Arithmetic in kind

In the recent issue of Nature (June 16), a short article was published about testing a new drug against melanoma. It says that the new medicine works on almost half of the patients, and after six months 84% ​​of patients remain alive. In the control cohort, which was treated with an old drug that only worked on 5% of patients, 64% survived.

What is the effectiveness of the new drug? Let x% of those affected by the medicine survive, and y% of those not affected by it. Then, based on the test results, you can create the equation 0.5x+0.5y=84, and based on the control results, the equation 0.05x+0.95y=64. Having solved this system, we find that x=106.2%.

But maybe the point is that the effectiveness of drugs varies? Let's look at some extreme cases. If the old medicine is not effective at all, i.e. it's just a placebo, we get x=104%. On the contrary, if the effectiveness of the old medicine is absolute and everyone on whom it affected survived, then x = 105.9%. Well, let’s say the old medicine is poison, and all those it affected died. But even then x=100.6%.

The only way to achieve the natural condition x<100% is to assume that “almost half” is more than half, or more precisely, 57.(7)% (seven per period). Which already contradicts the Russian, i.e., English, language...

M.G.