14 ms·
Log-log plot of new vs. total Covid-19 cases by country
- outside1234 7y agoIts crazy how correlated the outbreaks are sort of regardless of policy differences outside of China. So correlated that it also makes you wonder if Japan hasn't been sweeping a lot of cases under the rug trying to salvage the Olympics. It will be interesting from here to see what happens with their cases and if they magically "rejoin the line."
- cptroot 7y agoThere's a nice video about this on the minutephysics channel: https://www.youtube.com/watch?v=54XLXg4fYsc https://www.youtube.com/watch?v=54XLXg4fYsc
- drivers99 7y agoYes! That’s where I saw it, so I started making my own graphs like that for the US states that I and my relatives live in. In excel you have to use a scatter plot and then set both axes to logarithmic. But it doesn’t let you use more than one data series on the same graph. (At least, not in the Mac version which tends to be inferior.) And it’s not animated so I was thinking of throwing something together in Python.
- hn23 7y agoBut are all these graphs comparable? Testing and reporting is not comparable in these countries.
- dredmorbius 7y agoA takeaway is that the underlying epidemiological behaviour is consistent despite significant regional differences in management and monitoring. The accompanying video makes this point explicitly. Do watch it if you've not. https://invidio.us/watch?v=54XLXg4fYsc https://invidio.us/watch?v=54XLXg4fYsc I'd also suggest extreme attention be paid to locations with improbably low case and death reports, or where severity mix and/or mortality are strongly out of line with expectations.
- acqq 7y ago> or where severity mix and/or mortality are strongly out of line with expectations. Yes, that was the only conclusion I was able to make based on Germany's data being so different in the proportion of known cases against reported deaths. Some arguments from there like to explain their results as "superior" hospitals and the "lack of hygiene" as the cause of the results of Italy, Spain, France etc. and I just don't buy it. It seems to me rather a result of a combination of more factors: my explanation at the moment is that they already had more old people in hospitals, and that they had for a lot of such people already "diagnosed" what brought them there, not changing it now when they die. As we see from the user nathell reporting from Poland, they are not the only land with such an idea. It earns them short term prestige for "superior" health system, but it obscures what's going on. If they manage to keep doing this with the newly admitted cases remains at the moment unknown. The real story behind all the graphs, anyway, is not in the numbers which we can see from the statistics of "reported cases" or "deaths", but those that are only to read between the lines, and which are the actual causes for all the measures introduced by all the countries, and that is for the countries at the start: - how far are they from the health system being overflown and for the countries where it progressed: - how many people are without necessary medical care due to the health system not being able to handle, and how many people die due to that. Both of those are something that the countries would rather not directly report. So that's why, from some point on, the only conclusion we will be able to reliably have would be possible if we'd be able to have the actual death statistics (including the cases not claimed to be Covid-19 cases) and compare these statistics with the statistics in the "normal times." All surges are then surely indirectly (due to the disruption of all the country's systems) and directly caused by Covid-19, even if they aren't reported as such. Back to the data we have now, I also find the ft.com graphics the best on the web at the moment. https://www.ft.com/coronavirus-latest https://www.ft.com/coronavirus-latest The log-log graph from this title is only useful post-factum and I don't agree with its current advantages claimed in the video at the moment. It is obscuring the current severe issues in most of the countries: Contrary to the claims of the video, at the moment, most of the countries indeed should look at the charts of log of whatever on the y axis against the linear time on the x axis. With the doubling time of around 3 days, that means that whichever capacities you manage to provide, like hospital beds, or more health workers, whenever you double them, that "advantage" disappears in just three more days. Linear time on x axis is the only sensible choice. The charts should allow us having some idea what the future brings.
- deleted 7y ago[deleted]
- xscott 7y agoI like this chart because it shows when various countries jumped off the trend, presumably heading towards recovery. But I agree, to be useful as a comparison it should be normalized by total population per country in addition to the testing/reporting part that you mentioned. Additionally, it'll also show a second wave, if that starts happening anywhere.
- opium_tea 7y agoSwitch the view so it shows reported deaths (drop down in top right). Those numbers should be more reliable comparable.
- endogui 7y agoWouldn't it make more sense to compare new cases vs active cases? At the end of this plot you can see China's new cases increasing again, but the number of total cases is so large that the x axis doesn't move.
- andreareina 7y agoHard to use active cases since it's not monotonic. If you switch to linear the resurgence becomes more visible.
