Why do you tink the prediction for new patients is off? The only way to measure that is with simulated data. Predictions for new patients (or in general new groups in a hierarchical model) involves three kinds of variability: estimation variability, variability in the patients, then sampling variation.
P.S. I'm still having trouble tracking Discourse topics, so I occassionally go back and try to clear out ones I missed the first time around (if anyone knows how to set the "new" to include everythng that's come out that I haven't read, it'd be an enormous help).