#### A Glossary of Terms Suppose that a trial is constructed in which half of the participants receive the vaccine and the other half receive a placebo. Here are keywords used to communicate the results of the trial. - **Attack rates**, $\mathsf{ARU}$ (unvaccinated group) and $\mathsf{ARV}$ (vaccinated group). Proportion of members in each group who were assessed positive for the condition of interest. On a scale from 0 to 1. - **Relative Risk**, $\mathsf{RR}$: Attack rate among vaccinated participants divided by the attack rate among unvaccinated participants. - **Vaccine efficacy**, $\mathsf{VE}$: percentage reduction in attack rate among the vaccinated relative the that of the unvaccinated. | | Positive for condition | Negative for condition | Total | | ---------------: | :--------------------: | :--------------------: | :-------------------------------: | | **Vaccinated** | $V_+$ | $V_-$ | $V_\mathrm{tot} = V_+ +V_-$ | | **Unvaccinated** | $U_+$ | $U_-$ | $U_\mathrm{tot} = U_+ + U_-$ | | **Total** | $V_+ + U_+$ | $V_- + U_-$ | $V_\mathrm{tot} + U_\mathrm{tot}$ | The attack rates and the the relative risk can be computed as follows: $ \mathsf{ARU} = \frac{U_+}{U_\mathrm{tot}}, \, \mathsf{ARV} = \frac{V_+}{V_\mathrm{tot}}, \, \mathsf{RR} = \frac{\mathsf{ARV}}{\mathsf{ARU}}. $ Vaccine efficacy is then $ \mathsf{VE} = 100 \times \frac{\mathsf{ARU} - \mathsf{ARV}}{\mathsf{ARV}} = 100 \times (1 - \mathsf{RR}). $ ### Covid-19 Vaccine Data The Moderna vaccine VE_mRNA1273, [[2020 Baden COVID Moderna.pdf]] (2020) | | Covid-19 cases | No Covid-19 detected | Total | | ---------------: | :------------: | :------------------: | :----: | | **Vaccinated** | 11 | 15,199 | 15,210 | | **Unvaccinated** | 185 | 15,025 | 15,210 | | **Total** | 196 | 30,224 | 30,420 | #### On communication with the public The Misunderstanding of Vaccine Efficacy K Tentori, A Passerini, B Timberlake, S Pighin Social Science & Medicine 289 (2021) 114273 ![[2021 Tentori Misunderstanding Vax Efficacy.pdf]]