The Odds Ratio in Biased-Sample Case-Control Studies
I learned something this morning. When you’re trying to estimate the impact of a two-valued X on some two-valued Y with Y=1 being a rare event, you can get an unbiased estimate of the relative risk, Pr(Y=1|X=1)/Pr(Y=1|X=0), even if your sample is biased because you oversampled mainly Y=1 observations. This is not just restricted to logit estimation either. I learned this reading The analysis of case-control studies by NE Breslow and NE Day, but I have a writeup at http://www.rasmusen.org/x/2007/oddsratio.pdf that is much clearer.