Trollish Study Challenge / Poll

Follow up to the Cleveland Clinic "boosters increase infections" study.

A week ago (insanely; the holidays have certainly killed my productivity) I shot out a brief post regarding the already-infamous Cleveland Clinic Study purporting to associate increased doses with increased infection.

As I pointed out, this was merely an artifact of how “catching up with infections” would look in a “real-time” view, without taking overall (“lifetime”) infections into account.

Of course the uber-boosted are the ones being infected

Like most of what I write, my argument has had no influence on the groupthink opinion about the study. But I submit to the reader that the groupthink opinion is simply a product of widespread “statistical illusion illiteracy” — most people, including those like me who anoint themselves as outsider science journalists, simply cannot come to grips with how merely assigning categories to people creates distortions and bias all the time.

As a follow-up exercise to illustrate this point, I submit the following weekend poll.

Which of the groups of Cleveland Clinic workers in this graph from Shrestha, et al., has experienced the most infections in the last six months (July to December, 2022)?

Shrestha, NK. et al. Fig. 1.

Why a poll? Just to engage the reader with a tactile option-selecting experience. Scroll below for the answer and comments.

Cheat-Notes:

To save the reader from wasting time in the study text, here is the makeup of the groups in the plot above, even though it gives away the answer to the challenge:

As an additional note, subjects are censored for 90 days after a positive test (so that additional positives do not count as an “infection” until after the 90 day window, and meanwhile, subjects are not in the “at risk” pool). And, Table 3 “proximate exposure” windows are calculated separately and are not relevant to the categories in Fig 1.

Answer

Naturally, the correct answer in rhetorical quizzes is always whatever is “counter-intuitive.”

In this case, the 4,087 individuals in the BA.4/5 group [the flat orange line] experienced the most infections in the last 6 months (4,087 vs. some fraction of 2,452 for each of the other groups).

Although Shrestha, et al. are not precise with their time cutoffs for the variant definitions, we can be sure that all 4,087 of the BA.4/5 group were infected after mid-June because they do not begin to become “at risk” again until a week after September 12; after they have left the 90-day window since their positive test.

OK, but is there actually a point to this exercise?

Well, let’s take what has been the widespread, groupthink interpretation of the study: The most-previously-injected were the ones who became infected at the highest rate from mid-September to mid-December, “because negative efficacy.”

But if this is generalizable, then it means that they also became infected at the highest rate just before the study begins, from mid-June to mid-September. Which means they are heavily represented in the BA.4/5 group, which experiences the least infections from mid-September to mid-December. Which also means, that in the next three months, the heavily-boosted who were infected during the study period will be the least infected.

A paradox thus arises where the highly boosted are the most likely to be infected in any given current period “x,” and thus also most likely to be in the category of least likely to be infected in the “x+1” period. This paradox is only sustainable if it reflects arbitrarily segmenting a transition toward an equilibrium into discrete “real-time” units.

So all that the study is showing is that the highly-boosted are still catching up with natural immunity.

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