It's worth pointing out that traditional data brokers are able to track menstrual cycles based on purchase activity. Nobody can opt out of this and it's been going on for a few decades. It can be used for ad targeting by presenting the target with the optimal content for each week.
You run a 28 day autocorrelation and see what pops out. Start with the obvious purchases then artificially synchronize the purchase history of a group of women to be on the same phase and run another autocorrelation on their aggregate purchases to get the non-obvious signal.
I would imagine women who are buying menstrual products are very likely either about to begin their period or are in the midst of it. Also, things like midol are probably strong indicators.
Hmm, I'm not sure–all the women I know buy massive packs from Costco because it's something that they might as well buy in bulk and save money on. I didn't think of medicine, though–you're probably right about that.
For me the canonical example is this story in Forbes about a man who complained to Target about baby-product advertising directed at his teenage daughter.
To spoil an important point of the article: They had a personalized Target account and the daughter had been openly buying pregnancy related products for weeks, her father was the only one not aware of it.
It shows how this could be done for cycle analytics as well...If I remember the target case correctly it was not the buying of a pregnancy test, but general products like more body lotion etc. Things that correlate to the symptoms of the hormons present.