Full Version: Israeli study re 4th dose of Pfizer
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A study came out on Tuesday that claims the protection of the 4th dose of Pfizer against infection wanes by the 8th week relative to those with 3 doses.  (But also shows an increase in protection against severe illness, but no sign of decrease over time of the study).

The description of their study looked good, but there's something that doesn't add up to me.

Table 2 is the basis for claim for decreasing protection over time.  It shows a rate ration of confirmed infections of the 4-dose group in various weeks versus the 3-dose and internal control groups.  The rate ratio for the 7 separate weeks are  1.5, 2.1, 2.0, 1.7, 1.5, 1.2, 1.1 vs 3-dose  (similar numbers vs internal control group, with highest ratio of 1.9).

Yet in Table 1, where they compare the aggregat4ed 4-dose groups (all weeks) vs 3 dose and internal control groups, the number of infections in the 4-dose group was 177/100K days,

3-dose group: 361/100K days, Internal control group: 388/100K days.

So the risk ratio for the aggregate groups is 361/177 = 2.04 for  3-dose vs 4-dose, and 388/177 = 2.19 for internal control group vs 4-dose.

I don't understand that aggregated number vs their individual weeks.  How can the maximum for the internal control group be 1.9 when viewed weekly, but 2.19 when aggregated?


Separate from that technical detail, were there systematic errors that invalidate their purported results of the decrease in effectiveness?

They do note that the risk of infection varied over time for the general population.  "Because incidences of both confirmed infection and severe illness increased rapidly during January 2022, the risk of exposure at the beginning of the study period was lower than at the end of the study period."  

Their study ran from early January to early March.   Their statement seems to be flat out  backwards when compared to the chart of daily new cases in Israel at The new case graph shows 41,000 new cases on the first day of the study (Jan 10), peaking at nearly 84,000 on day 14, dropping to 10,000 on the last day (Mar 2) of the study.  Indeed, it appears that the risk of infection in the general population was highest for those risk days when week 2 was early in the study and much less for those when week 8 was at the end of the study.  For those who got their 4th dose late in the study, their week 2 had much less chance of exposure than for those who got their 4th dose early in the study.   The paper gives no direct indication of how many people got their doses early versus late, but it probably can be estimated by using their risk days for each of the weeks.

There is also the effect of when individuals got COVID.  If a person got COVID in an early week, I expect they were excluded from later weeks.   If someone had a (relatively) riskier life style, they would more likely show up in the early infections.  Those remaining at 8 weeks would include the people that may be leading more secluded or otherwise cautious lifestyles.  I saw no discussion about any changes in lifestyles (perhaps due to addition or removal of government restrictions, or perhaps due to holidays or other reasons people may be exposed more or less than at other times) over the course of the study.

The details of the selection of the 3-dose group and the internal control group were not made clear.  For the 3-dose group, there is no event date to judge their weeks by.  Was it the same 3-dose group every week?   While "week N" for the study group was based on their date of vaccination, was the "week N" for the 3-dose group based on the week of the study?  Likewise, for the Internal Control Group, was the "week N" based on the week of the study?

Ah....  That may explain their claims, in a negative manner.  If week 8 of either control group was the last week of February, then the number of infections was low, and the number of infections were high in week 2.  But the study group for week 2 includes some (who had early vaccinations) when the infection rate of the population was high plus some (who had late vaccinations) when the infection rate of the population was low.   If there were NO reduction in infections due to the fourth dose, the results would still show an improvement of study group for week 2 versus control group for week 2.