The total sample sizes aren’t the problem. It’s the number of people who contracted cervical cancer. I should have been more specific originally: I would want more data to show that early vaccinations are more effective than late ones.
40,000 seems like a lot, but just using data from the late-vaccine group would get an average contraction rate of ~1. That’s enough for an outlier or two to be significant. If 2 of those 40,000 had contracted cervical cancer, it would be a hard sell to say early vaccines cause cancer (though some groups would eat that up). In the same way, I’m not fully convinced here that an early vaccine prevents it more effectively than a later one.
I want more early vaccine data, actually, so that’s good.
There is a significant decrease in cancer rates among vaccinated compared to unvaccinated, but the early/late divide is less clear. If my statistics is up to snuff (no guarantee there), you can expect an error of ~sqrt(n) in discrete data where n is your count. With the late vaccines, this means an error in the cancer rate of about 2 because they saw ~4 cases (3.2 * 124,000/100,000 ≈ 4). If this is actually overestimating, we could see the rate as 2/124000 or 0.64/40000. In this case, you wouldn’t necessarily expect to see any cases in a sample of 40000.
So it’s not clear from this that early is better than late, though it certainly doesn’t suggest that it’s worse.