Overfitting in prediction models - is it a problem only in high dimensions?

The growing recognition that human diseases are molecularly heterogeneous has stimulated interest in the development of prognostic and predictive classifiers for patient selection and stratification. In the process of classifier development, it has been repeatedly emphasized that in situations where the number of candidate predictor variables is much larger than the number of observations, the apparent (training set, resubstitution) accuracy of the classifiers can be highly optimistically biased and hence, classification accuracy should be reported based on evaluation of the classifier on a separate test set or using complete cross-validation. Such evaluation methods have however not been the norm in the case of low-dimensional, p