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  • Writer's pictureEleos

Questioning the Snapshot

It's looking more and more like PHMDC may be fudging its COVID numbers in order not to lose the narrative that life is always riskier for the unvaccinated.


The agency's COVID Dashboard currently claims that 78.4% of eligible Dane County residents have now completed at least an initial vaccination series. So, one can easily understand how the notion that vaccinated individuals remain better protected isn't one the agency wants to give up. Breakthrough cases are a worrisome topic. The problem is, mathematical analysis has now begun to poke serious holes in what PHMDC is telling us.


On Thursday, January 20, 2022, PHMDC published its weekly "Data Snapshot," a newsletter in which the agency covers a variety of COVID-related statistical analyses and graphs. This week, for the first time, the Snapshot attempted to take vaccination status into consideration in a breakdown of case rates, something Aletheia has already noted they've been hesitant to do in anything but a veiled way. PHMDC notes on page 4 of the Snapshot that they've based these categorized case figures on data from the State Department of Health Services (DHS) for the previous month, stating:


"The Wisconsin Department of Health Services provides statewide data for COVID case, hospitalization, and death rates by vaccination status and age group for the previous month. We are also providing this data for Dane County residents after the 15th of each month for the previous month."


Since the Snapshot we're discussing is "after the 15th" of January 2022, they are providing data for the previous month: December 2021.


On January 20, 2022 the PHMDC COVID Dashboard indicated the following numbers for December 2021 cases and tests:

























I ran a check on these numbers to try to get a feel for how many unvaccinated, vaccinated, and vaccinated with booster or additional dose have been showing up to get COVID tests. Then ventured into verifying case rates for all three groups. I've provided headings for greater clarity below as I walk you through the majority of my process...


Variables

In relationship to PHMDC's December 2021 numbers, I determined to let:

  • C_u be the total number of CASES among UNVACCINATED individuals detected

  • C_v be the total number of CASES among VACCINATED BUT UNBOOSTED individuals detected

  • C_b be the total number of CASES among BOOSTED individuals detected

  • T_u be the total number of TESTS given to UNVACCINATED individuals

  • T_v be the total number of TESTS given to VACCINATED BUT UNBOOSTED individuals

  • T_b be the total number of TESTS given to BOOSTED individuals

Equations 1 to 3

Page 5 of the January 20th Snapshot reports the following case rates for December 2021:


Unvaccinated: 6,068.2 cases per 100,000

Vaccinated w/a completed initial series: 2,527.2 cases per 100,000

Vaccinated w/a booster or additional dose: 848.2 per 100,000


These case rates result from the following three equations:


[Equation 1]

C_u / T_u = 0.060682 (which we'll call R_u or UNVACCINATED RATE)

[Equation 2]

C_v / T_v = 0.025272 (which we'll call R_v or VACCINATED BUT NOT BOOSTED RATE).


[Equation 3]

C_b / T_b = 0.008482 (which we'll call R_b or BOOSTED RATE)


Equation 4

From the data table above and the definition of CASES, we also know that for December:

C_u + C_v + C_b = 13,725 (which we will call C or TOTAL CASES)


Restatement of Equations 1 to 3

To solve for the variables in Equation 4, we can restate the relationship in Equation 1 as C_u = R_u * T_u and plug in the information we already have for R_u:


C_u = 0.060682 * T_u


We can do the same with Equation 2, so that C_v = R_v * T_v:


C_v = 0.025272 * T_v


And with Equation 3, so that C_b = R_b * T_b:


C_b = 0.008482 * T_b


Restating in this manner will ultimately allow us easily to plug variables into Equation 4.


Equation 5

Next, we need an equation to solve for the three different TEST variables: T_u, T_v, and T_b. From our table above and the definition of TESTS, we know that for December 2021:


T_u + T_v + T_b = 134,775 (which we'll call T or TOTAL TESTS)


Equation 6

Remember that PHMDC reports 13,725 total CASES for December 2021, as of January 20, 2022. We also know the three CASE RATES. So, to begin solving for the test variables, we can use the following equation:


[Equation 6]

R_u * T_u + R_v * T_v + R_b * T_b = C


Which looks like this when you plug in the numbers:

0.060682 * T_u + 0.025272 * T_v + 0.008482 * T_b = 13,725


Equation 7

Next, we can start using constants (i.e., unchanging numbers) to solve for still unknown variables. To do so, we can divide Equation 6 through by one of our three known rates: R_u, R_v, or R_b. I've chosen R_u for Equation 7, below, but any of the three rates would work:


T_u + (R_v/R_u) * T_v + (R_b/R_u) * T_b = C / R_u


Equation 7 looks like this when we plug in the numbers:


T_u + (0.025272 / 0.060682) * T_v + (0.008482 / 0.060682) * T_b = 13,725 / 0.060682


Dividing by R_u enables us to eliminate T_u.


