When you look at studies, the amount of participants matter. A larger sample size means you have a more accurate representation of the population.
Recently a CDC study made headlines wherein it claims to show that people who have allegedly already contracted COVID-19 and are unvaccinated are 5x more likely to get a SARS-CoV-2 PCR positive result than those who have have received a shot for COOVID-19.
But how big was this study? How come larger studies find the opposite?
Martin Kulldorff, Senior Scientific Director of Brownstone Institute wrote about both studies to give us a better understanding.
Israeli study:
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.
Ultimately, 191 patients in the vaccinated group and 8 in the Covid recovered group got symptomatic Covid disease
US Study:
During January 1–September 2, 2021, a total of 201,269 hospitalizations for COVID-19–like illness were identified; 139,655 (69.4%) patients were hospitalized after COVID-19 vaccines were generally available to persons in their age group within their geographic region. Molecular testing for SARS-CoV-2 was performed for 94,264 (67.5%) patients with COVID-19–like illness hospitalizations. Among these patients, 7,348 (7.8%) had at least one other SARS-CoV-2 test result ≥14 days before hospitalization and met criteria for either of the two exposure categories: 1,020 hospitalizations were among previously infected and unvaccinated persons, and 6,328 were among fully vaccinated and previously uninfected patients (Table 1).
Let’s look at the numbers. Of the 413 cases (i.e., Covid positive patients), 324 were vaccinated, while 89 were Covid recovered.
Instead, they use Covid-negative patients with Covid like symptoms as their control group, of which there were 6,004 vaccinated, and 931 Covid recovered. With these numbers in hand, we can calculate an unadjusted odds ratio of 1.77 (not reported in the paper). After covariate adjustments, the odds ratio becomes 5.49 (95% CI: 2.75-10.99).
The CDC study did not address the first question, while the Israeli study showed a small but not statistically significant benefit in reducing symptomatic Covid disease.
Read more about the differences to see that once again the relative risk reduction is being used by the US government agency to tout superior efficiency. But in the end, that's not the real absolute risk posed. The results are statistically insignificant to say there is even a significant difference between vaxxed or unvaxxed alleged infection rates.
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