My last post took shape less as a communique than as an exercise in thinking out loud. In the midst of that ordeal I did run a new analysis that enables a more direct and streamlined method of estimating the rate of covid contagion through the US population.

It’s well known that daily dx-positive case counts underestimate new infections. In June the CDC estimated that, in the US, there had been ten times as many infections as case-positives. But that ratio isn’t a constant: early in the pandemic, when very little testing was being done, the infections-to-cases ratio was far higher. As testing increased over the months the ratio decreased.

The other day as part of my convoluted last post I ran week-by-week analyses on data from the past four months looking for the best predictor of the subsequent week’s covid death counts. It turned out that the prior week’s death count and the case count from 3 weeks prior were the two best predictors. They’re not interchangeable predictors, so I used an average of the two in my analyses. However, as individual predictors each proved to be pretty accurate.

I’ve been using death counts as a 3-week *lagging* indicator of infections, and that algo was supported by the 4 months’ worth of data. But it turned out that the inverse relationship was also supported: *changes* in case counts are a good *leading* indicator of *changes* in death counts 3 weeks later.

Given the stable relationship over the past four months between case counts and subsequent deaths, along with the stable relationship between deaths and infections, it seemed likely that the relationship between case counts and infections had also stabilized. It’s still true that case counts underestimate infections, but based on the data it seemed possible to compensate for the case-count underestimate by means of an empirically supported conversion formula.

The method for deriving the conversion formula was based on three variables:

- Take the weekly total death and divide it by the estimated covid fatality rate of .0065.
- Take the weekly total case count from three weeks prior to variable 1.
- Divide variable 1 by variable 2: that’s the ratio of estimated infections to cases.

I ran the numbers week by week across the last four months of data, and the value for variable 3 proved quite stable, averaging around 2.7. So that’s the proposed conversion formula:

**New infections = 2.7 x new cases**

So, from 27 November to 11 December, there were 2.82 million new dx-positive cases reported in the US. Multiply 2.82 million by 2.7 = 7.61 million new cases, or about 2.3 percent of the US population. That estimate falls snugly within the 2.15% – 2.75% I estimated in the last post.

On the go-forward I’m going to use this conversion ratio for estimating infection rates in the US, which are likely to continue climbing even as the vaccine is being rolled out. I’ll also keep track of the week-to-week data to see if the ratio needs adjusting.

Update with data through 18 December: 3-week case count lag and prior week’s death count are still the best predictors of death rate; the conversion rate for case to estimated infections was again 2.7. So, using 2-week case data, there are now 9.3 million active covid infections in the US, accounting for 2.8 percent of the population.

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As a point of comparison, IHME projects that, due to the vaccine rollout, the US daily infection rate will begin to drop starting December 24, and that the death count will begin to drop January 12. That’s a lag of 19 days, which is about what I arrive at with my univariate data modeling.

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As I wrote in the post, the ratio of new infections to case counts is variable over time. As of 11 December the ratio had stabilized at around 2.7; over the past 5 weeks it’s dropped to 2.1. Part of that is an artifact of spotty recording and reporting over the Thanksgiving and Christmas holidays.

Using projected death counts 3 weeks from now, the algo estimates that around 2.6% of Americans are presently covid-infected. Multiplying the last 2 weeks’ case count by the 2.7 ratio yields an estimate of 2.7% currently infected. Pretty close.

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Here’s an epidemiological model estimating that, to date, there have been 5 times as many covid infections as dx case-positives in the US. That amounts to 135 million infections, or over 40 percent of the US population. My model and the IHMEs estimate that 22-25% of the population has been infected — half this new model’s estimate. This guy uses case counts and phone tracking to see how much contact case-positive people are having. Using deaths as lagging indicator of infections, with a multiplier derived from seroprevalence surveys, seems like a more sound methodology.

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Over the past two months of weekly data, from 12/12/20 through 2/6/21, the estimated US case rate conversion ratio has dropped: new infections = 2.2 x new cases. One possible explanation is that the covid fatality rate has increased, which is unlikely. The other explanation is that diagnostic testing is now identifying a higher proportion of actual new cases. This latter interpretation is likely, since testing rates have increased throughout the duration of the pandemic.

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Since my most recent comment on this post, the case rate conversion ratio has gone back up to around the 2.7 figure that had held stable from August 2020 until early 2021. HOWEVER…

The ratio is predicated on a covid fatality rate of 0.65% of infections, adjusted to the median US population age of 38 years. From the beginning of the pandemic, more than half of the US covid deaths occurred among the 6% of the population aged 75 and older. Per the most recent US vaccination data, around 60% of the 75+ demographic has received at least one shot; assuming at least 80% immunity for those with one or more shots, the overall acquired immunity of the 75+ age demographic has been reduced by .6 x .8 = 48%. Reduced contagion means fewer deaths, so the fatality rate among this oldest demographic should have dropped in half due to vaccinations. And since this demographic has accounted for more than half the covid deaths, the overall US covid fatality rate should have dropped by at least .5 x .5 = 25% due to vaccinations.

Overall, around 21% of Americans have received at least one vaccination shot. So, overall, vaccinations should have reduced infections by .21 x .8 = 17%. Overall then, the odds of dying from a covid infection among the non-immunized population has decreased to (1-.25)/(1..17) = 0.90. I.e., the covid fatality rate should now be 0.65% x .90 = .59%.

I don’t think that’s enough to argue that the case rate conversion ratio should be radically altered. After all, the IHME has already been using a 0.6% fatality rate; plus or minus ten percent isn’t much, given all the other uncertainties in the estimates.

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