- deleted 7y ago[deleted]
- dredmorbius 7y agoLog-log of daily growth vs total cases is a neat graphics hack, one I'd not seen before, let alone thought of. FT have been headlining a semi-log plot of deaths per country, normalised to days after the first ten deaths were reported. https://www.ft.com/coronavirus-latest https://www.ft.com/coronavirus-latest Because dead bodies tend to behave characteristically, are inconvenient both directly and via surviving relations, and present a smaller testing target (about 1% of total cases) as well as representing a full course-of-illness endpoint, these data should be generally more reliable and cross-regionally consistent than confirmed cases. Deaths are, however, lagged by about two weeks. FT also provide numerous other graphical representations, including an excellent small-multiples (Tufte fans) matrix of multiple countries' case trajectories. My view is that all serious reporting should lead with similar visualisations. Wikipedia's COVID-19 pages have similarly featured semi-log plots from early on, as does Worldometers. https://en.wikipedia.org/wiki/2019–20_coronavirus_pandemic#Diagrams https://en.wikipedia.org/wiki/2019–20_coronavirus_pandemic#D... https://www.worldometers.info/coronavirus/ https://www.worldometers.info/coronavirus/ (Numerous additional pages with regional and specific behavioural characteristics within both sites.) Anoter data visualiser, allowing arbitrary multi-country comparisons: https://rys.io/covid/ https://rys.io/covid/
- bermanoid 7y agoThis looks like an actual log-log plot, but of new cases vs existing cases. Not a super useful view except to point out that yes, growth rate tends to be proportional to infection count (pure exponential growth) until something majorly changes. A linear plot would tell exactly the same story, just be compressed too far towards the origin to be very readable.
- dredmorbius 7y agoYes, I realised that and edited my comment, apparently before you'd completed yours. The view is useful in that it makes departure from the exponential growth trend blindingly clear. A bit fiddly trying to work out timelines however.
- xscott 7y ago
- jve 7y agoCan zoom on mobile to tick more countries, but can't unzoom if my viewpoint is on the plot:(
- wtcac 7y agoI think we need to stop taking China's numbers as the reality. It's giving us a totally wrong perspective of what has and is going on.
- gandutraveler 7y agoWhy is the growth rate with time faster in every other country except China ?
- anonytrary 7y agoSimple -- because China found the cure. /s
- Retric 7y agoChina had longer for it’s quarantine to show up in the data. Remember, time is not an axis of this graph, just # of new infections vs total infections.
- thecleaner 7y agoSoftware question - what library did you use for the chart ?
- 3xblah 7y agoDid anyone else notice how worldometers.info, which maintains a table listing number of cases, recoveries, deaths, etc. for each country, ordered by number of cases, had China listed first even after USA surpassed it in number of cases. No explanations were given. Then they removed China from the table altogether. What is going on behind the scenes at that website.
- Someone 7y agoI’m not sure what to make of this. “Lots of distributions give you straight-ish lines on a log-log plot” (http://bactra.org/weblog/491.html http://bactra.org/weblog/491.html) so it isn’t surprising that the slopes of the lines are somewhat constant over time. Because taking the logarithm is such an equalizing operator, I also doubt whether it is surprising that lines seem to overlap for each country. Zooming in, there still is a difference of about 20% in new cases/total reported cases between countries, even in the range of 5k-10k total confirmed cases. Taken over the course of multiple days, that can make quite a difference.
- quietbritishjim 7y agoThe graph doesn't make much sense without a bit of explanation. (It certainly didn't to me, anyway.) The minutephysics video linked to from cptroot's comment, and also here [1] for your convenience, does a great job of that. In short, you're right it's not surprising that the lines are log-log linear for uncontrolled growth of the virus, and that it's similar for lot of countries. What's interesting is the few (so far) cases where it drops below that log-log linear line, which indicates a containment strategy that's starting to work. [1] https://www.youtube.com/watch?v=54XLXg4fYsc https://www.youtube.com/watch?v=54XLXg4fYsc
- heavenlyblue 7y agoBut that containment strategy isn't working for Italy at all.
- fxj 7y agoIt takes at least 2 weeks until the number of deaths starts to decrease. Look at the graph in the weeks to come and you will notice the difference.
- heavenlyblue 7y agoThey’ve started containment 9th March, how is that now two weeks ago?
