  The topological data analysis method "concurrence topology" is applied to
mutation frequencies in 69 genes in glioblastoma data. In dimension 1 some
apparent "mutual exclusivity" is found. By simulation of data having
approximately the same second order dependence structure as that found in the
data, it appears that one triple of mutations, PTEN, RB1, TP53, exhibits mutual
exclusivity that depends on special features of the third order dependence and
may reflect global dependence among a larger group of genes. A bootstrap
analysis suggests that this form of mutual exclusivity is not uncommon in the
population from which the data were drawn.
