  In medical risk modeling, typical data are "scarce": they have relatively
small number of training instances (N), censoring, and high dimensionality (M).
We show that the problem may be effectively simplified by reducing it to
bipartite ranking, and introduce new bipartite ranking algorithm, Smooth Rank,
for robust learning on scarce data. The algorithm is based on ensemble learning
with unsupervised aggregation of predictors. The advantage of our approach is
confirmed in comparison with two "gold standard" risk modeling methods on 10
real life survival analysis datasets, where the new approach has the best
results on all but two datasets with the largest ratio N/M. For systematic
study of the effects of data scarcity on modeling by all three methods, we
conducted two types of computational experiments: on real life data with
randomly drawn training sets of different sizes, and on artificial data with
increasing number of features. Both experiments demonstrated that Smooth Rank
has critical advantage over the popular methods on the scarce data; it does not
suffer from overfitting where other methods do.
