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  • Writer's pictureEleos

PHMDC Case Rates: C'mon Guys, Show Your Work

As noted in my last post, Public Health of Madison and Dane County (PHMDC) has finally begun talking about case rates among three different vaccination classes:

  1. unvaccinated;

  2. vaccinated with primary series; and

  3. fully vaccinated with a booster or additional dose

On page 4 of their Jan 20, 2022, Data Snapshot, they write: "The age-adjusted case rate in December was 6,068.2 per 100,000 not fully vaccinated people, 2,527.2 per 100,000 people fully vaccinated with the primary series, and 848.2 per 100,000 people fully vaccinated with a booster or additional dose." It's important to think about just how PHMDC might have calculated those numbers. Moreover, one has to wonder why PHMDC has not explicitly divulged how they actually calculated them. There are actually a few ways they might have gone about calculating these case rates:

  1. Test Every Person in Dane County for Covid-19 - PHMDC might theoretically have compelled every last person living in Dane County to take a COVID test during the month of December. PHMDC would then count up the infections in each vaccination class, divide each sum by the total number of tests given to people in each vaccination class, and multiply that number by 100,000. PHMDC is clearly not achieving its rates in this way. If they were, everyone would have received an order compelling them to take a single test. It would also mean Dane County gave 561,504 tests a month. In point of fact, this isn't even a realistic scenario, since there no doubt would be people who refused to comply, and those people would be noticed on local news coverage. In other words, we'd see the lack of compliance, and PHMDC would be highly unlikely to achieve testing of the full population.

  2. Randomly Sample People from Around Dane County - PHMDC might have randomly selected a sizeable sample of people from around Dane County and compelled/invited them to take a COVID test in December. PHMDC would then count up the infections in each vaccination class, divide each sum by the total number of tests given to people in each vaccination class, and multiply that number by 100,000. Doing so would provide a representative sample of people in the county. However, PHMDC is not doing this either. If they were, we'd likely have a sizeable number of people being sampled who would object not just to being compelled to take a test and/or having to share their vaccination status. We would no doubt see protests or court cases to assert these medical freedoms. We have not seen such protests or court filings. So, not only is this scenario not happening presently, it's not currently a likely avenue.

  3. Use numbers from Voluntary Testing in Dane County - PHMDC could access data generated during voluntary testing, either by asking people their vaccination status as a part of the testing procedure, or ask for ID during testing in order to access the testee's individual record in the Wisconsin Immunization Registry (WIR). PHMDC could then query WIR, count the number of infections in each vaccination class, divide each sum by the total number of tests given to people who show up to be tested in each vaccination class, and multiply that number by 100,000. We know that voluntary COVID testing *IS* happening in Dane County. We also know that PHMDC is deriving and leveraging various kinds of data from that voluntary testing on the PHMDC COVID Dashboard and in other publication channels, such as the agency's weekly Data Snapshots. It stands to reason, then, that vaccination status is a data set that PHMDC is obtaining through the voluntary testing process. Identification, like a driver's license or Social Security number, is likely used at the point of vaccination to determine vaccination class in the WIR database, since self-reporting of vaccination status would otherwise battle significant inaccuracies--people not remembering, lying, or refusing to answer. However, using voluntary testing as a principal means of collecting any kind of data, including vaccination status, comes with some problems. Since nobody is compelled to show up, the tests given may not accurately reflect the actual makeup of the county. For instance:

    • There may be quite a few asymptomatic people in the county, some of whom would test positive for COVID, while many would not. It's reasonable to assume that most asymptomatic people would be unlikely to go for a test unless otherwise required by a workplace, to access a venue, for travel, or perhaps in advance of a medical procedure. Asymptomatic people thus likely remain highly under-sampled in a voluntary testing scenario.

    • Alternatively, people who don't feel well are more likely to show up for a voluntary test, to see if they're COVID-positive. So the symptomatic will likely be oversampled in a voluntary testing scenario.

