Vaccine effectiveness and confounding

Factors affect both vaccination status and Covid-19 death rates.

Anthony B. Masters


One major question during the pandemic is: how effective are vaccines? Observational studies look at people without vaccines, comparing outcomes to vaccinated people.

Two possible study designs are:

  • Prospective cohort: the study follows groups of individuals over time. The study then examines how vaccination affect outcomes (such as Covid-19 deaths).
  • Matched control: the study matches vaccinated people to similar people without vaccination.

Systematic errors may remain in these observational analyses. Such studies use statistical analysis to adjust for confounding factors. Confounding variables affect both exposures and outcomes of interest. Failing to control for a confounding variable can lead to biased results.

A prominent confounding factor is age.

To see the influence of confounding factors, we look at the Delta (B.1.617.2) case table in the latest PHE briefing:

  • Non-vaccinated: 34 deaths out of 35,521 cases.
  • Vaccinated: 37 deaths out of 17,642 cases.

Should we conclude vaccines double the Delta case fatality rate? No.

This is simplified. (Image: DAGitty)

In England, vaccine prioritisation uses age groups. As a result, older people have higher vaccination coverage than younger people.

Some older age groups have over 90% coverage with one dose. (Image: Public Health England)

Older people are more likely to die after a Covid-19 infection than younger people. In October 2020, ICL estimated the infection fatality rate among those aged 15–19 was 0.02% (0.00% to 0.17%). For people aged 90 and over, it was around 16% (9% to 28%). Estimated infection fatality rates which do not adjust for sero-reversion are higher.



Anthony B. Masters

This blog looks at the use of statistics in Britain and beyond. It is written by RSS Statistical Ambassador and Chartered Statistician @anthonybmasters.