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Fortunately Wisconsin GOP and @SCOTUS ensured good access to early voting to prevent long lines from forming at polling stations in Milwaukee County, which has highest #COVID incidence in state and >2x disparity in black-white mortality https://twitter.com/UrbanMilwaukee/status/1248724282777251845
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The >2-fold disparity statement was admittedly a hunch. To check that I wasn't spouting nonsense, I calculated the risk ratio.
It's 5.2.
The calculation is an example of how a risk ratio can be computed with limited information using the magic math of case-control studies. 1/
It's 5.2.
The calculation is an example of how a risk ratio can be computed with limited information using the magic math of case-control studies. 1/
From the @urbanmilwaukee article,
66% of deaths from virus were among black people.
27.2% of population of Milwaukee County is black.
Using these percents, calculate the exposure odds ratio (EOR) as if it were a case-control study. 2/
66% of deaths from virus were among black people.
27.2% of population of Milwaukee County is black.
Using these percents, calculate the exposure odds ratio (EOR) as if it were a case-control study. 2/
EOR = odds black among deaths / odds black in population = (0.66/(1-0.66))/((0.272/(1-0.272)) = 5.2
OK, that's the exposure odds ratio. What about the risk ratio?
RR = risk of COVID death among black people / corresponding risk among people who aren't black
3/
OK, that's the exposure odds ratio. What about the risk ratio?
RR = risk of COVID death among black people / corresponding risk among people who aren't black
3/
In this case, the EOR equals the risk ratio (RR).
No assumptions are needed to relate the two. By simply rearranging terms, the EOR=RR.
(A1/A0)/(N1/N0) = (A1/N1)/((A0/N0)
4/
No assumptions are needed to relate the two. By simply rearranging terms, the EOR=RR.
(A1/A0)/(N1/N0) = (A1/N1)/((A0/N0)
4/
where
A1 and A0 are exposed (black) and unexposed (not black) deaths
N1 and N0 are exposed and unexposed in total pop.
The algebraic rearrangement is the same math used to justify estimating a risk ratio or rate ratio in case-control studies without assuming rare outcome.
5/
A1 and A0 are exposed (black) and unexposed (not black) deaths
N1 and N0 are exposed and unexposed in total pop.
The algebraic rearrangement is the same math used to justify estimating a risk ratio or rate ratio in case-control studies without assuming rare outcome.
5/
In this case, the risk ratio is calculated as if from case-base sampling (sampling from the full population at risk), but there's no sampling here. The exposure distribution in the full population is known (27.2%).
6/
6/
As in a case-control study, the relation between the exposure odds ratio and the risk ratio is useful because it allows calculation of the RR without knowledge of absolute exposure-group-specific risks.
The RR was calculated here with % deaths black and % black in pop.
7/
The RR was calculated here with % deaths black and % black in pop.
7/
Finally, interpreting the risk ratio as the risk ratio that it is:
The risk of COVID death has been 5.2 times as high among the black population of Milwaukee County as the corresponding risk in the not-black population.
5.2
#epitwitter
8/8
The risk of COVID death has been 5.2 times as high among the black population of Milwaukee County as the corresponding risk in the not-black population.
5.2
#epitwitter
8/8
