Simpson's Paradox: Covid

A dataset on Delta Variant Covid-19 cases in the UK. This dataset gives a great example of Simpson's Paradox. When aggregating results without regard to age group, the death rate for vaccinated individuals is higher -- but they have a much higher risk population. Once we look at populations with more comparable risks (breakout age groups), we see that the vaccinated group tends to be lower risk in each risk-bucketed group and that many of the higher risk patients had gotten vaccinated. The dataset was brought to OpenIntro's attention by Matthew T. Brenneman of Embry-Riddle Aeronautical University. Note: some totals in the original source differ as there were some cases that did not have ages associated with them.

Usage

simpsons_paradox_covid

Format

A data frame with 286,166 rows and 3 variables:

age_group

Age of the person. Levels: under 50, 50 +.

vaccine_status

Vaccination status of the person. Note: the vaccinated group includes those who were only partially vaccinated. Levels: vaccinated, unvaccinated

outcome

Did the person die from the Delta variant? Levels: death and survived.

Source

Public Health England: Technical briefing 20

Examples

library(dplyr)
library(scales)
# Calculate the mortality rate for all cases by vaccination status
simpsons_paradox_covid |>
  group_by(vaccine_status, outcome) |>
  summarize(count = n()) |>
  ungroup() |>
  group_by(vaccine_status) |>
  mutate(total = sum(count)) |>
  filter(outcome == "death") |>
  select(c(vaccine_status, count, total)) |>
  mutate(mortality_rate = label_percent(accuracy = 0.01)(round(count / total, 4))) |>
  select(-c(count, total))
#> `summarise()` has grouped output by 'vaccine_status'. You can override using
#> the `.groups` argument.
#> # A tibble: 2 × 2
#> # Groups:   vaccine_status [2]
#>   vaccine_status mortality_rate
#>   <chr>          <chr>         
#> 1 unvaccinated   0.17%         
#> 2 vaccinated     0.41%         

# Calculate mortality rate by age group and vaccination status
simpsons_paradox_covid |>
  group_by(age_group, vaccine_status, outcome) |>
  summarize(count = n()) |>
  ungroup() |>
  group_by(age_group, vaccine_status) |>
  mutate(total = sum(count)) |>
  filter(outcome == "death") |>
  select(c(age_group, vaccine_status, count, total)) |>
  mutate(mortality_rate = label_percent(accuracy = 0.01)(round(count / total, 4))) |>
  select(-c(count, total))
#> `summarise()` has grouped output by 'age_group', 'vaccine_status'. You can
#> override using the `.groups` argument.
#> # A tibble: 4 × 3
#> # Groups:   age_group, vaccine_status [4]
#>   age_group vaccine_status mortality_rate
#>   <chr>     <chr>          <chr>         
#> 1 50 +      unvaccinated   5.96%         
#> 2 50 +      vaccinated     1.68%         
#> 3 under 50  unvaccinated   0.03%         
#> 4 under 50  vaccinated     0.02%