Sunday, August 29, 2021

How to read medical statistics correctly?

The Bright Light News website claims to be "Shining a light on the Covid-19 narrative. Investigate. Facts matter." An article on the website dated August 23, based on statistics from the British government, is titled "More Fully Vaccinated Dying of Delta Variant Than Unvaccinated". This conclusion is surprising, and on the surface of it, is difficult to explain. I checked the original data of the British government website (see the small print after Source for the URL), and found that the Bright Light article quoted the data correctly (see Table 5 on pp.22-23): In the survey, 57.1% of the people who died of the Delta variant of the coronavirus in England were completely vaccinated, and 32.8% of those have not been vaccinated. So where is the problem?

The reality is that the vast majority of the people in the UK, about 90%, are fully vaccinated. Therefore, the ratios 57.1% and 32.8% cannot be compared in isolation. If the former were 90% and the latter 10%, i.e. matching the ratios of the vaccinated and unvaccinated population, and if there is no other factor that confounds the matter, we would be able to conclude that vaccination does not increase or decrease death rate; if the former were to exceed 90%, the latter less than 10%, then it would be that vaccination will increase the chance of dying. In case this is not clear enough, let's see another example. Imagine you have 1000 apples, 900 of them being red and 100 green. If there are a total of 10 apples that have gone rotten, 9 of them red and 1 green, and suppose there are no other confounding variables related to rotting of apples (e.g., some apples are kept in the refrigerator and others are not), then we can say that the color of the apple is unrelated to whether it rots, but we cannot say "Look! Red apples are more likely to rot than green apples, in fact by 9 times more likely!" If 6 out of 10 rotten apples are red and 4 green, we can't say that the color of the apple is unrelated to whether it's going bad or not. On the contrary, we should say that red ones are less likely to go bad, even though 6 is greater than 4!

Medical students must receive formal training in epidemiology. I have read such a textbook, in which there're plenty of such logical questions. But the case above is much simpler than the exercises in this type of textbook, and no special training is required to draw correct conclusions. Sadly, the website that claims "Shining a light" is lacking in basic logical thinking and misleads gullible people into vaccination rejection.