comparing countries, although data tend to lag.
One must also be careful when trying to determine why some countries succeed better than others, comparing just two countries isn’t enough. There are countries that enforced lockdown that have succeeded and those with even higher mortality than Sweden.
No. That would be true if it were Switzerland were the nation not doing much testing. But if there is a large burden of undetected CO19 cases in Sweden, then that only gives additional force to Tamino’s point.
Detected cases is a bad measure regardless of the direction of the error. If Tamino had mentioned the different level of testing and how it would bias the result it might have been justifiable, but he didn’t. He just used the numbers as if they represented reality.
The main flaw in Tamino’s argument is that he base it only on two selected countries and then decide that the difference between these are just due to lockdown. Look at more countries with different policies and the picture becomes a lot more complex and hard to understand. It’s equally possible to pick two other countries to “prove” that lockdown causes more casualties, look at the link to Brigg’s analysis further down in the comments.
Common sense suggest that a lockdown should reduce spread of Covid, but it’s sloppy science to then cherrypick data in a way that confirms what you thought you knew.
Well if there were a diagnostic or quality check available on case data — or deaths data, for that matter — this could be used to tell if modeling was appropriate.
However it is an exaggeration to say they are useless everywhere. Some governments take such counts very seriously and impose checks, which have been maintained even during these difficult times.
There is a new paper in Science this week which looks at data from Germany and infers that policy measures and changes by their government were effective to modulate viral spread. You can quibble with how they went from change points to arguing about policy. (I would rather they used the Brodersen Causal Impact, available in R to estimate the counterfactual and do the causal inference properly, but this is not relevant to the basic point about data here.)
I have wrestled with these series from many countries. The publicly announced data from China are essentially worthless for any inference. Policy and data collection changes from New York State make them difficult to use. Data from Switzerland, Iceland, and Germany seem sound. I don’t know what to say about U.S. data yet.
Mm. Your points are in the main sensible, but I’m quite certain Tamino, who knows perfectly well what the standards of a peer-reviewed paper look like, would not claim that this blog post was science, properly speaking. (I’d call it an illustrative exercise, myself, FWIW.)
The Briggs ‘analysis’ seems to me much more problematic, in that while it considers many cases–potentially good, in that it would avoid the problem of cherry-picking–it does so apparently with the underlying assumption that the only significant variable is the (binary!) presence or not of something categorized as a “lockdown.”
Some issues OTOMH (and you could likely think of more, I expect):
–Confounding variables (in addition to the testing issue you mentioned): population density, transport patterns, medical capability, governance, ongoing conflict;
–Other response modes exist: intensive contact tracing & individual quarantine, social distancing;
–Recursive causality: countries may suffer more cases due to failure to lock down, but countries may also lock down because they are suffering lots of cases;
–Failure to consider time appropriately: what happened in each given nation following the imposition of lockdown? willie eschenback is horrible at that, assuming on the basis of one poorly-chosen metric that ‘the emergency is over,’ and thereby putting everything in the past, even though the epidemic is still visibly developing.
But then so is Briggs; amongst his ‘pictures’, for example, he’s got one histogram and one scatter-plot, neither of which, of course, considers evolution over time.
Even worse–while I’m talking about Briggs–he appears to be pushing uncertainty, somewhat in the mode of Judy Curry in climate: basically, he muddies the picture as much as possible, like this:
Huh? Sort of a Gish gallop, but less relevant to anything.
Having muddied the picture, apparently to convince us that there is no real explanation as to why outcomes differed, he then slips in the assumption that if lockdowns matter “as much as advertised” then their influence must invariably show up in the bottom-line numbers, and everything else be damned. Uh, no.
What might work would be a comprehensive analysis of lockdowns vs. the evolution of the epidemic in many nations. Attribute changes in growth patterns for each nation separately: what are the contributions from lockdowns, from other behavioral change, from any extraneous factors, and from pure epidemiological saturation? Then compare cases among nations to discern patterns of response. It’d sure be a pain to do, and there would undoubtedly be data availability and reliability issues. But it’s possible you’d end up learning something–an outcome that Brigg’s piece seems to me set up to avoid. And basically, it’s an expansion of Tamino’s approach–vastly expanded and systematized, to be sure, but conceptually the same thing at bottom.
Sweden reported 3674 deaths now.
