Phase 3 clinical trials for Covid-19 vaccines have been completed, and the "effectiveness" values have been made available. The trials involved a placebo arm, such that if the vaccine were completely ineffective, the control arm and the intervention arm would show the same (statistically equivalent) results. The difference in the intervention results are what was publicized as the effectiveness of the vaccine.
This question is about whether the same math can be applied to a situation where a group was split by whether they had recovered from the disease (equivalent to the intervention arm) or had never had the disease (equivalent to placebo arm). This was done in the SIREN trial.
I have assumed the numbers of individuals counted in the vaccine trials were were based on symptomatic individuals, so to be consistent, only symptomatic counts were used from the SIREN trial. So out of the 44 people in that trial that got sick, 30% were symptomatic, which leads to the value 13, below.
|Trial||Total||Vaccinated||Placebo||ACTUALLY GOT SICK Symptomatic No Intervention||Symptomatic EXPECTED count if completely Ineffective Intervention||OBSERVED (saw symptoms) Vaccinated||Reduction In Likelyhood (Effectiveness)|
|Prev Disease||No Prev Disease||No Prev Disease||Ineffective Intervention||Prev Disease||(Effectiveness)|
The above calculations, on the surface, seem to indicate that having recovered from the disease is slightly less beneficial than having had the course of the vaccinations. Is the premise behind this math generally sound? If not, why not? If generally sound, then, based on the procedures and details in the vaccine trials and SIREN trial, and what factors might detract from this kind of analysis, and what factors might support this kind of analysis?