[skybrian]

I largely agree, except that choosing a denominator of 8 billion is really dubious. The number of people for whom this study will result in them getting a hearing aid when they otherwise wouldn't is unknown, but unlikely to be nearly that high.

You can't actually do that math. Or rather, you can but the inputs to your spreadsheet are whatever you made up.

[LeifCarrotson]

Attempting to do the math is better than the alternative of going with your gut. The numerator is also an overestimate, not everyone suffered excessive cognitive decline.

If this was a critical decision (like it was for the authors of the study, unlike it is for the authors of Internet comments) you can work for better inputs.

Most importantly, though, we're trying to understand if that fraction is greater than one or less than one. There's a number that might be 8 billion or might be a tenth or a hundredth of that in the denominator, and a number that's on the order of 100 - or maybe 10x that, or maybe 1/10th that. But it doesn't matter, because it's not close, the ratio is still a million to one.