And 29677 cases. If you account for a delay between infection and death of 20 days as observed in average in other countries, there were 18640 reported cases 20 days ago. This would mean a IFR of nearly 20% if there were no undetected cases in Sweden. For Switzerland the IFR would be 6.5% calculated the same way. Hopefully there were many undetected cases if not the death rate would be horrible high. But if the death rate is similar in both countries the number of undetected cases is much higher in Sweden.
Does Sweden require autopsies for everyone?
Testing rates available here:
We may need another “Does Willis Eschenbach have Any Honor?” blogpost from tamino, given Eschenbach writing this a couple of days ago:
“The virus hardly affects anyone—it has killed a maximum of 0.1% of the population in the very worst-hit locations. One-tenth of one measly percent.”
[ http://archive.is/Iy0Ez#selection-567.0-567.147 ]
With respect to the need for another ““Does Willis Eschenbach have Any Honor?” post, I will merely quote Ian Betteridge’s law of the headline:
“Any headline that ends in a question mark can be answered by the word no”.
A 0.1% death rate would mean over 300000 dead in the US and 7.5 million deaths globally–deaths, not cases. Add to this the mounting evidence that many survivors of the disease suffer significant major organ damage (usually kidneys, but also heart/circulatory, liver and brain), and any sane, decent person would conclude this is not a disease with which to trifle. Eschenbach clearly does not belong to that tiny subclass of humans (sane and decent) but rather to the fundie death cult contingent. The only question is whether his cult worships Supply-Side Jesus or Ayn Rand.
So… 1 tenth of a measly percent… Willis is fine with 330,000 dead in the US?
Also – there are six US counties with greater than 0.2% death rates (as well as regions of other countries like Lombardy) (that’s 0.2% death rates relative to the whole population, despite lockdown, so if lockdown was lifted would be likely to increase again by a factor of two to five). So Willis is not only immoral, he’s wrong.
Here in South Carolina, the worst-hit county is Clarendon, about an hour’s drive from where I live. It’s rural, with a population of ~33,475, and has suffered 31 deaths. That’s basically willie’s 0.1% right there. First, does anyone seriously think that the casualties are going to magically stop today? Second–and more fundamentally–it’s pretty goddam offensive to dismiss those 31 deaths–or the 12 in my county of 65,000–as “measly.” We’ve lost more Americans three months than we lost in the 10 years or so of the Viet Nam war–87,706, as of now. Is that “measly?” The world has lost over 300,000. Is that “measly?” What a–!
OK, then. “What a person, utterly bereft of honor, humanity or decency.”
Yeah. Let’s go with that.
How many times do we need to answer the question in the negative?
Gah. Looked at willie’s post; probably a mistake. I note that the headline, which asserts that the “emergency is past”, is supported only indirectly by a bunch of graphs showing that those jurisdictions have passed a peak in daily *deaths.* From my perspective, that’s the wrong metric; the real “peak”, IMO, is the largest number of active cases.
Willis’s chosen metric has a lot more to do, IMO, with the medical learning curve in dealing with a novel disease than it does with the pure epidemiology. It’s quite clear, given a moment’s thought, that a prolonged period of continued mortality can potentially account for a whole lot more deaths than an initial ‘peak.’ And while Sweden did indeed ‘peak’ by willie’s criterion on May 2, it was only a few days before that mark was once again eclipsed. The current active caseload–20,082–is on the order of 8% higher.
So, no, willie, Sweden has not ‘peaked’–unlike many of the other nations which did do lockdowns, such as Italy or Spain. I’d add that the numbers of daily deaths in Sweden are small enough, and more than erratic enough, that the trend claimed with such an air of authority, is very probably lacking in any statistical significance whatever.
We could have a look at the graph below, in which Sweden is plotted among a lot of other clountries (Belgium, Brazil, France, Germany, Italy, Russia, Spain, UK, USA):
You see Sweden in black, between
– UK (blue) / USA (green) and
– the worst candidates, Brazil ( light green) / Russia (brown).
Sweden has no reason at all to be proud!
The best is that I posted 2 or 3 days ago a comment on Eschenbach’s superguest post at WUWT:
Attention, Citizens! The #COVID19 Emergency Is Over!
containing the link to this chart together with a decent critique of Eschenbach’s fixation on his death per million stats, and an ironic remark about Trump and Johnson.
