Statistical Detection of Boolean Regulatory Relationships

A statistic tool for the detection of multivariate Boolean relationships is presented, with applications in the inference of gene regulatory mechanisms. A statistical test is developed for the detection of a nonzero discrete Coefficient of Determination (CoD) between predictor and target variables. This is done by framing the problem in the context of a stochastic logic model that naturally allows the inclusion of prior knowledge if available. The rejection region, p-value, statistical power, and confidence interval are derived and analyzed. Furthermore, the issue of multiplicity of tests due to presence of numerous candidate genes and logic relationships is addressed via FWER- and FDR-controlling approaches. The methodology is demonstrated by experiments using synthetic data and real data from a study on ionizing radiation (IR) responsive genes. The results indicate that the proposed methodology is a promising tool for detection of gene regulatory relationships from gene-expression data. Software that implements the COD test is available online as an R package.