Conditional probabilities and imperfect vaccines III

Exploring a paradox of high vaccine coverage.

In the Washington Post, columnist Kate Cohen argues for two regular statistics:

I propose a running tally in bold type: covid deaths among unvaccinated vs vaccinated citizens. Two numbers, side by side.

This proposal may sound simple. Many public health analyses demonstrate effectiveness of approved Covid-19 vaccines against infection and hospitalisation. In a population without high coverage, most deaths from a disease will be among those not vaccinated.

Survival analysis suggests high effectiveness against hospital admission. (Image: Public Health England)

When coverage widens, immunisation failures can outnumber unvaccinated outcomes. There are numerous explanations of this phenomenon, including in my co-written column in The Observer.

Going forwards in the calculation

One way is to take the reader through each step of the calculation. Suppose we had vaccine coverage of 95%. The vaccine is 94% effective against hospitalisation with a disease.

Assume 1,000 people would go to the hospital without the vaccine. Vaccine coverage is 95%, so 950 of our cohort got their doses. In the whole group, 50 are not vaccinated, and so go to hospital. The effectiveness of an unused vaccine is zero.