How much better is a vaccine whose efficacy is 90% than one whose efficacy is 70%?
With a 90% effective vaccine, you have a 20% lower chance of contracting a diseases after being exposed to it. Therefore, our intuition tells us that the 90% vaccine is 20 percentage points better. But is there more to it?
Let’s say a disease infects 10% of a population of 1000 population.
Without a vaccine, 100 people would fall sick. With a 70% effective vaccine, merely 30 people would fall sick. With a 90% vaccine, only 10 people would fall sick. A 90% vaccine would leave 3x fewer people sick than a 70% vaccine (30/10) and 10x (100/10) fewer patients than no vaccine at all. A 99% effective vaccine would only have 1 person falling sick – it reduces incidence by a whopping 30x when compared to a 70% vaccine.
The statistical measures that experts use can often fool our intuition. While percentage efficacy maybe a useful metric for an epidemiologist, we perhaps need to translate it into another measure (e.g. times fewer infections) for more common folks to understand their importance.
If the common person doesn’t understand a statistical measure, finding a better depiction is easier than having everybody take a university course.