data-raw/formula.md

In QuartzSoftwareLLC/shiny.fluToolKit: What the Package Does (One Line, Title Case)

Prevention

The prevention module allows you to input a theoretical VE to calculate the number of prevented illness, medical visits, hospitalization, and deaths at that VE. The formula used to calculate these metrics is derived below.

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Using unvaccinated attack $A_{uv}$ and vaccinated attack rate $A_v$, we can calculate vaccine effectiveness $E$.

$$E = \frac{A_{uv} - A_v}{A_{uv}}$$

Which can be simplified to

$$ E = 1 - \frac{A_v}{A_{uv}}$$

Attack rate ($A$) can be calculated from incidence ($I$) and population ($P$):

$$A = I / P$$

Furthermore, vaccinated population ($P_v$) and unvaccinated population ($P_{uv}$) can be calculated using total population ($P$) and vaccine uptake $u$.

$$P_v = P * u$$

$$P_{uv} = P * (1 - u)$$

Consequently,

$$E = 1 - \frac{I_v}{P*u} / \frac{I_{uv}}{P (1 - u)}$$

$I_{uv}$ is the difference between total incidence ($I$) and vaccinated incidence ($I_v$)

$$E = 1 - \frac{I_v}{P*u} / \frac{I - I_{v}}{P (1 - u)}$$

Solving for ($I_v$)

$$I_v = \frac{(1 - E) * u * I}{1 - u + u * (1 - E)} $$

After solving for ($I_v$), we calculate the number of cases in the vaccinated population if effectiveness were 0 ($I_{E0}$)

$$ I_{E0} = \frac{I_v}{1 - E} $$

Next, we calculate the number of predicted cases ($I_n$) at the new effectiveness provided ($E_n$)

$$ I_n = I_{E0} * (1 - E_n) $$

Lastly, we take the difference between ($I_n$) and ($I_v$) to calculate the change in incidence ($I_{\Delta}$)

$$I_{\Delta} = I_n - I_v

QuartzSoftwareLLC/shiny.fluToolKit documentation built on April 28, 2022, 6:25 a.m.