Logistic Regression Research: 97% Concordance, No Sig Variables

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I am doing an independent research project and I have written a logistic regression program in SAS. The percent concordance is 97%, but hardly any variables are significant. Can anyone help me understand why this would happen?
 
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There are many possible reasons for this. Would you be able to describe the situation in more detail?
If all of the significance is in only a few variables, then you will not have many significant variables.
Otherwise, you may have some dependence issues, and the program can't determine which variables are better than others.
I would try reducing the model, and then applying some stepwise regression techniques to find the most significant factors.