  In medical research, it is often needed to obtain subgroups with
heterogeneous survivals, which have been predicted from a prognostic factor.
For this purpose, a binary split has often been used once or recursively;
however, binary partitioning may not provide an optimal set of well separated
subgroups. We propose a multi-way partitioning algorithm, which divides the
data into K heterogeneous subgroups based on the information from a prognostic
factor. The resulting subgroups show significant differences in survival. Such
a multi-way partition is found by maximizing the minimum of the subgroup
pairwise test statistics. An optimal number of subgroups is determined by a
permutation test. Our developed algorithm is compared with two binary recursive
partitioning algorithms. In addition, its usefulness is demonstrated with a
real data of colorectal cancer cases from the Surveillance Epidemiology and End
Results program. We have implemented our algorithm into an R package maps,
which is freely available in the Comprehensive R Archive Network (CRAN).
