While I expect most women buy in advance, I expect they also don't buy enough and so are out there mid-period at least some of the time. Their cycles also affect their buying patterns, so even women who are stocking up are more likely to buy differently in different parts of the cycle.
The real question is what does the manager do with the data. Across a city on any given day there are about the same number of women in every day of their cycle so it isn't like they are marking up pads on the 25th-28th day of the month to get women who didn't stock up. As such I don't think this data is useful, what is useful is when they discover a women missed her cycle and thus needs to get ads for pregnancy wear in a couple months. Since that is their need for data, the fact that it is noisy and not very accurate is still close enough.
That said, they probably are more accurate than you would expect despite all the noise. Not 100% accurate, but being greater than 50% accurate is a lot better than chance and should be obtainable.
Just knowing what is bought together with menstrual products can influence how they're marketed. It can influence where certain products are placed on shelves relative to menstrual products, where and how they're marketed, which brands in your conglomerate to co-market with, and so on. This is the most innocent use of data in aggregate. The real creepy shit follows now that it's individualized and easily deanonymized.
> The real question is what does the manager do with the data.
Direct-mail (or these days, in-app with notifications) coupons. If you know you'll pay full price at CVS, but it's 30% off at Rite-Aid, you'll go to Rite-Aid and buy other stuff as long as you're making the trip.
I mean, maybe there really are enough women buying last-minute to be able to predict, at least for those women -- and identify who those women are.
If that is your motivation you just blanket send those advertisements all month. Because you want women to think of you when they have need. Some women are stocking up before they have need, and so the coupon when they are having their period is when they won't be buying supplies. Even those who are buying as they have need, if they are out they are buying from the closest store at whatever price, while those who are not in an emergency know where the low prices are (wal-mart or such)
So... the risk to women's safety is that they might end up paying less for hygiene products?
No, the risk to women's safety is that someone the woman doesn't want to know, could find out that they're pregnant. (Or using birth control or whatever)
Someone being an advertiser buying the data?