Mixture modeling of progression pathways of heterogeneous breast tumors

Uncovering pathways of tumor progression is an important topic in cancer research that has led to numerous studies, including several pathway models proposed and investigated by Sontag and Axelrod [Progression of heterogeneous breast tumors. J. Theoret. Biol. 210, 107–119, 2005]. In their comparative studies, the authors focused on relative goodness of fits of the various pathways, but a simple test revealed that even the “best” model did not provide an adequate explanation for the observed breast tumor data. The heterogeneous nature of breast tumors leads to the question of whether more than one (i.e., a combination of) pathway models are needed in order to explain the observed data. In the current paper, we address this question based on the finite mixture modeling framework and utilizing the four pathways proposed in Sontag and Axelrod as our individual pathway models. The expectation–maximization algorithm was used to derive estimates for the mixing proportions of the mixture models. Indeed, a two-pathway mixture provides a dramatic improvement over any of the single pathway models for explaining the data derived under either the Van Nuys or the Holland system. In particular, for data graded under the Van Nuys system, the mixture model was shown to be consistent with the observed data at the 1% significant level.