I’ve just heard a nice talk by Stephen Senn, entitled “In search of lost infinities. What is the ‘n’ in big data?”
The moral was that, in clinical trials and observational trials, everyone assumes that more data mean more accurate estimates; but, if you have not thought carefully about the model, and even sometimes if you have (because of unavoidable effects) this is not so, the variance of the difference between estimates may not tend to zero as the number of observations tends to infinity. This is especially the case with using historical data.
Somewhat technical, but you can read at least part of it here.
Perhaps best of all, he had some very nice one-liners. My favourite was this:
Being a statistician means never having to say you’re certain.