Things: 2022

Saturday, December 17, 2022

Graphs from NPR, December 6, 2021:

Click on image for a larger view

Fun with math

The following is an email I sent on February 14, 2022

    According to the CDC, unvaccinated individuals are 20 times more
    likely to die of Covid than vaccinated and boosted individuals.

    According to polling by the Kaiser Family Foundation, 9% of
    Democrats are unvaccinated, whereas 36% of Republicans are
    unvaccinated. This is consistent with long term polling by
    Kaiser and others.

    Using these self-reported vaccination rates and the CDC's
    probability data, we can employ some simple math to predict
    relative death rates between Democrats and Republicans. Such
    calculations track closely with other data and analysis, and
    county-level death rates.

    For simplicity, assume there are equal numbers of Democrats
    and Republicans, with N denoting the number of each of them.

    Let U be the probability of an unvaccinated person dying, and
    Let V be the probability of a vaccinated and boosted person dying

    So according to the CDC:

        U = 20 x V

    Also:

        U x 0.09 x N    is the number of unvaccinated Democrats
                        expected to die

        V x 0.91 x N    is the number of vaccinated Democrats
                        expected to die

        U x 0.36 x N    is the number of unvaccinated Republicans
                        expected to die

        V x 0.64 x N    is the number of vaccinated Republicans
                        expected to die

    The total number of Democrats expected to die is:

          (U x 0.09 x N) + (V x 0.91 x N)

        = (20 x V x 0.09 x N) + (V x 0.91 x N)

        = (1.8 x V x N ) + (0.91 x V x N)

        = 2.71 x V x N

    The total number of Republicans expected to die is:

          (U x 0.36 x N) + (V x 0.64 x N)

        = (20 x V x 0.36 x N) + (V x 0.64 x N)

        = (7.2 x V x N) + (0.64 x V x N)

        = 7.84 x V x N

     The ratio of expected Republican deaths to expected
     Democratic deaths is:

        7.84 x V x N     7.84
        ------------ = ----     =   2.89
        2.71 x V x N     2.71         ====

    Thus, based on self-reported partisan affiliation, self-reported
    rates of vaccination, and the relative death rates between
    vaccinated and unvaccinated populations, almost 3 times as many
    Republicans as Democrats would be expected to die of Covid.

    And when partisan affiliation is inferred at the county level
    using election returns as a proxy, we see that actual
    on-the-ground vaccination rates broadly track with polling
    results. Across more than 3,000 counties nation-wide, redder
    counties have significantly lower vaccination rates than bluer
    ones.

    Finally, when partisan affiliation is inferred at the county
    level using election returns as a proxy, we see that actual
    on-the-ground death rates track with what we would expect from
    the calculations above that use self-reported data.

    And once again, all of this is succinctly encapsulated in the
    graph attached to this email, that shows that deaths increase
    sharply across a gradient from blue to red counties.

    As we'd expect with a strong result, regardless of the angle
    from which you approach the analysis, the conclusion is the same.