The actual efficacy of the Pfizer vaccine is still close to 90%. What we see in Israel is the so-called “Simpson paradox”: the data actually confirm the goodness of immunization. An argument used by no vax disassembled by the analysis of numbers
There has been much talk of recent data from Israel which seem to suggest a decrease in vaccine efficacy against serious Covid cases due to the Delta variant.
The Simpson paradox
Numbers this week showed that, of 515 patients currently hospitalized for severe Covid, 301 (58.4%) were fully vaccinated. It doesn’t mean that vaccines aren’t effective (or they are less than expected), but only that the numbers are “deceptive” if not related to a specific context. These percentages, in fact, are confused by the age of the vaccinated and Israel’s high vaccination rate and give rise to the “Israeli paradox“Which is what is known in statistics as”Simpson’s paradox“. Let’s see what it is and how the numbers are actually telling us that vaccines still protect well (in this case Pfizer, being Israel, ed).
According to the latest data, vaccination is effective in the country against severe cases appears to be quite low, coming in at about 67% when it would be expected at around 96%. The same effectiveness measured within two age groups, however, oscillates between 85% and 92%: why? It is the “Israeli paradox”, as seen in Table 1 (below, ed) compiled by Jeffrey S. Morris, professor and director of Biostatistics at the Perelman School of Medicine of the University of Pennsylvania (based on data provided by the Israeli government).
The starting set
When we talk about percentages, we must always refer to a set. How it is composed the starting set it is basic. Let’s assume that hospitalizations concern 100% of vaccinated people and 0% of unvaccinated people. The mathematical explanation for this singular situation could be that the starting set concerns a 100% vaccinated population. Obviously, each percentage would only concern vaccinated people.
With SARS-CoV-2 the important variables are the age of the people (because the risk of hospitalization is directly proportional to seniority), the percentage of the population vaccinated with two doses, but not only, too how vaccination rates are distributed across age groups. Only in this way can we make good distinctions on the effectiveness of vaccines. Only in this way the values seen in Table 1 become those of Table 2 described below: effectiveness regarding individual age groups and their risk of ending up in hospital for Covid is “aligned” again with what we would expect from vaccines, with almost all values around 90% efficacy in preventing severe cases among vaccinated elderly.
The calculation and the “revenge” of vaccines
Here’s how it gets there: Israel’s Covid data panel shows that nearly 60% of all hospitalized patients are vaccinated. Although these numbers are true, citing them as evidence of low vaccine efficacy is wrong. The key factors contributing to the “confusion” cited by Professor Morris in his blog are: the high vaccination rates in the country, the fact that 85% of the unvaccinated are young people, that 90% of the elderly are vaccinated and that the elderly themselves are more likely to be hospitalized than young people (over 50s 20 times more than children under 50). “After taking vaccination rates into account and stratified by age groups, from these same data it can be seen that vaccines maintain high efficacy (85-95%) with respect to severe diseases, showing that Pfizer is still doing very well against the Delta variant, even in Israel. In the case of vaccine efficacy with respect to severe disease, the fact that both vaccination status and risk of severe disease are systematically higher in the older age group makes the overall efficacy numbers (when estimated without age stratification) misleading. Writes Morris.
Example between two groups
This effect is called “Simpson’s paradox», A well-known phenomenon in statistics, so sometimes a trend which applies within each group can be reversed if group information is not taken into account. In a group with 95% vaccinated, infections among the vaccinated would outweigh those among the unvaccinated simply because there are many more vaccinated people among whom the virus can spread. In a group with 20% vaccinees where everyone is exposed to the virus, most of the unvaccinated would get infected and most of the vaccinated would not. It all depends on the starting set.
This explains the high hospitalization rates in the US
Data from Israel suggested a reduced efficacy of the Delta variant vaccines, or a decline in the same efficacy after 4-6 months. This has fueled anti-vaccine sentiment, but as it turns out, the numbers do not “disprove” the vaccines.
The same difference between the hospitalization rates in the UK and the US (to the detriment of the United States, where hospitals are under stress) could be explained with the same caution, going to understand how many elderly people are not yet vaccinated in the two countries: the US has vaccinated their elders less compared to what is done in the UK. In the image above, Figure 3, compiled on CDC, NHS England and ONS data by Colin Angus, researcher at the School of Health and Related Research at the University of Sheffield, you see the margin of people without vaccination in the various age groups is grayed outa margin that in Great Britain almost does not exist in the elderly population.
Vaccines “hold” even against Delta
These analyzes referring to what the numbers say, can be applied to all percentages that “sound out of tune”, even those referring to victims or infections among vaccinated in the various countries: they must be studied by stratifying by age and vaccination rate. The ones described above are just examples. The bottom line is that there is very strong evidence that vaccines are highly effective in protecting against serious diseases, even for the Delta variant, and that also Israeli data, which on the surface seem to suggest that the Pfizer vaccine may have waning efficacy, in reality they confirm the goodness of immunization.
August 18, 2021 (change August 18, 2021 | 18:50)
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