For the first time since I post there (5 years I guess), the comment simply disappeared. It wasn’t even snipped by Watts or by a moderator…
Maybe that is Watt’s new Trumpy Heartland world… what a poorish behavior.
There was a very short, but interesting interview with the architect of Sweden’s program. He said that it wasn’t about herd immunity or maintaining an open economy, but rather about the lack of Constitutional mandate for the central government to intervene on a massive scale. I think they may come to regret that lack of power. Sweden is so far doing a pretty good job of maintaining the new case load, but they are walking on a knife’s edge, and you could easily see the case load get out of hand. If it did so, it would be very difficult to re-assert control. And then there are all of the survivors–many of whom may be left disabled or infirm.
This ain’t the flu.
Technically that is correct, but if there was unanimous support from the major parties a law allowing lockdown could be implemented and the constitutionality of it debated afterwards, and I have no doubt that if the situation escalate to the point where hospitals are overloaded that is going to happen.
I think that it is more that Anders Tegnell, the expert advising the government, is cautious to implement any drastic measures unless he is certain they will work, and given the lack of firm knowledge of what does work, that means that only limited measures have been taken.
I am really sorry I have jut been using this blog post as an example on comparing statistics on the guardian comments page. I should have asked permission first and I did not think about it. I hope you don’t mind!
I hope you get some more readers for a great blog
Below is the piece. It just made me really angry.
all the best
> The Swedish point of view (with which I do not agree) is that Switzerland is merely delaying the inevitable.
There is some merit to that, but it rests on a few important considerations…among them that there would be no vaccine developed before the fast/short, slow/long approach to infections would equalize, and as well, there would be no therapeutics developed during that longer time frame that would significantly reduce fatality rates.
Also, mixed into this is a simplistic notion that the “lockdowns” have a significant differential negative effect on the economy as opposed to the kind of economic outcomes that Sweden will realize based on its approach. (1) that is a highly dubious assumption, even to the point of determining which direction the effect might go in the long term. In the short term, a comparison of the economic effect of a “lockdown” in Denmark versus a “no lockdown” in Sweden shows no such differential effect and, (2) it’s waaay too early to be drawing any conclusions anyway.
In short, I think that these cross-country comparison are of very limited value. In part, because they fail to control for very important variables, such as hospital capacity, rate of comorbidities among the citizenry, access to healthcare, population density, % of people who live in single-family households, etc. ‘
This NYTimes article touches on some of those factors – and also discusses how the comparison to excess deaths versus deaths per capita might be important to consider.
There’s an elephant in the tent here. The choice is not lockdown and control or no lockdown and deaths and widespread sickness.
Attributing the need for lockdown to SARS-CoV-2 is erroneous. Why we need to resort to a crude public health measure like quarantine is only because Western countries were not ready to deal with a pandemic, whether in finance, robustness of their public health systems, disease surveillance, and robustness and depth of medical care to be able to both handle spikes of patient loads and continue to successfully fund hospitals, doctors, nurses and everyone else who makes that possible.
In brief, the West fell on its face, for the most part, because it was too cheap to adequately provide for the possibility of pandemic. As a consequence, to keep the nightmare away, quarantine was necessary, at the cost of the economy. As I’ve noted elsewhere many times, that sure was a bad bet.
And if we don’t want this to happen again we need to set up the pandemic response measures we’ve been told we need for 20-30 years.
Another statistician begs to differ: https://wmbriggs.com/post/30833/
[Response: My conclusion is that the numerologist to the stars is selling snake oil.]
Well, given that he publishes with Monckton, I’m not an enthusiast.
Wow, now I remember that thread. Dude is all hat, no cattle.
I read there
” Belgium has about as many people as Sweden, 11.5 million, though more spread out. They had 53,449 reported cases and 8,707 reported deaths, or 4,612 and 751 per million respectively, the worst of all countries. ”
Such a comparison hardly could be dumber and shows how useless death per capita / per million statistics can be if you don’t weight them with the countries’ density.
Sweden has 22 inhabs/km², and Belgium… 370.
It’s a bit like comparing Montana with Big Apple.
Infection spread is much less a matter of population than a matter of contacts per area.
Doesn’t that depend upon other factors rather than raw population density? I mean, it could depend upon intensity of personal contact for transacting business and other things, as well as distance. I can’t imagine a more unhealthy place, in this regard, than an auction, for example, whether for general things, or a trading floor.
