In the Gerds and Kattan Medical Risk Prediction text they mention that " Including the cohort variable as a random effect in a logistic or Cox regression model would make it possible to predict new patients from other centers. However, doing this is not well motivated. There are two problems. The first is that adding a random effect corresponds to conditioning on another predictor variable (the random effect), although this variable has not been observed. Hence, if the random effect turns out to be important this means that an important predictor variable is not available and hence the predicted risk may be systematically too high or too low. The second problem is related to the non-collapsability of logistic regression models and Cox regression models."

If this is accurate what is the appropriate method for dealing with prognostic factor models using data from multiple centers?