When to divide data into training & test set in logistic regression? I am using Logistic Regression in a low event rate situation.
Overall universe: 46,000
Events: 420
Conventional logistic regression models divide the data into training and test sets and compute the error rates.  The final coefficients and threshold levels are chosen and a model is created.
OTH, I'm just trying to prove that so and so coefficient is significant and has positive association with the event in study.  I'm not developing a model as of now.  I don't focus on error rates (too many true negatives!) and chose my threshold level ~ hit rate.  
Should I consider dividing my universe into 2 samples, the conventional way?  With such a low event rate, I'm worried that doing this to bias my coeff. estimates.
 A: I do not think you need to divide the set if you are interested in the significance of a coefficient and not in prediction.  Cross validation is used to judge the prediction error outside the sample used to estimate the model.  Typically, the objective will be to tune some parameter that is not being estimated from the data.
For example, if you were interested in prediction, I would advise you to use regularized logistic regression.  This is similar to logistic regression, except for the fact that coefficients (as a whole) are biased towards 0.  The level of bias is determined by a penalty parameter that is typically fine tuned via cross validation.  The idea is to choose the penalty parameter that minimizes the out of sample error (which is measured via cross validation.)  When building a predictive model, it is acceptable (and desirable) to introduce some bias into the coefficients if said bias causes a much larger drop in the variance of the prediction (hence, resulting in a better model for predictive purposes.)
What you are trying to do is inference.  You want an unbiased estimate of a coefficient (supposedly to judge the effect that changing one variable may have on another).  The best way to obtain this is to have a well specified model and a sample as large as possible.  Hence, I would not split the sample.  If you are interested in sampling variation, you should try a bootstrap or a jacknife procedure instead.  
EDIT:
Short version: You want an unbiased model.  Cross validation can help you find a good predictive model, which are often biased.  Hence, I do not think cross validation is helpful in this situation.  
A: (1) Split sample is likely not the conventional way to approach this problem. Obviously conventions differ by fields of research and subject area. But I don't think it is unreasonable to say that bootstrapping for optimism would be the standard here, and I think you would have to justify in some detail if you were planning on using alternative methods.
(2) You're right, you might most probably don't need to validate model if you're only planning on looking at the association/coefficients. But you should know that the coefficients (and their p-values) are only valid for the pre-specified model. If you've included splines, variable selection etc. these values are inflated and might well have limited meaning. The validation process attempts to estimate the over-fitting of the model - the degree of optimism. It validates the model building process, not the model. If there is no model building - only a pre-specified model - not that useful for you. If there is model building - not unhelpful to have some estimate of how much it lead to over-fitting.             
A: Why not use cross validation, maybe with a higher X, like 10X. LOOCV might also be interesting but that could go really slowly. 
You could alternatively do some kind of more fancy custom CV where you leave one of the 420 positive events out, and the same proportion of the negative events (1/420 of them to preserve the relative proportion?) out at a given round. You would then have 420 CV iterations to calculate stats on, and you only give up training on a single positive sample at each round. That way you can get away with smaller training/testing splits. You could modify that to have fewer CV iterations if 420 would be too slow, maybe leave out 5 positives at a time, and 5/420 negatives?
