It's true, the results are weaker than if they had done a comparison study, but a lot of medical research is just post-facto observation reports. Like, to do a proper double blind study here, you'd have to start with healthy people and then knowingly expose some of them to something you suspect may be a carcinogen.

That's not going to pass the ethics board.

You can look at people who have already gotten cancer and try to lump them into those who have used talc-based products and those who haven't, but then how do you actually measure the impact of the talc there? Do you look at the number of patients who did use talc-based products vs those who didn't? Those might just reflect the rate at which those products are used among different subsets of the population.

The key bit here is that the kind of cancer they're looking at -- mesothelioma -- is known to be caused by asbestos. It's also known that talcum powder contains asbestos. So, the observational link here is seeing whether people with mesothelioma have had known significant exposure to environmental asbestos and how much exposure they've had to talc-based products. And if you can see in your observations that higher or more prolonged exposure to talc is correlated with increased mesothelioma rates, and can assume that these people -- based on their own memories -- have not been exposed to environmental asbestos at a rate higher than any other average person, then environmental exposure becomes an independent factor and you can assert the correlation between talc exposure and cancer rates.