I'm trying to fit a logistic regression where there is a huge difference in the number of data points in either group (70 Vs 10,000). A statistician friend of mine has told me that this is a known problem with logistic regression and that for those kinds of numbers it overfits the data and basically doesn't work. When I bin the data and compare to the model, it is fairly obvious that this is definitely the case.
I'm wondering if anyone is aware of a better / more flexible method for fitting this kind of binary response data?
(I'm not a statistician by the way so go easy on me!)