An international comparison of the second derivative of Covid-19 deaths [pdf]

https://www.medrxiv.org/content/10.1101/2020.03.25.20041475v1.full.pdf

by hdivider • 6 years ago

58 54 6 years ago

medrxiv.org

hdivider• 6 years ago

Full title (not possible to put as title because of HN limits):

An international comparison of the second derivative of COVID deaths after implementation of social distancing measures

chipperyman573• 6 years ago

It's been a long time since I took calc. What does the second derivative show us?

lsb• 6 years ago

Acceleration.

The rate of change of the rate of change of deaths.

The word exponential only occurs once in the paper, and the rate of change of an exponential is an exponential, so take as many derivatives as you want and it's still going up. Why they don't take the log of deaths over time isn't explained.

dpwm2• 6 years ago

I've seen very little coverage that really uses the term exponential in a way that suggests those reporting know the implications of that. I've seen one plot with a logarithmic y-axis, and that was in the Guardian some time ago. From it, it appeared a crude heuristic could be drawn that from the point that lockdown is implemented, the cumulative deaths appear to grow between two and three orders of magnitude.

I've been grabbing the data put out by Johns Hopkins [0] for the last few days to update some plots in a very hacky Jupyter notebook.

Crucially, the plots are normalized to (estimated) populations and the y-scale is logarithmic. I've put them on github in case anyone else is interested [1].

[0] https://github.com/CSSEGISandData/COVID-19

[1] https://github.com/dpwm/covid19-analysis/blob/master/Coronav...

edit: Clarified that though exponential growth is widely used, the implications of that are not followed up. It's past my bedtime!

3solarmasses• 6 years ago

yep. My first thought was why the hell they didn't they use the word acceleration for better readability.

babesh• 6 years ago

It's not an exponential. It's a shifted sigmoid.

dboreham3• 6 years ago

Rate of change of rate of change.

They explain this in the paper: a constant (flat line across the graph) would correspond to exponential growth. The actual graphs drop (mostly), indicating sub-exponential growth, which is a good thing.

zeroimpl2• 6 years ago

A constant 2nd-derivative means quadratic growth, not exponential.

I'm bit confused by the graphs, because they show the 2nd-derivative going to 0. But to stop this thing, we actually need to decelerate, eg going negative on the 2nd-derivative.

fortran77• 6 years ago

1st: Velocity

2nd: Acceleration

3rd: Jerk

4th: Jounce

analog31• 6 years ago

As others have mentioned, acceleration, or the rate at which the rate is changing. Now... I admit to being an armchair epidemiologist. I've been graphing the data from the JHU website myself, but I've just been using semi-log plots. This is an option at some of the "dashboard" sites.

In a semi-log plot (vertical axis is logarithmic), a constant rate of exponential growth is seen as a straight line, the slope of the line is proportional to the doubling rate, and changes in that slope show that the exponential growth rate is changing. This is a way to "eyeball" the graphs without trying to read anything too profound into them. But just comparing the graphs of the US, Italy, and South Korea is interesting.

What I'm not doing is publishing conclusions from this armchair analysis.

stefan_• 6 years ago

This looks like one of those P versus NP papers.

bernardv• 6 years ago

Very little details on the methodology

dboreham3• 6 years ago

How so? They said they computed the second derivative. What more is there to say?

willis936• 6 years ago

You can’t compute the second derivative of data from May 2020 when it is currently March 2020. Where did the data come from?

lonelappde• 6 years ago

Better comparison:

http://91-divoc.com/pages/covid-visualization/

xiphias2• 6 years ago

This visualization doesn't show the lockdown effects that the paper estimates

internet_user• 6 years ago

No Taiwan?

They had the most proactive response in the world.

bigpumpkin• 6 years ago

Can't expect China-like second derivative when countries are not doing these counter measures:

Isolation of suspected cases and close contacts

Universal masking

Restrictions on travel inside country

Sending doctors from the rest of the country to epidemic centers.

kspacewalk2• 6 years ago

This presumes all of these measures are highly effective, which is far from certain or obvious.

justicezyx• 6 years ago

"No decision is the worst decision"

daxfohl2• 6 years ago

No, it only requires that one of the methods is slightly effective.

vkou• 6 years ago

Not taking any of these measures is highly effective at failing to control the virus. We're currently seeing it play out across Europe and the US.

FuckButtons• 6 years ago

Or that they have significant additional effect over social distancing alone, which we won’t know for some time yet.

avs7336• 6 years ago

Can't expect China-like second derivative when countries are not doing these counter measures

* not reporting cases accurately.

squidproquo• 6 years ago

If anyone has a forecast for the United States, this website is aggregating forecasts:

https://www.unitarity.com/app/challenges/us-coronavirus-outb...

daxfohl2• 6 years ago

I have a hard time believing Spain will have a higher peak than USA.

fermienrico• 6 years ago

You can't look at Spain and USA without considering the total population.

