In our original studies, the combination of unsupervised analyses (hierarchical and k-means) and Kaplan-Meier survival curves, allowed the identification of three phenotypic clusters in B-CLLs, one corresponding to a good prognosis B-CLL subset, the remaining two clusters characterized by shorter median survivals, although with different immunophenotypic profiles .
The next logical step is the identification of the phenotypic signature, i.e. the minimal number of surface markers succinctly characterizing each B-CLL prognostic group. For this purpose, we chose to apply the "nearest shrunken centroid" algorithm, as proposed by Tibshirani et al [17, 20]., utilized by taking advantage of the publicly available PAM software package [19, 20]. This method basically derives from the "nearest centroid" classification. Briefly, the "nearest centroid" method computes a standardized centroid for the expression values of a given antigen in a given subgroup. A "centroid" has to be intended as a measure of the average expression of a given antigen in a given set/subset of samples. The "nearest centroid" classification method takes the antigen expression level of a new sample and compares it to each of these centroids. The subgroup whose centroid is closest to, is the predicted subgroup for that new sample.
The "nearest shrunken centroid" classification makes one important modification to standard "nearest centroid" classification. For a given antigen, it shrinks each centroid corresponding to each subgroup toward the overall centroid (i.e. the centroid computed by considering all the subgroups) by a fixed amount, called "threshold". This shrinkage consists of moving the centroid towards zero by a value corresponding to the threshold, setting it equal to zero if it hits zero. After shrinking the centroids, the new sample is classified by the usual nearest centroid rule, but using the shrunken centroids. This shrinkage has the operational advantages (i) to make the classifier more accurate by reducing the effect of noisy antigens, and (ii) to do an automatic selection of the antigens. In particular, if a given antigen is shrunk to zero for all the subgroups, then it is eliminated from the prediction rule. Alternatively, it may be set to zero for all subgroups except one; in this latter case, we learn that above- or below-average expression for that antigen characterizes that subgroup.
In the "nearest shrunken centroid" method, the user decides on the value for threshold to be employed. Typically, different choices are examined, and to guide the user to this choice, PAM performs k-fold (where k is usually set at the value of 10) cross-validation (CV) for a range of threshold values. Basically, a model is fitted on 90% of the sample and the class of the remaining 10% is predicted; this procedure is repeated 10 times, with each sample being part of the 10% utilized as tester at least once. The overall error is obtained by summing the errors of all the 10 parts added together. This procedure is done for a series of threshold values, and the number of CV misclassification errors for each threshold level allows the user to choose the value giving the minimum cross-validated misclassification error rate.
In the case of our original B-CLL studies, we randomly divided immunophenotypic data (123 cases) into training data (90 cases) and test data (33 cases) ; data from the 90 training samples were employed to train a classifier by means of 10-fold CV, while test samples were utilized as validation of the found procedures [17, 20]. In particular, we selected three increasing values of threshold (0.66, 1.32 and 2.0), all corresponding to acceptable misclassification errors on cross-validated data. By increasing the threshold level, the minimum number of antigens correctly classifying a given B-CLL case shrank in parallel. At the highest acceptable threshold level (2.0), close to the point at which CV error started to rise , as low as 12 phenotypic markers were selected . As reported , the estimated probabilities to classify B-CLL training and test samples within a given group (i.e. I, II or III) by using the threshold value of 2.0 were fairly good for training samples, less for test samples (e.g. 10-fold CV errors = 6/90; test error = 6/33). The accuracy of sample classification increased by lowering the threshold, although, in these cases, the number of essential phenotypic markers increased up to 18 (threshold = 1.32) and 23 (threshold = 0.66) antigens, always including the 12 markers selected by setting the threshold at the highest acceptable value (2.0) .
A list of the 12 selected markers overall representing the immunophenotypic signature of the three B-CLL subsets with different prognosis are reported in Fig. 3. Briefly, the good prognosis B-CLL group I was characterized by the specific above-average expression of CD62L, CD54, CD49c and CD25. Among B-CLL cases with shorter survival (groups II and III), two clearly recognizable immunophenotypic patterns were identified: the first one, with above-average expression of CD38, CD49d, CD29 and CD49e, was specific for group II B-CLLs, whereas group III was characterized by the expression below-average of all the above reported markers in the presence of a relative overexpression of some common antigens, such as CD23, CD20, SmIg and CD79b (Fig. 3) .
Even though information regarding correlations with IgVH mutations and ZAP-70 expression as well as the biological implication underlying differential expression of critical molecules in the newly identified B-CLL subsets have been extensively discussed elsewhere , we briefly report herein the most relevant concepts about this matter.