  Cancer progresses with a change in the structure of the gene network in
normal cells. We define a measure of organizational hierarchy in gene networks
of affected cells in adult acute myeloid leukemia (AML) patients. With a
retrospective cohort analysis based on the gene expression profiles of 116
acute myeloid leukemia patients, we find that the likelihood of future cancer
relapse and the level of clinical risk are directly correlated with the level
of organization in the cancer related gene network. We also explore the
variation of the level of organization in the gene network with cancer
progression. We find that this variation is non-monotonic, which implies the
fitness landscape in the evolution of AML cancer cells is nontrivial. We
further find that the hierarchy in gene expression at the time of diagnosis may
be a useful biomarker in AML prognosis.