- polote 7y agoTell me why I'm wrong, usually the more a chart is 'perfect' the more the data is 'averaged' and so the less you can actually see what's going on Also this chart is about number of cases, which is not a good way to compare evolution between countries as all countries have different test method
- ferzul 7y agoit's the ratio of new cases to total, which accounts for the comparability. most countries remain comparable with themselves, and those that do change method, since the growth is exponential, it tends to drown out any incomparabilities quickly enough. anyway, the proof is in the pudding. the data isn't smushed to the point of making individual variability invisible
- friendlyghost 7y agoDoes anyone know of a source for hospitalisation numbers by country? I know some states in the USA provide this (https://covidtracking.com/data/ https://covidtracking.com/data/) and some countries in Europe do the same, but I can't find a site that collects all this data. It seems to me that if you want to eliminate the effect of the totally different testing strategies (which moreover vary substantially over time), then hospitalisation numbers are far more indicative of the spread than positive test results. At least in the sense that you can compare them on different days.
- mzs 7y agoI think "influenza-like illness (ILI) and severe acute respiratory infections (SARI)"* numbers would be the best, it would remove testing differences and could be compared to expected numbers from prior years. In the US states send the data to the National Syndromic Surveillance Program (NSSP) but I can't find a public source for the numbers that IL sends. Here are some plots that I make for IL (a state that does not report hospitalizations yet but will likely do so starting some point this week): https://msliczniak.github.io/COVID19IL/plots/index.html https://msliczniak.github.io/COVID19IL/plots/index.html * https://www.who.int/influenza/surveillance_monitoring/ili_sari_surveillance_case_definition/en/ https://www.who.int/influenza/surveillance_monitoring/ili_sa...
- IndrekR 7y agoThere is also explanatory video about that graph on minutephysics Youtube channel: https://youtu.be/54XLXg4fYsc https://youtu.be/54XLXg4fYsc
- jimhefferon 7y agoIs there a good reason, that I am not seeing, why the total population is not relevant?
- PeterisP 7y agoAs far as we know, no country is approaching saturation yet - e.g. if 10% of population has been infected, then that would slow the infection speed just by 10% which would not be noticeable in these scales. The total population will become obviously relevant if, say, 30% or 50% of the country is infected, but that's kind of the worst case scenario that we'd like to avoid.
- theemathas 7y agoWhat happened to Qatar? This one country's plot looks weird after clicking "select all".
- amai 7y agoWhen comparing countries only relative numbers (cases per capita) should bei used. Everything else is misleading.
- mzs 7y agolg(cases/pop) = lg(case) - lg(pop) = lg(case) + C
- jimmyswimmy 7y agoExcellent math. For those who aren't so comfortable with the mathematical notation, the point of this comment was that the log of the cases per capita is the same as the log of just the cases, plus a constant offset. This constant offset is present in the linked chart, but is visually compressed - you don't really notice it that much. So if you look at the chart and see how the lines do/don't line up on top of one another, that's partly due to the constant offset.
- amai 7y agoYou are right if you are just interested in the slope. But most people don't just look at the slope, they look at the numbers and what to know, which country is doing better or worse. And that is when the constant (which is different for each country) matters.
- mzs 7y agolg(1000 * 1000 * 1000) - lg(1000) = 6
- hwillis 7y agoComplete opposite. Arguably better would be to look at local population density, but even that is just a proxy for how easily the virus should spread. Total number is much better than per-capita, because the point is to see how quickly the disease spreads, which it does from a single point. No country is even close to majority infected so weighting by the size of the arbitrary borders enclosing the outbreak is only misleading. What useful information would it convey, when moving the US 4x farther up the line than China? Or Italy? The point is to show how quickly the virus spreads through a population, which it does with great consistency. Per capita doesn't even tell you anything about how effective the response was been, it only tells you how big the country is. Per-capita would de-normalize this data!
- DrNuke 7y agoThe most transparent number is a direct comparison between deaths last year and deaths this year, in the same timespan (eg. Jan 2019 vs Jan 2020, and so on). But there is a lot of gamesmanship at play among nations, both for internal security and external geopolitics reasons, so these numbers are too much too often false after convenient miscalcultation or plain manipulation.
- learnstats2 7y agoDeaths are hardest to hide, so I'd always go with that over the other options - but Intensive Care beds seem to be the most critical stat now.
- azepoi 7y agoThey are harder to hide but will only be known later. Some countries report only hospital death for now. But many die at home and in retirement communities. But it can track growth if the data stay consistent.
