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I posted a preliminary projection yesterday (here), at the end of one of my regular reports, but I wasn’t very happy with it. Here is my official COVID-19 projection for the US. I’ll post it so that I can be properly humiliated if I’m wildly wrong, or improperly smug if I turn out to be right.
I’ll show my rationale, in case it is of any interest to you.
I’ve been closely tracking the changes in the rate of increase in reported deaths for each country. In my post yesterday, I got as far as creating a time-series of this variable for each country, with the data series for each country starting when it first passed 2.5 reported deaths per 100,000. My data source is Johns Hopkins as usual (here), and I’ve been analyzing the US and the Western European countries — Germany, the UK, France, Italy, Spain, and a combined “Other Western Europe” for the others (down to the size of Luxembourg).
I used a linear model yesterday, which didn’t seem quite proper, as I’d expect the rate of growth to follow something more of an exponential decay function. So I decided to do a logarithmic transformation in the regression, conveniently available in MS Excel via the “LOGEST” function.
The linear model takes the mathematical form y=mx+b. The LOGEST model takes the mathematical form y=bm^x, so x is in the exponent. If I recall the way that the math works on this one — and I think that I last studied this during the Reagan administration — the formula simply takes the logarithm of both sides of this equation and then does a linear regression (so y=bm^x is equivalent to log y = mx + log b).
Anyway, here’s how it looks applied to the data set for all of the Western European countries, plus the US:
The “days offset” indicates the number of days after March 1 on which the series starts. So, for example, Italy is offset five days (starting March 6), and the US is offset 24 days (starting March 25).
This looks like a pretty decent fit, but I’m not very happy with the far right end. It looks like the estimate line is consistently overpredicting the rate of growth after 20-30 days. I’ve blown this up in the next graph, which shows only days 16-30 from the graph above (note that some countries drop out, because they have not yet reached their day 16).
It really looks here like there’s overprediction at the right end of the curve. I could go back to the drawing board and create a different mathematical model, but I don’t have anyone to please (or answer to) except myself, so I decided on an alternative approach. I created an alternative estimate curve based solely on the data for days 16-30. Here’s what it looks like:
So I decided to use the red estimate line for the first 15 days (and actually to project backward before March 1, also), and use the blue estimate line for days 16 onward. I did this analysis with data through April 4, which was day 11 for the US. So the change in projection estimate occurs on April 9.
Here’s how the projection looks for cumulative deaths — 95,574 through July 5, 2020:
If that looks eerily familiar to you, you’re not alone. I can only give you my assurance that I did this calculation completely independently, but here’s how it compares to the latest IHME graph, first cumulative:
Not much difference, is there? I labor mightily to tell you what you already knew. Here’s how it looks on a daily basis:
So what did I learn? Basically that I agree with the IHME model. This actually is useful information to me.
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