As someone in this thread pointed out: http://91-divoc.com/pages/covid-visualization/

Take a look at the charts of cases/1M people. It is obvious that US will have more cases simply because of the population.

avs7336• 6 years ago

it is notable that this work is done by an electrical engineer and a cardiologist, not epidemiologists. More than anything, the arm chair epidemiology is the our current second biggest danger. Epidemiology is hard. incredibly hard. It isn't viral marketing. It isn't electrical engineering. Data isn't pure or assumed to be correct. There data source was basically websites.

anacrolix• 6 years ago

Their

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avs7336• 6 years ago

thanks. there are a couple other typos I noticed this morning as well. shouldn't HN with Bourbon.

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thu21112• 6 years ago

Based on what we've seen so far, electrical engineering and cardiology are significantly more rigorous than epidemiology, which appears to be more like economics or social psychology in terms of the robustness of its methods and quality of its work.

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avs7336• 6 years ago

Define rigor.

In context I suspect you mean something like "treat data as objective." I can go to France and pickup and hold the literal kilogram. U can't do that, yet, with people's brains to the level needed for psych measurement.

Personally, I prefer social sciences and epi methods (get economics out of here...) Because they are more transparent about the role of the researcher and the limitations of their data. They don't bluntly trust it...the engineers I work with largely do. They assume data represents truth and is largely without meaningful error.

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reinkaos2• 6 years ago

Are you an epidemiologist? If so, can you be more specific about the problems and propose alternatives? Thanks.

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avs7336• 6 years ago

I am not...however i am married to one. The ranting recently is kind of fun to listen too. My partner is working on covid. I learn a lot, I'm no expert in epidemiology...but...I also do/teach statistics in a biology field. My degrees are is in mechanical engineering and education statistics. (And that's probably enough info to out me to any real life friends in HN ::waves::)

Basically the problem is the authors don't know enough about the data they are getting to run analysis on it. They are not clear, and absolutely need to be clear, on all things data for this paper to work.

Specific examples:

Are the websites they gather from reporting presumptive positives or confirmed positives?

Are they Getting information on when specific deaths occurred? Or are they using the latest update time, and the total number of deaths to date and then assuming a connection?

Are countries accurately reporting? Are they even capable of accurately reporting?

Are they testing enough (all) of the dead or are they relying on presumptive positives?

It's a data thing. Epidemiology is really really good at high quality data and analysis...but that takes time, more time than we have had to do good science during a crisis. It's why you don't do brain surgery in an ER. They are also really good about not over interpreting data...because data can be hinky.

One of the biggest things people in my undergraduate stats course cover with is specificity and sensitivity...false positives and negatives exist. That gets more complex when you consider that when talking about true positives versus false positives you have to have a gold standard test to reference against. So largely you are looking at one test versus another, even if one of those tests is really accurate, or pathology based, then things take time. That test doesn't typically produce a truly binary result but some chemical threshold that we treat as a binary. Decisions at each of those changes in data representation affect your outcomes. Then we talk about how it's impacted by prevalence and I try and teach them ROC curves and someone tells at me about how if you test positive for a disease you have that disease. (Seriously this happens about once a semester)

Where the students are really struggling isn't math, it's philosophical. The idea that a test result isn't objective truth is kinda bonkers the first time you encounter it. Especially for my engineers. I jokingly talk in class about how it's not a math class it's an estimation and bs detection class. I've seen this so much with covid...test results are not perfectly accurate. You can, and often should, bias them towards certain clinical goals. The first tests from cdc were problematic because they were overly sensitive (or contaminated...don't know yet, probably just too sensitive).

The reality more than anything is that there is so much miscommunication about covid, unavoidable communication, that I'm not sure anything is fully trust worthy yet. Weeks ago one of the first rapid studies published in JAMA ( or was it NEJM?) By a German group was submitted, reviewed, published, and withdrawn in about a week. People use words like 'positive test result' and can mean fundamentally different things when taking to each other and don't realize it.

And apologies I'm not following my normal anal hn comment style and citing this a bunch. Responding from my phone.

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X6S1x6Okd1st• 6 years ago

The methodology don't really explain how they aligned the second derivative curve to China or why that's reasonable.

I wouldn't put much faith in their predictions.

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twoslide• 6 years ago

I tried fitting a third order polynomial for JHU Covid data, just as a way to kill time. For all countries, the 95% confidence interval of the second derivatice overlapped zero (i.e. it can't be estimated very well). We only have about three weeks of data from the 10th death, for most countries, you can't fit a very good curve with that.

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An international comparison of the second derivative of Covid-19 deaths [pdf]

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