Log-Linear Models for Gene Association

• Published in: Journal of the American Statistical Association Vol. 104; no. 486; pp. 597 - 607
• Main Authors: Hu, Jianhua, Joshi, Adarsh, Johnson, Valen E.
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.06.2009; American Statistical Association; Taylor & Francis Ltd
• Subjects: Activating transcription factors; Algorithms; Applications; Applications and Case Studies; Bayes factor; Bayesian analysis; Bayesian method; Biology; Breast cancer; Deviance statistic; Ewens' sampling distribution; Exact sciences and technology; Gene expression; Gene interaction; General topics; Genes; Genetics; Genomics; Markov chain Monte Carlo; Markovian processes; Mathematics; Modeling; Monte Carlo simulation; Multivariate analysis; Parametric inference; Parametric models; Probabilities; Probability; Probability and statistics; Sampling; Sampling distributions; Sciences and techniques of general use; Statistical methods; Statistics; Rank statistic; Density estimation; Ewens' sampling distribution; Gene interaction; Probability distribution; Multivariate analysis; Statistical simulation; Microarray; Linear model; Sampling distribution; Parametric method; Discretization; Markov chain Monte Carlo; Distribution function; Contingency table; Selection method; Sampling; Posterior distribution; Bayes estimation; Data analysis; Approximation; Prior distribution; Model selection; Interaction; Loglinear model; Likelihood ratio; Statistical association; Bayes factor; Algorithm; Discretization method; Statistical method; Deviance statistic; Selection problem; Posterior probability; Application
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/jasa.2009.0025

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 that have 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 a microarray study for which it was possible to obtain biological confirmation of detected interactions.