- s1artibartfast 7y agoI'm not sure if we will be able to separate the confounding factors such as economic impact at the population level. Do you have an idea how this can be done? I have seen a few studies using this method to look at excess mortality during the great recession [1],[2], but there wasn't a pandemic at the same time. https://www.thelancet.com/journals/lancet/article/PIIS0140-6736(16)00577-8/fulltext https://www.thelancet.com/journals/lancet/article/PIIS0140-6... https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3070776/ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3070776/
- paganel 7y ago> but there wasn't a pandemic at the same time. There certainly was a pandemic, the 2009 H1N1 one. [1] In the last few months I've started to suspect that that was what killed my grandma in July 2010, she died very suddenly because of some respiratory issues (I live in Eastern Europe). [1] https://en.wikipedia.org/wiki/2009_flu_pandemic https://en.wikipedia.org/wiki/2009_flu_pandemic
- Yajirobe 7y agoWait, but if you plot the total number of cases with respect to time on a log-normal scale, you're still going to get a straight line, right? So why is plotting against time a bad idea?
- MereInterest 7y agoIt depends on how you are modeling the data. In a logy plot, an exponential trend y=a * exp(b * x) appears linear, and is easiest to visualize/extrapolate. In a log-log plot, a power law y=a * x^b appears linear instead.
- Yajirobe 7y agoBut since virus spread is exponential, why is plotting the number of cases vs time a bad idea? It would also give us a line plot.
- MereInterest 7y agoIt depends partly on your assumptions, and how you are modeling it. An exponential curve assumes that all members of a population have equal contact with all other members of the population. A power law assumes that there is some social graph that maps into N dimensions, and that infections occur along an N-1 dimensional surface in that space. Either is a valid way to model the infection, and result in different preferred ways to plot the data.
- fxj 7y agoThe plot is function against derivative of function. This is also called a phase space plot which is quite often used in the dynamic systems theory. https://en.wikipedia.org/wiki/Phase_space https://en.wikipedia.org/wiki/Phase_space
- Yajirobe 7y agoThat doesn't answer my question.
- 7y ago
- sorenjan 7y agoThe number of confirmed cases is not really a great value to track, because countries test differently and change tactic after a while. Look at this graph for instance, number of tests per million people vs number of confirmed cases per million people. They're highly correlated, which means the more you test the more confirmed cases you'll have. In some countries it's the opposite, the more cases you'll have seeking medical assistance, the more tests you do. https://ourworldindata.org/grapher/tests-vs-confirmed-cases-covid-19-per-million https://ourworldindata.org/grapher/tests-vs-confirmed-cases-...
- _nalply 7y agoThis is missing one of the most affected countries: Switzerland.
- froj 7y agoAccording to [1] the numbers for Switzerland are about 13k tests and 1.7k cases per million, which would be somewhere below the Faeroe Island. [1] https://www.bag.admin.ch/dam/bag/de/dokumente/mt/k-und-i/aktuelle-ausbrueche-pandemien/2019-nCoV/covid-19-lagebericht.pdf.download.pdf/COVID-19_Epidemiologische_Lage_Schweiz.pdf https://www.bag.admin.ch/dam/bag/de/dokumente/mt/k-und-i/akt...
- bravura 7y agoYou missed the point, that this sampling bias applies equally to the x axis and the y axis in this plot. So this plot allows you to fairly compare growth across different countries, regardless of their testing regime.
- _nalply 7y agoNo, there are two different biases at work and they might not cancel out each other.
- mkl 7y agoUnless I'm missing something, the data for that seems pretty dubious. It says New Zealand has done 120.8 tests per million people, which would be ~4.97*120.8 = 600 tests in total, but NZ has been doing more than double that per day. This data is also 9 days out of date.
- deleted 7y ago[deleted]
- fxj 7y agoThis kind of analysis is also called a phase space plot: the function is plotted against its derivative. And when the function is an exponential growth then the derivative is the same which gives a similar plot for all the different countries. When the function deviates from the exponential like in China you can spot the difference very early in these kind of plots. https://en.wikipedia.org/wiki/Phase_space https://en.wikipedia.org/wiki/Phase_space or for an example: https://en.wikipedia.org/wiki/Duffing_equation https://en.wikipedia.org/wiki/Duffing_equation or in math notation: the governing equation for exponential growth is : y' = ay which is a linear function where the slope is the growth rate. The plot shows y' vs y. This is the straight line in the plot. Any deviations from exponential growth can be easily spotted now.
- jacquesm 7y agoTitle should read 'confirmed Covid-19 cases by country', that makes a very large difference. Those figures are not to be trusted to begin with so any kind of processing you apply to them does not result in graphs that output a picture that you can then draw conclusions from. Each country has their own standards in what is a confirmed case and what isn't and some countries actively discourage accurate reporting.
- 9nGQluzmnq3M 7y agoIt makes a difference in the absolute numbers, but it doesn't really matter for the trends, since each country's testing policy is relatively consistent with itself. In other words, the graph shapes & trends are stil comparable, whether a country's testing captures 1%, 10% or 100% of its cases.