I don’t know why you think of me reducing such an incredibly complex story to density. I did no more than writing a hint to C. Cadou that solely considering death per capita is a bad idea.
Above the evident phenomenon of density, there are huge factors contributing to case increase, e.g.
– the exclusively profit-oriented ideology in trade and industry, which leads to cheap workers living in hygienically miserable, overcrowded accommodations and infect each other extremely quickly;
– all the idiots like state haters, conspirators, those who refuse to vaccinate, fans of freedom even if it harms others , ultra-rights, etc.
And if all that lands into crowded hospitals with lack of intensive care units, then… you suddenly see in the German news a Brasilian doctorwoman telling us the same as did her colleagues months before in Italy, Spain and France, namely that it is simply horrible when one has to decide who will survive and who won’t.
Reicht es Ihnen, ecoquant?
@Bindidon, possibly out of sequence …
I was merely responding to this paragraph. No doubt those other factors affect things, but those kinds of influences are for the most part quantitatively unobservable. Accordingly, demonstrating that they are significant first means coming up with some good indexes of them and then doing the inference to see if they have greater explanatory power.
I don’t think anyone believes either density or number of economic contacts are the entire story, but both can be measured or at least estimated and, so, assessing their explanatory power is at least possible.
I ask what could be the future of the countries.
Switzerland could, if the cases falls more, came to a state when individual tracking of cases become cheaper, and so and the lock down if the individual tracking can prevent the cases from rising again. Complete eradication of the virus seams possible in a few weeks or months. But then imported cases remain as long as the virus circulates in other countries.
Sweden on the other hand can remain on its state for many years without any progress. And then?
I always have problems with logarithmic plots of cases/deaths per million, and prefer a uniform scaling to percentiles of cases/deaths, imho allowing for a fair comparison:
But… only a professional statistician like Tamino can tell us whether or not the percentile view is really correct. There might be, behind this view, a statistical artifact the layman can’t manage to discern.
What do you think, Tamino?
Not gonna answer, leaving that to Tamino, but I have gotten the same question, too.
The idea to use these percentiles for comparing disparate value ranges came from here
First I think that is a mistake to presume any sort of sincerity from either Eschenbach or Briggs. Both seem to have succumbed to the unofficial motto of the U. of Chicago Economics Department: “Well, that’s fine in practice, but how does it work in theory.”
However, I don’t think that there is any simple metric one could use to differentiate responses to the pandemic. On the one hand, there is little doubt that an effective imposition of isolation will decrease transmission. But the operative word there is effective. Here in the US, we have had many states that have “locked down,” only to see the regulations flouted and watered down to the point where they had little effect. On the other hand, while Sweden did not have a “lockdown,” they have implemented regulations to enforce social distancing. That has been sufficient to keep cases manageable, but it is walking a knife’s edge.
Where they have had effective isolation programs, good testing and contact tracing, they’ve managed to not just flatten the curve, but to turn it over. Countries in this category include Germany, Austria, NZ, S. Korea, Taiwan…
On the other hand, the countries that have fared the worst are those that downplayed the significance of the disease, relied on their isolation or “exceptionalism” for protection and sidelined or hamstringed the experts–with the US at the top, followed by Brazil, Russia, the UK, pretty much the entire Middle East, India, Pakistan. The governmental policies and culture of science denial in these countries have arguably made the outbreak worse there. The US approach has been especially abysmal, driven by stupidity from the top down to the foot soldiers of stupidity at the lockdown protests.
One could argue that the entire goal of the lockdown protests has been to worsen the performance of those states like Michigan that did have an effective response so that the basketcases like TX don’t look quite so bad.
Both seem to have succumbed to the unofficial motto of the U. of Chicago Economics Department: “Well, that’s fine in practice, but how does it work in theory.”
thanks for that Snarkrates, a nice quote which I will steal!!!!!!
what’s amusing is the wholly predictable response from the usual suspect, yet more evidence of crankmagnatism
I live in Florida where the state has had poor practices. On the other hand, many cities or counties have had stronger rules. In addition, the local paper claims that many individuals are social distancing well (I am) even when the authorities have poor rules. How can you quantitate the actions of individuals who are stricter than required? I think it will require a lot of data mining.
