Shrinkage, cross validation calibration, and the construction of prognostic indices

The use of shrinkage methods for the construction of prognostic indices has been paid increasing attention in the literature on medical statistics in the last years. One approach for the construction of a shrinkage factor is cross validation calibration as suggested by van Houwelingen and le Cessie (1990). We investigate this approach in more detail. First we try to clarify, why shrinkage factors constructed by cross validation calibration tends to be smaller than 1. Second we explain, why use of this shrinkage factor results in an improvement of the average prediction error. Third we argue that nevertheless such a shrinkage cannot be recommended for the construction of prognostic indices. Fourth we explain that selection bias resulting from the application of model building procedures is not necessarily an argument in favour of shrinkage methods. Finally we conclude that it is necessary to rethink the use of loss functions like the average prediction error in constructing prognostic indices.