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 AML 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 non-trivial. We further find that the hierarchy in gene expression at the time of diagnosis may be a useful biomarker in AML prognosis.