Adjusting sample sizes based on interim analyses in on-going clinical trials is a hot topic in statistical literature. There are oodles of plans and schemes concerning how to update sample sizes in on-going clinical trials, complete with all the bells and whistles about maintaining Type I error rates. But these formula-based methods can be naive and short-sighted; as with almost everything in the real world, "it's more complicated than that."
I will recount a true story of sample-size updates in a real-life clinical trial and discuss how the straight-forward statistical approach was inadequate. I will present a methodology that allows one to do unblinded early looks at the data and increase the sample size without suffering a Type I error penalty.
And, if time allows, I will present a demonstration of a Kelvin wheel-and-disk integrator (a mechanical analog computer that computes integrals) made entirely of Lego.