Citizen reports of AEs took off as injections rose by 114% in June-July 2021, and looking at injections 1, 2, and 3 reveals how much your risk increases with each shot
The case you consider regarding cumulative AEIR/I is the case of equal chance of AE for each jab. Indeed, 15,024 AEs for 8,768,355 injections is an overall AER of 0.171%, and the cumulative AEIR/I (probability of suffering at least one AE) after three injections would be 1 - (1 - 0.171%)^3 = 0.513%. Probability of suffering two or more AEs is negligible.
However, consider the two hypothetical cases at the extremes:
- Case 1: AEs only happen with the first jab (if you're through that, you're fine). In this case, the cumulative AEIR/I for three jabs is equal to 15,024 / 3,616,466 = 0.415%
- Case 2: AEs only happen with the third jab (the first two are just saline solution). In this case, the cumulative AEIR/I for three jabs is equal to 15,024 / 2,185,632 = 0.687%.
Another interesting possibility: the first jab determines if you're an AE case, and you either get no AE at all (no matter the number of jabs), or an AE for each jab. AEIR/I for three jabs is then 0.171% - but it means buy one, get two free.
You're right, my friend, about this (major) flaw in my risk/injection calculation. It's a small, highly abstract attempt at modelling, and I'm grateful you brought this up.
I'm not sure about the low probability of suffering two or more AEs; you know, a while ago I spent some time going through the EU database for 2021 to check out the 0-2yo AEs, and, yes, there were a number of cases with one AE, but there's also large number of incidents with multiple medical conditions. That said, the latter case is also a kind of reporting artefact, for the AE reporting is done according to int'l coding practices, hence 1 AE = any number of medical conditions from the (presumed) same source (in this case 1 injection).
Re your two hypotheticals: I don't (yet) know how to factor in the age/gender/comorbidity profiles ratios into my model. I mean, it's noted as confounding variables, but noone who publishes these data shows these breakdowns (although I'm fairly sure that these data are collected).
Re the final aspect--I'm unsure. If you take an injection, whatever follows must logically be 100% deterministic in terms of you cannot undo the injection. If, say, you take 3 injections and nos. 1 and 3 are saline or whatever, but injection 2 causes a severe AE, you'd still not get as low a AEIR/I of .17%, I think, for you as the 'vaccinee' don't know which injection is the hot one.
Hence, there's certainly additional variability involved, but the one parallel I could think of for this is Russian Roulette, played three or more times, but for every round to be played, a new gun with one bullet in the chambers is used. Sure, you'd get away scot-free two times, but the risk is always there, isn't it?
Your computations do not have to be wrong at all; there are just many models fitting the data (and in those models with high AE dependence between doses, multiple AEs can not be ignored). My anecdotal evidence attributes the highest chance for AE to the second dose (at least for Pfizer/Biontech).
The case you consider regarding cumulative AEIR/I is the case of equal chance of AE for each jab. Indeed, 15,024 AEs for 8,768,355 injections is an overall AER of 0.171%, and the cumulative AEIR/I (probability of suffering at least one AE) after three injections would be 1 - (1 - 0.171%)^3 = 0.513%. Probability of suffering two or more AEs is negligible.
However, consider the two hypothetical cases at the extremes:
- Case 1: AEs only happen with the first jab (if you're through that, you're fine). In this case, the cumulative AEIR/I for three jabs is equal to 15,024 / 3,616,466 = 0.415%
- Case 2: AEs only happen with the third jab (the first two are just saline solution). In this case, the cumulative AEIR/I for three jabs is equal to 15,024 / 2,185,632 = 0.687%.
Another interesting possibility: the first jab determines if you're an AE case, and you either get no AE at all (no matter the number of jabs), or an AE for each jab. AEIR/I for three jabs is then 0.171% - but it means buy one, get two free.
You're right, my friend, about this (major) flaw in my risk/injection calculation. It's a small, highly abstract attempt at modelling, and I'm grateful you brought this up.
I'm not sure about the low probability of suffering two or more AEs; you know, a while ago I spent some time going through the EU database for 2021 to check out the 0-2yo AEs, and, yes, there were a number of cases with one AE, but there's also large number of incidents with multiple medical conditions. That said, the latter case is also a kind of reporting artefact, for the AE reporting is done according to int'l coding practices, hence 1 AE = any number of medical conditions from the (presumed) same source (in this case 1 injection).
Re your two hypotheticals: I don't (yet) know how to factor in the age/gender/comorbidity profiles ratios into my model. I mean, it's noted as confounding variables, but noone who publishes these data shows these breakdowns (although I'm fairly sure that these data are collected).
Re the final aspect--I'm unsure. If you take an injection, whatever follows must logically be 100% deterministic in terms of you cannot undo the injection. If, say, you take 3 injections and nos. 1 and 3 are saline or whatever, but injection 2 causes a severe AE, you'd still not get as low a AEIR/I of .17%, I think, for you as the 'vaccinee' don't know which injection is the hot one.
Hence, there's certainly additional variability involved, but the one parallel I could think of for this is Russian Roulette, played three or more times, but for every round to be played, a new gun with one bullet in the chambers is used. Sure, you'd get away scot-free two times, but the risk is always there, isn't it?
Your computations do not have to be wrong at all; there are just many models fitting the data (and in those models with high AE dependence between doses, multiple AEs can not be ignored). My anecdotal evidence attributes the highest chance for AE to the second dose (at least for Pfizer/Biontech).
Interesting news from Germany (WELT article is behind paywall; haven't read it: https://www.welt.de/politik/deutschland/plus237106177/Coronavirus-Mehr-Impf-Nebenwirkungen-als-bisher-bekannt.html): health insurance providers have analyzed their data, which seem to indicate much higher AE rates (around 2.0%; the PEI official figures are at around 0.3%).
https://twitter.com/argonerd/status/1496571782094110721/photo/1