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"*Nature is pleased with simplicity. And nature is no dummy*." -Sir Isaac Newton

One of the problems with statistics is that it becomes embedded in specializations guarded by the system, so the practitioners of those arts have the option of educating you or pulling the wool over your eyes. With PharmaMagik!

Before I dive into the primary content of this article, I'd like to point to Mary Beth Pfeiffer's article on the physician summit in Ocala, Florida---one of numerous that are springing up around the nation where doctors are free to discuss suppressed views about early medical treatment and vaccination of COVID-19. Some of the leadership in attendance:

**Two Studies, Two Highly Different Conclusions**

A few days ago, Martin Kulldorff wrote up an evaluation of two studies that each compare vaccination to immunity conferred by natural defenses marshalled upon recovering from COVID, but came to wildly different conclusions. One study out of Israel suggested that those who were vaccinated were 27 times as likely to suffer COVID than those who had recovered from COVID already.

Breakthrough cases = 27 x Reinfection+Symptoms

The other study, by the Center for Discourse Control (see what I did there), found that cases of reinfection were five times as likely as breakthrough cases per individual.

Breakthrough cases = 0.18 x Reinfection+Symptoms

The relative results differ by over two orders of magnitude! And that's quite bizarre. Even quick and dirty methods from a reasonable database shouldn't be *wildly* different from true effect comparisons. Was one or both of the studies flawed?

Kulldorff points out that the Israeli study looks pretty straight forward and solid as an epidemiological comparison:

In the Israeli study, the researchers tracked 673,676 vaccinated people who they knew not to have had Covid and 62,833 unvaccinated Covid-recovered individuals. A simple comparison of the rates of subsequent Covid in these two groups would be misleading. The vaccinated are likely older and, hence, more prone to have symptomatic disease, giving the Covid recovered group an unfair advantage. At the same time, the typical vaccinated patient received the vaccine long after the typical Covid-recovered patient got sick. Most Covid recovered patients got the infection before the vaccine was even available. Because immunity wanes over time, this fact would give an unfair advantage to the vaccinated group.

To make a fair and unbiased comparison, researchers must match patients from the two groups on age and time since vaccination/disease. That is precisely what the study authors did, matching also on gender and geographical location.

For the primary analysis, the study authors identified a cohort with 16,215 individuals who had recovered from Covid and 16,215 matched individuals who were vaccinated. The authors followed these cohorts over time to determine how many had a subsequent symptomatic Covid disease diagnosis.

On the other hand, the CDC study worked backward from a point at which any number of conditionals or statistical sieves could apply factors to the final result:

The CDC study did not create a cohort of people to follow over time. Instead, they identified people hospitalized with Covid-like symptoms, and then they evaluated how many of them tested positive versus negative for Covid. Among the vaccinated, 5% tested positive, while it was 9% among the Covid recovered. What does this mean?

Kulldorff explains one example of a conditional that likely confounds the results.

In the CDC study on Covid immunity, the cases are those patients hospitalized for Covid disease, having both Covid-like symptoms and a positive test. That is appropriate. The controls should constitute a representative sample from the population from which the Covid patients came. Unfortunately, that is not the case since Covid-negative people with Covid-like symptoms, such as pneumonia, tend to be older and frailer with comorbidities. They are also more likely to be vaccinated.

Suppose we wanted to know whether the vaccine rollout successfully reached not only the old but also frail people with comorbidities. In that case, we could conduct an age-adjusted cohort study to determine if the vaccinated were more likely to be hospitalized for non-Covid respiratory problems such as pneumonia. That would be an interesting study to do.

I don't disagree with anything Kulldorff says at this point, in general, though the CDC study (as he points out) does some statistical corrections that push the result by a factor of 3, when maybe it would tend a bit in the other direction, but shows no math at all. So, while I agree firmly with Kulldorff that the Israeli study is clearly superior in design, I disagree with his discussion of the confounders. I also worry that he has taken enough public abuse, so many not have dug in the direction I'm about to dig as a result.

Here are numerous potential confounders to the CDC study:

Vaccine mortality survivor bias clipping off more of the tail, and it's the tail that we're weighing, here. Far out on a statistical tail, any parametric bias can result in dramatic changes in ratios, including changes of orders of magnitude difference. The probability of flipping at least 49 heads out of 50 flips of a coin weighted so that heads comes up 55% of the time is around 159 as likely as the probability of flipping at least 49 heads out of 50 flips of a fair (50%) coin. While that example is artificial, the ratio is about the same as the relative risks between the two studies.

Definition bias may or may not have been properly accounted for as it pertains both to whether group assignment takes place purely without a conditional (the Israeli study ensured that) and also how patients are tested or treated.

If the vaccines suppress symptoms, then the proportion of silent hypoxics might be larger among the vaccinated group adding an additional conditional to the circumstance of hospitalization.

Financial incentives of a system protecting itself.

Understand that this is nothing like a slam on Kulldorff's article. He clearly explains why the superior paper is a quality study by design and why the second study design is open to problematic conditionals. He strikes me as an honest man, punished for good work during this pandemic. He has himself critiqued the ethics of the medical system, which relates to my second and fourth points, and the third is not at all likely to result in the 2.2 orders of magnitude difference between the studies. * But my first point remains a major elephant in the room*, and so I wanted to call readers' attention to it. I plan to talk a great deal more about it in upcoming articles.

If you want to go further into the evidence to find out if I'm here to educate you or to pull the wool over your eyes, Paul Alexander has compiled a list of 81 research studies that conclude the superiority of natural immunity. In an email thread, I asked why there would ever be a need to go beyond 79 studies. At least one person replied with a serious answer, so I guess I'm not that funny.

## Natural Immunity and Martin Kulldorff's Study Autopsy

MSM media Germany reports that This covid wave will be the last one. What relief:)

I was thinking if Israel keeps getting nailed by these waves and they have a small-ish population. How come they haven’t reached herd immunity yet?

"Center for Discourse Control" 😂 Brilliant! (No, I didn't see what you did until you brought my attention to it. More proof that we look for patterns, which even though efficient, is often to our detriment.)