- jacquesm 7y agoIn some countries it will even matter for the trends. There are some countries that actively cook the numbers to make their politicians look good, and where there are very sudden kinks in the graphs you can be sure that the whole story hasn't been told. As or the testing capacity, that's a big factor too and it is non-linear in many places: testing criteria are changed based on how much stock there is of test materials and how much capacity on the machinery. The closer to capacity, the stricter the criteria.
- deleted 7y ago[deleted]
- bagacrap 7y agoThe testing policy in most countries is to increase the number of tests over time. How is that consistent? consistent would be testing a random sample of size n every day without changing n.
- rootusrootus 7y agoIn addition, some places like the US are really a collection of states. The federal government has little to do with testing policy, so it varies considerably by the state. Producing a total for the aggregate United States really blurs things.
- HellDunkel 7y agoThis means absolutly nothing. Please stop making dramatic charts out of pure sensationalism.
- kortex 7y agoLog(dX)/log(X) shows how the outbreak behaves compared to pure exponential growth ( y = x) so any deviation shows how effective a country is at preventing exponential growth. It's super useful.
- HellDunkel 7y agook i may be completly off here but focusing on counting Covit-19 test positives seems rather useless- what we should be focusing on is context. lots of work to be done here. start by comparing deaths with similar cause (flue) from same timespan last year. or even simpler: look at recovered cases. Also: the effects caused by actions by goverments will be barely visible.
- nardi 7y agoPlease add per-capita options!
- jimmyswimmy 7y agoOn a plot of log(cases), per capita is just an offset. It shifts the line up or down on the plot, and doesn't make a difference. In a post upthread, mzs reminds us of the math: log(cases/pop) = log(cases) - log(pop) = log(cases) + C Log plots tend to visually compress relatively small effects such as these, so you don't really notice it, but it is much of why the lines aren't completely on top of one another. In other words - a per-capita plot should look the same, but the lines would be harder to distinguish, because they'd be mostly right on top of one another.
- amai 7y agoYou are assuming people are only interested in the slope. Then the constant doesn't matter. But it does matter when you want to know which country is an infection hot spot or not. A thousand cases in the US is something completely different from a thousand cases in Vatican city.
- pnathan 7y agoI strongly distrust any figures from pretty much any country without a complete and transparent testing regimen - (Hi South Korea, you know what you're doing!). The wide variance of testing protocols, even within countries - is going to kill our ability to really do much with these numbers. I'd be far more interested in _death_ rates. I.e., what was the normal death rate, and what is it now? It's not sexy, it needs to be seasonally adjusted, and it's subject to noise, but it's a much better heuristic than "covid case", because the base number isn't as gameable.
- deleted 7y ago[deleted]
- coding123 7y agoOne plot I was hoping for by now is a back-in-time plot. Something that assumes for each case we find positive today, we assume that person has been polluting the world with covid-19 viruses in an effort to track events and spread based on todays data with the notion that they really caught it 2 weeks ago. The idea is that even if we started social distancing about 7 days ago, we won't see any benefits to that for another 7 days (since the average symptom time is about 2 weeks). And so any spikes you see in these graphs is all of the people that got infected 2 weeks ago, and aren't really sick until right now.
- mensetmanusman 7y agoIf only it was true. All of these articles need to say ‘tested’ and ‘published’ cases. If you aren’t testing randomly, or if you aren’t publishing (China), then the data is really showing the rate of testing of sick people.
- matt_the_bass 7y agoOne thing the I don’t see discussed is imho analysis should not rely on a single plot. Multiple different plots describe different thing. Let’s use “all the plots”
- nojvek 7y agoEven within US (Washington - my state) has way lower numbers than New York even though it was hit first. The first reported case and death weren’t far from where I live. So either Washington has flattened the curve or we’re doing a lot fewer tests than New York. I know a couple of friends who have covid-19 symptoms but haven’t been tested since there aren’t enough kits and they are quarantining themselves at home. So my guess is Washington cases number are at-least 2X higher than what’s reported. Overall at this rate US will hit a million reported cases in a couple of weeks. It seems we are the country doing a great job at testing and reporting but the virus is spreading like wild fires in metros.
- acid__ 7y agoWell, consider the population difference too — NY State has 20M residents to Washington’s 7.5M, which is less than the population of NYC alone. Be wary of comparing raw counts when the underlying population sizes are so different!
- silverdrake11 7y agoI've been working on this which is confirmed cases per state population https://us-covid19-per-capita.net https://us-covid19-per-capita.net It might make more sense if it tracked deaths per state population instead of confirmed cases b/c of the different testing rates.