A pharmaceutically acceptable composition and method of therapy for a kinase-dependent malignancy in a patient in need of such therapy is provided. The composition contains, as the only active agents, the combination of (a) an inhibitor of c-Fos, (b) an inhibitor of Dusp-1, and (c) an inhibitor of a tyrosine kinase. The composition is administered to the patient in a dosing regimen for a period sufficient to provide therapy for kinase-dependent malignancy. Also provided is a method to eradicate leukemia initiating cells (LIC) or cancer stem cells (CSC) in a patient being treated with a tyrosine kinase inhibitor.