    • People who've already completed an initial vaccination series or received a booster may believe that they are immune and not show up to be tested.

    • People who have natural immunity due to a past COVID infection are also less likely to voluntarily show up, trusting that they cannot be infected.

So, it's not exactly clear what the vaccination classes of those who show up voluntarily would be. It's also not at all clear whether these vaccination classes are representative of the population of Dane County as a whole. A voluntary testing sample likely skews "sicker" than the county in general, especially during periods of higher outbreak. Still, even with the sampling problems noted above, it's very likely that PHMDC is indeed obtaining their vax-class data through voluntary testing, and using that data to calculate rates of infection for each vaccination class.


If anyone knows of another way that PHMDC may be calculating these numbers, I would be very interested to hear about it. Please email eleos@daneundivided.com, referencing the title of this article in the subject line. It would be especially useful if you had a link to a PHMDC blog post, dashboard page, or any Data Snapshot content that contains details of PHMDC's calculation process.


PHMDC really should be explicit about how these numbers are calculated.


Assuming Method #3, above, is how PHMDC calculates its vax-class case rates, they would have to gather the following numbers from State of Wisconsin databases, which PHMDC acknowledges it leverages:


C_u = Number of CASES found among those UNVACCINATED in December

T_u = Number of TESTS performed on those UNVACCINATED in December

C_v = Number of CASES found among those VACCINATED* in December

T_v = Number of TESTS performed on those VACCINATED* in December

C_b = Number of CASES found among those BOOSTED in December

T_b = Number of TESTS performed on those BOOSTED in December


*Vaccinated presumes only a completed primary series.


PHMDC would then need to calculate as follows:


100,000 * (C_u / T_u) to get the cases per 100,000 unvaccinated in December

100,000 * (C_v / T_v) to get the cases per 100,000 vaccinated in December

100,000 * (C_b / T_b) to get the cases per 100,000 boosted in December


Now, note that nowhere does PHMDC report to the public real values for any of the following variables:

  • C_u

  • C_v

  • C_b

  • T_u

  • T_v

  • T_b

Via bar graphs on its COVID dashboard, PHMDC only reports total daily cases (screen 2) and total daily tests (screen 3). From this data, one could get the total tests performed in December (which we will call T) by rolling over the appropriate bars on the graph and recording the number that pops up for each date of that month. One can discover the total number of December cases detected (which we will call C) in the same way. It's a giant pain to have to grab all those numbers, but they are available.


But obtaining total daily cases and total daily tests only gets us part way to where we need to be. Again, in order to know whether the vaccination case rates PHMDC provides in the Jan 20, 2022 Data Snapshot are legitimate, we still need a breakdown of how many people IN EACH VACCINATION CLASS took a test in December and, of those who took a test, how many CASES were detected in December IN EACH VACCINATION CLASS.


Moreover, If PHMDC is going to discuss vaccination-class data for December 2021, the Data Snapshot in which that discussion takes place should include the appropriate monthly totals. Instead, one finds only total cases and total tests for the previous 14-day period. The fact that PHMDC makes you go to the dashboard, roll over two separate graphs on two separate screens, and add up numbers on your own indicates a lack of transparency.


Of far greater concern is the fact that PHMDC does not share with the public all of its raw numbers going into the December vaccination-class calculations. PHMDC should explicitly state their inputs for C_u, C_v, C_b, T_u, T_v, and T_b for all to see. Not "showing their work" for the calculation of these important values not only misses an important chance to educate the public as to PHMDC processes; it also wastes an opportunity to build trust with the public. We hope that PHMDC will quickly take steps to educate and build trust by sharing a good deal more about the manner in which it calculates its figures. Doing so would place everything above board and eliminate any possible misunderstandings going forward. The question is, will they do so?


In my next post, I'll dig deeper into the weird problems with PHMDC's December vaccination-class case rates. No matter what assumptions one makes, the results fail to add up, and PHMDC's data looks like it's been manipulated somehow.

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