There are several components to your question - but first I would ask why is your sample so skewed? You have an under-sampled training set which as you point out is odd. Can you assume that the two classes were sampled randomly from the population? If not, that is your most serious problem.

Assuming representative samples, the issues are:

1. Will this imbalance keep the classifier from properly discriminating between classes? Maybe. You must cross validate any resulting model so this should be testable and you may find you need over sample the negative cases to get the data set into balance. It depends on the type of classifier being used and the data. If you are using random forests or GBM I might not be concerned. If you are using a single decision tree, i would.

2. Will the predicted probabilities from the model align to the population. The answer is no. If this is important to your application (i.e. the model must be well calibrated and not just concerned with ranking or separating the classes) it is a problem but can be overcome. Any time a training data set is used where the class density does not match the population, the resulting probabilities of class membership will be biased. Here is a general purpose way to re-calibrate them:

LINK

There are several components to your question - but first I would ask why is your sample so skewed? You have an under-sampled training set which as you point out is odd. Can you assume that the two classes were sampled randomly from the population? If not, that is your most serious problem and potentially not something you can recover from. The best you can do is build a model, calibrate it and then test it in a pilot on the population.

Assuming representative samples, the issues are:

1. Will this imbalance keep the classifier from properly discriminating between classes? Maybe. You must cross validate any resulting model so this should be testable and you may find you need over sample the negative cases to get the data set into balance. It depends on the type of classifier being used and the data. If you are using random forests or GBM I might not be concerned. If you are using a single decision tree, i would.

2. Will the predicted probabilities from the model align to the population. The answer is no. If this is important to your application (i.e. the model must be well calibrated and not just concerned with ranking or separating the classes) it is a problem but can be overcome. Any time a training data set is used where the class density does not match the population, the resulting probabilities of class membership will be biased. Here is a general purpose way to re-calibrate them:

LINK