How can I improve the predictive power of this logistic regression model? I am using SPSS to analyze a data set which aims to predict whether individuals have cancer based on five symptoms (a, b, c, d, e). In this data set most individuals have cancer. I ran a Binary Logistic Regression and got the following output:

This tests the model with which only includes the constant, and overall it predicted 91.8% correct. I understand that the fact that I have significant predictors in the "Variables not in the Equation" table means that the addition of one or more of these variables to the model should improve its predictive power. 
I then looked at the model after all the predictors were included: 

The prediction is only very slightly different. Now it's predicting that two individuals will not have cancer. The overall percentage correct remains 91.8%. 


*

*Why did no improvement occur, despite the predictors being significant?

*Where should I go from here with this data set? Is it possible to improve the predictive power of the model without including new predictors?

*How should I assess the model? Is the fact that it doesn't improve over the model with only the constant evidence that the model is useless?


Full output viewable here.
Data set downloadable here as a google doc.
 A: One thing to check is whether there is a linear relationship between the log odds of cancer and each of your 5 predictor variables. This is an assumption in logistic regression. If this does not hold you might want to consider adding higher order terms to the model, or even a nonlinear relationship between log odds of cancer and some of the variables (by fitting a generalized additive model). 
From your output, it looks like these 5 predictors do not do a good job of classifying cancer vs non-cancer. 
I'll take a look at the data and add more to this question later. 
After taking a look at the data I have confirmed that indeed these variables are terrible at predicting cancer. If you plot the variables against cancer status you will see that, although for some of them the non-cancer patients have a little less variability, there is very little difference between the cancer and non-cancer patients. For example:

So if you told me that you had a patient who had a C variable of 30...I would have no idea if that is a cancer patient or a non-cancer patient. 
A bit more about your output: When you don't add any variables in it says you correctly predict 91.8% of the patients. The next table that lists significance values for adding in more variables means if you add them in one at a time. 
A: Ignore the classification tables completely.  They are not based on sound statistical methods, and are completely arbitrary.