Reports in the newspaper claim that the lockdown protests, where few wear masks, might transmit the virus to many new locations. That is the opposite of people self distancing.
Actually, it’s not that difficult. Google receives anonymized tracking information from any cell phone and has used it to tell, for instance, when stores listed on Google Maps are busiest. They have recently turned it into a lockdown compliance reporting instrument and publishes these at least weekly.
See the report for Florida.
See the report for our Massachusetts.
By the way, there are others besides Google, and some of them judge states’ behaviors using international standards.
Unfortunately your data does not convey as optimistic a picture as the newspaper article I read. Perhaps we can hope that if we have seen some improvement with poor compliance with the lockdown we may see better results later with better compliance. On that idea there are more newspaper reports of people disregarding social distancing in the US.
Next year it will be interesting to compare countries with better compliance with those that ignore scientific advice.
That’s from statistician Howard Wainer, CHANCE magazine, a publication of the American Statistical Association. The article was entitled “Defeating Deception: Escaping the Shackles of Truthiness by Learning to Think like a Data Scientist“, 29(1), 2016, 61-64.
Apparently the disregard of social distancing and other management tools is even worse in Brazil than in the US, as Bolsonaro tries to out-Trump Trump himself:
I note, on the other hand, that while managing a 7.9% daily increase in cumulative caseload while standing on the brink of 300k cases is impressively bad, at that juncture the US actually ran 13.2%. So there’s that.
Newspaper pictures from the weekend so far prove beyond doubt that many Americans cannot be expected to social distance on their own. What a disaster!
I have found the data you post to be very interesting and helpful to me. Keep up the good work.
In trying to understand the growth of the cases, it is not enough to look at total cases, or per capita cases. That’s because there seem to be two different initial factors:
1. How many initial cases did a state or country get; and
2. What has been the trajectory of cases since then.
For example, take a country where the trajectory of cases is identical once the pandemic gets going (I’ll say what I mean in a bit). If one of them by bad luck gets ten people infected and the other by good luck gets only one, then even if they both handle the pandemic equally, the one will end up with ten time as many cases as the other. This factor is basically dominated by chance combined with the flow of infected people into the state.
By the “trajectory” I mean the change in the daily number of cases. This has to be standardized in some manner. The two easiest ways are 1) as the fractional daily change in number of cases, or 2) the curve of daily change but normalized to some standard population – basically per capita. In this case, the data should be viewed on a semi-log curve so that the *rates* can be compared. Both ways turn out to show essentially the same thing.
Consistently, across many states (and countries) I have looked at, there is the same pattern: an initial erratic period when initial cases are reported, then often die away. Then there are more instances, and finally the daily curve starts to take off. Sometimes the initial injection of cases is so large that the daily number actually reduces as it settles down.
In this second phase, virtually all states (and most countries) increase their daily cases by close to 30% per day. It’s quite striking how similar they all are. This growth rate seems to correspond to an R0 value of about 3. It’s hard to resist the idea that this is the natural rate of infection of the virus in most countries and states. (I say “most” – I have a set of them that I follow closely; there are exceptions, but fewer than you would think).
After a period of time in this high growth rate, the daily growth curve starts to reduce its slope. In some places, it may start to decline; in others, it may just stay at some fixed but lower rate.
If you shift the curves in time so that they seem to match once the persistent growth starts, most of the trajectories look nearly identical (you need to allow for very noisy data, though!). It is after the curves start to reduce in slope, to flatten off, or even (we hope) decline, that noticeable differences start to show up.
Any attempt to explain differences in, say, per capita cases by invoking population density, sparse communities, etc., needs to be able to explain how it happens that large or small, dense or sparse, almost all places follow the same trajectories at the beginning. In my view, it is probably because a given infected person will, on the average, infect a certain number of people. After all, an an urban or a rural area, a person will deal with family and friends, go to the grocery store, go to the pharmacy and to restaurants just like anyone else. So the initial growth will depend on the number of infected people and not too much on the overall population factors.
” By the “trajectory” I mean the change in the daily number of cases. ”
Do you mean something like this?
The daily cases of all countries were normalised by uniformly scaling them to percentiles (weak colored lines).
The thicker lines are weekly centred running means.
You see on the chart that Sweden (black line) doesn’t look so pretty good as is usually pretended.
