We describe a class of log-linear models for the detection of interactions in high-dimensional genomic data. This class of models leads to a Bayesian model selection algorithm that can be applied to data which has been reduced to contingency tables using ranks of observations within subjects and discretization of these ranks within gene/network components. Many normalization issues associated with the analysis of genomic data are thereby avoided. A prior density based on Ewens' sampling distribution is used to restrict the number of interacting components assigned high posterior probability, and the calculation of posterior model probabilities is expedited by approximations based on the likelihood ratio statistic. Simulation studies are used to evaluate the efficiency of the resulting algorithm for known interaction structures. Finally, the algorithm is validated in two microarray studies for which it was possible to obtain biological confirmation of detected interactions.
Statistical Methodology | Statistical Theory
Hu, Jianhua and Johnson, Valen E., "Log-linear Models for Gene Association" (October 2007). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 38.