Sampling Defective Pathways in Phenotype Prediction Problems via the Fisher's Ratio Sampler

In this paper, we introduce the Fisher's ratio sampler that serves to unravel the defective pathways in highly underdetermined phenotype prediction problems. This sampling algorithm first selects the most discriminatory genes, that are at the same time differentially expressed, and samples the high discriminatory genetic networks with a prior probability that it is proportional to their individual Fisher's ratio. The number of genes of the different networks is randomly established taking into account the length of the minimum-scale signature of the phenotype prediction problem which is the one that contains the most discriminatory genes with the maximum predictive power. The likelihood of the different networks is established via leave-one-out-cross-validation. Finally, the posterior analysis of the most frequently sampled genes serves to establish the defective biological pathways. This novel sampling algorithm is much faster and simpler than Bayesian Networks. We show its application to a microarray dataset concerning a type of breast cancers with very bad prognosis (TNBC). In these kind of cancers, the breast cancer cells have tested negative for hormone epidermal growth factor receptor 2 (HER-2), estrogen receptors (ER), and progesterone receptors (PR). This lack causes that common treatments like hormone therapy and drugs that target estrogen, progesterone, and HER-2 are ineffective. We believe that the genetic pathways that are identified via the Fisher's ratio sampler, which are mainly related to signaling pathways, provide new insights about the molecular mechanisms that are involved in this complex disease. The Fisher's ratio sampler can be also applied to the genetic analysis of other complex diseases.