When I have some idle time, I’ll update the data below the link.
Data below the link now updated.
Here is the corresponding chart for the ‘percentiled’ death toll increments:
To make charts out of data is a simple matter. But to accurately interpret them isn’t…
Wonder what the charts would look like phase-wise if the starting point was something like the first day 100 deaths (or more) were registered?
In the above comment – sorry for its length! – I forgot to say that the case details such as trajectories all come form John Hopkins time series data:
Sweden is pulling it off:
So far, not bad?
I’d want to know how accurate those anti-body tests were at the end of April. I’d read that such testing was not very accurate and I tend to think that many similar studies seem to have vastly overestimated the number of people affected (partly because I feel that a far higher positivity rate for Covid-19 infection testing would have been warranted). Meanwhile, Sweden’s fatality rate of closed cases (recovered plus dead) is about 40%.
And, muddying the waters more, four states admitted they have been merging numbers of positive PCR tests with antibody tests in their reports of cases. Virginia and Vermont have admitted their mistake and have separated them out again. Texas says it will separate them this week. Georgia, on the other hand, claims the procedure is consistent with CDC guidance and have not intention of separating.
Mixing these up makes it look like the state has done more testing than it actually has, not to mention making variability, specificity, and sensitivity a mess. Also, since antibody tests lag infections by a lot, unwittingly, these processes are making it look like there are more cases in the states, not fewer.
@David B Benson,
Oh yeah, they’re doing great. Not.
Not the conclusion I would draw from that story. Obviously, with more infections come more folks with antibodies; not exactly surprising. Sweden is currently #8 in the world for deaths per capita, and since linear growth appears to be the story in terms of active cases, that ranking is likely to continue to worsen.
Right. this other look at the same story gives a different slant to it. It looks to me like someone didn’t like the 7.3% figure and so made up their own (20%).
“Sweden has managed to hold the epidemic at a steady level, a little over 50 new cases per day per million population. That’s enough to strain the health care system, but not break it. What they’re doing now only holds the outbreak at bay; loosening will let it escape.”
There are so many imponderables to consider.
Tamino and the Swiss put a good case for strict controls to reduce and hopefully eliminate the disease.
New Zealand even better.
But being persnickety as usual I would still like to raise the following points for consideration.
1. Which will be the long term best path for the people and the country.
This does depend on a lot of variables including both vaccines and mutation of the virus.
2. Why the immense differences in both true infection rates and true death rates in different countries to date.
3. What will the depth of penetration be for the population in general and for individual countries specifically.
This is not being touched on but is vitally important for proper use of the statistics as Tamino would possibly agree.
Finally for the statisticians, Testing has both sensitivity and specificity rates and it is amazing [unbelievable actually but great] that so many tests are now being produced in such a short time. However it comes with a kicker.
False positives are an issue.
Not so much in sick people where a high level of correlation is expected and a misdiagnosis is not going to alter the management for people who are severely ill.
But in the issue of general population testing in a resolving situation the likelihood of any positive test being truly positive, Say in New Zealand is highly unlikely.
Would like to comment further on Sweden Switzerland alternatives if possible.
As well as , now meet .
Oh, and the paper describing said is:
J. O. Lloyd-Smith, S. J. Schreiber, P. E. Kopp, & W. M. Getz,
“Superspreading and the effect of individual variation on disease emergence“, Vol 438|17 November 2005|doi:10.1038/nature04153
Essentially the typical number, , infected by an infected person is not
Of course, if you prefer some other expression of rather than , like , that can be dropped in in the former’s place in the above.
It’s often been said, and true, that because this is a novel coronavirus, not much is known, and that remains true, although progress is being made. Still, Lloyd-Smith, et al is from 2005. With antibody-dependent enhancement, we’ve known about these possibilities since 2013. No one is (yet) saying ADE is going on with COVID-19, but it’s a poorly understood immune mechanism and it would have been nice to have known more about it before the novel coronavirus emerged.
Thought I had some new comments up that were both relevant and worthy of comment without exhibiting bias, just outcomes. Writing them made me feel they were important so I had posted them elsewhere as well. If I have made a mistake in posting please let me know and I will attempt to retrieve them and repost here.
Thank you for your article.
There are many different possible outcomes and speculation now is good even if only to look back at later on to re-evaluate why we thought the way we did.