Equation 8

Now we can leverage an additional bit of algebra known as simultaneous equations. You may remember your math teacher telling you, way-back-when, that if you add the same amount to both sides of an equation, the equation will remain true. It's actually true of subtraction, multiplcation, and division as well. We're going use division.


We first require two equations that we know are true. We know Equation 5 must be true about TOTAL TESTS.


T_u + T_v + T_b = T


We also know that Equation 6--a restating of Equation 4--must also be true. We've just given ourselves different variables to work with by replacing case with rates multiplied by tests:


R_u*T_u + R_v*T_v + R_b*T_b = C


Now comes the division, which we're going to use in order to eliminate the T_u variable and make the rest easier to resolve:


[Equation 8]

T_u + (R_v / R _u) * T_v + (R_b / R_u) * T_b = C / R_u


Which looks like this with the known values inserted:


T_u + (0.025272 / 0.060682) * T_v + (0.008482 / 0.060682) *T_b = 13,725 / 0.060682


Calculated:


T_u + 0.416466167891632 * T_v + 0.139777858343496 * T_b = 226179.097590718829307


We can now subtract Equation 8 from Equation 5 to eliminate T_u:


T_u + 1 * T_v + 1 * T_b = T

-T_u + (R_v / R_u) * T_v + (R_b / R_u) * T_b = C / R_u

_______________________________________________

(1-(R_v/R_u)) * T_v + (1-(R_b/R_u)) * T_b = T - (C / R_u)


Or, if we plug in the numbers:


T_u + 1 * T_v + 1 * T_b = 134775

- T_u + 0.416466167891632 * T_v + 0.139777858343496 * T_b = 226179.097590718829307

_____________________________________________________________________________

0.583533832108368 * T_v + 0.860222141656504 * T_b = -91404097590718829307


Equation 9

The result of subtracting Equation 8 from Equation gives us Equation 9, which, in the abstract appears thus:

(1-(R_v/R_u)) * T_v + (1-(R_b/R_u)) * T_b = T - (C / R_u)


With numbers plugged in, as shown above, it looks like this:


0.583533832108368 * T_v + 0.860222141656504 * T_b = -91404097590718829307


We're left with two unsolved variables, but we have a far more immediate problem.


Ruh-Roh! Negative Number!

Notice that, with the numbers plugged in and calculated, the righthand side of our resulting Equation 9 is negative (actually very negative). Since the coefficients on the lefthand side of the equation are positive, T_v or T_b (or possibly both) must also be strictly negative. But such a result simply cannot be true, because T_v is the number of tests administered to the vaccinated (but not yet boosted) and T_b is the number of tests administered to the boosted. T_v and T_b must be non-negative. You can't administer a negative number of tests.


So, I question the numbers we're getting from the PHMDC Snapshot, regarding case rates among unvaccinated, vaccinated, and boosted. What we've just shown with the calculations above is that the Snapshot data doesn't match with their daily numbers. We realize that they are reporting "age adjusted" cases in the snapshot--another means of obfuscating real numbers--but that should not adjust the totals (which include all age groups) when looking at vaccination categories.


Making Sense of Bizarre Data

So, in plain terms, we now know all three of the case rates PHMDC just gave us in it January 20th Snapshot are bogus, in that they don't agree with their own dashboard data.


To make these case rates work with their December 2021 data, here are some things we (or PHMDC) would need to consider. Looking at the abstract version of Equation 9, we could choose an R_v that results in a negative coefficient. Here's an example, in which we choose the coefficient of T_v to be negative:


1-(R_v/R_u) < 0


Adding R_v/R_u to each side of the inequality:


1-(R_v/R_u) + (R_v/R_u) < 0 + (R_v/R_u)


Simplifying the inequality, gives us:


1 < R_v / R_u


We can then multiply the inequality by R_u


1 * R_u < (R_v / R_u) * R_u


Simplified:


R_u < R_v


But here's the thing: This inequality would indicate that the case rate for the unvaccinated is lower than the case rate for the vaccinated (but unboosted). And if that's true, it would suggest that a completed initial vaccine series has negative efficacy.


Similary, one could choose an R_b so that:


1-(R_b/R_u) < 0


which implies


R_u < R_b


That would indicate that the case rate for the unvaccinated is lower than the case rate for the boosted. And if that's true, the result is even more troubling, because it would suggest that a completed initial vaccine series with a booster or additional dose likewise has negative efficacy.


In Conclusion

Something is clearly wrong with the numbers being reported in PHMDC's January 20th Snapshot. It makes one wonder not just whether but how the reported numbers are being manipulated. They clearly cannot be true as reported.


A few questions we should all be pondering:

  • Is PHMDC perhaps reporting rates that attempt to hide negative efficacy for vaccines?

  • Why do they obfuscate with age-adjusted data?

  • Why don't they include the number of tests given to boosted, vaccinated, and unvaccinated persons?

  • Why don't they provide the actual number of cases found in each of the three groups?

PHMDC has some explaining to do...



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