Confidence intervals for predictors in multivariate logistic regression I've got a question. 
I am dealing with medical data which contain 5 predictors and 1 binary outcome. When I try to classify the data using all 5 predictors I get 0.84 area under roc-curve which is quite good for me. However when I consider confidence intervals for these 5 parameters, I see that just 1 of them is significantly different from 0, its confidence interval doesn't include value "1". For all other predictors confidence interval include value 1 (from 0.78 to 1.2, for example).
When I try to classify the dataset based on just this 1 predictor (the one with good confidence interval), I still have good confidence interval for it but the area under roc-curve is 0.74 and combinations of specificity and sensitivity are really worse than in first example.
The question is: how should I treat the situation when not all of the predictors are significantly different from 0? Can I consider such deciding rule as a good one and use it in further analysis?
Thanks a lot!
 A: Much has been written about your issues on this site.  Briefly, statistical significance testing is not a good way to develop a multivariable regression model (note that multivariate would refer to more than one dependent variable).  A possible exception is using a very liberal $\alpha$ level such as 0.5 in a backwards step-down approach.  The higher $\alpha$ is the less damage to statistical inference and prediction.  But often better is to use penalization or data reduction.  The latter is easiest to implement, using tools such as variable clustering and redundancy analysis, all blinded to $Y$ to avoid bias/overfitting.
You might also use bootstrap validation for your 5-variable model to quantify how much of the $c$-index (area under ROC curve in this special case) is due to overfitting.
In the R package rms some of the functions that implement the above suggestions are lrm, validate, calibrate, and in the Hmisc package, varclus and redun.
Note that you are making strong linearity assumptions.
