An international comparison of the second derivative of Covid-19 deaths [pdf]
medrxiv.org
medrxiv.org
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.
It's not just how much data is trusted (though note: Professor Ferguson at Imperial appears to trust the data coming out of Italy almost completely). It's the whole set of problems.
>Right now I absolutely want to see papers written by physicists studying COVID-19. Why - because physics is a significantly more rigorous field than epidemiology. I trust the average physicist to have at least slightly higher standards, for instance I trust them to at least pretend to care about statistical uncertainty, and I suspect many of them will upload their source code. I don't expect any of them to email their paper straight to known-friendly newspapers. (from your other post)
Is a really...bad idea. Let's not presume knowledge transfers from one discipline to another, that standards look the same, or that Alan Sokal was anything other than an egomaniac.
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.
An international comparison of the second derivative of COVID deaths after implementation of social distancing measures
They had the most proactive response in the world.
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.
* not reporting cases accurately.
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.
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!
You mean like the widely cited NYT Coronavirus death tracker[1]?
[1] https://www.nytimes.com/interactive/2020/03/21/upshot/corona...
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.
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.
Edit: Now that I think about this some more, you're right. There has to be a decrease in the daily cases, which implies a negative 2nd-derivative. They mention "relative 2nd-derivative." It seems to be defined in the paper in a way that leaves me more confused:
> Daily fatality rates from the included countries were then used to calculate estimates of the relative second derivative of total deaths, N, 1/N d²N/dt², for a period of at least ten days.
Does this mean they are taking the second derivative of the reciprocal of the cumulative deaths?
You are treating the curve of daily deaths as the thing to be differentiated. They are treating the curve of total deaths as the thing to be differentiated.
While the curve of daily deaths certainly would have a negative acceleration, the curve of total deaths is monotonically non-decreasing and therefore the second derivative is always positive but trending towards zero.
Like I mentioned above, the only way for total deaths to decrease (making the function not monotonically increasing and therefore capable of having a negative acceleration) would be through errors of accounting.
A constant relative second derivative of total deaths is what they are talking about, meaning that they are flattening the 2nd derivative of the exponential by dividing by the exponential, making it constant.
Of course, this is all numerical methods, not analytical methods, so it doesn’t necessarily make pure analytical sense that they are even talking about an exponential.
2nd: Acceleration
3rd: Jerk
4th: Jounce
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.
I wouldn't put much faith in their predictions.
https://www.unitarity.com/app/challenges/us-coronavirus-outb...
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.