Asymmetry causes chaos in our brains; lack of data helplessness. Start with this news headline.
So what does this mean? The simple answer is – nothing! Because the percentage quoted in the headline (and the subsequent text) is the death of unvaccinated in the total deaths. It makes an implicit assumption that in the system, an unvaccinated can get serious illness in about 70 – 30 compared to vaccinated. That does not give the right picture about the vaccine.
Take a location with 1000 people, 100 deaths and create three scenarios.
Scenario 1
| Vaccinated | Unvaccinated | |
| % of population | 90% | 10% |
| number of people | 900 | 100 |
| breakup of death | 30% | 70% |
| number of death | 30 | 70 |
| risk of dying | (30/900) = 0.033 | (70/100) = 0.7 |
| risk ratio | 0.047 |
Take the second scenario:
| Vaccinated | Unvaccinated | |
| % of population | 50% | 50% |
| number of people | 500 | 500 |
| breakup of death | 30% | 70% |
| number of death | 30 | 70 |
| risk of dying | (30/500) = 0.06 | (70/500) = 0.14 |
| risk ratio | 0.43 |
A third scenario
| Vaccinated | Unvaccinated | |
| % of population | 10% | 90% |
| number of people | 100 | 900 |
| breakup of death | 30% | 70% |
| number of death | 30 | 70 |
| risk of dying | (30/100) = 0.3 | (70/900) = 0.077 |
| risk ratio | 3.9 |
Discussion
Three scenarios using the same death-break up among vaccinated and unvaccinated tell three different stories. Scenario 1 shows a highly effective vaccine, the second is very modest, and the third is likely a substance to avoid! If you are not convinced, change the population from 1000 to any other number; you should get the same answer.
I agree journalists have a role in bringing information to the public. They also have a duty to provide data that enables the public to understand something. I doubt the news had any such intentions.
Finally
So, what is the big picture in Maharashtra? It’s difficult to say without details. But, assuming the number of deaths is more likely among adults, and its vaccination rates (at least one dose) are closer to 90%, the vaccine seems to protect as it promised.
