Title: "Logic regression for localizing interacting quantitative trait loci"
Speaker: Malgorzata (Gosia) Bogdan, Politechnika Wroclawska, Instytut Matematyki i Informatyki, Wroclaw, Poland
Place: PHYS 223
Date: February 21, 2012, Tuesday, 4:30pm


Logic regression was introduced by RUCZINSKI et al. 2003 to identify important gene-gene interactions in association studies based on SNP data. The logic regression model can be understood as a natural extension of the standard generalized linear model. The role of regressors is played by logic expressions, dependent on the genotypes of one or several interacting SNPs. Thus, logic regression models allow for a natural description of gene-gene interactions, under which the mean value of the trait (or the disease risk) is modified only under a certain specific combination of genotypes of several SNPs. From the mathematical point of view, every logic regression model can be represented by a generalized linear model (GLM) with interactions and some restrictions on regression coefficients. However, standard estimation procedures for GLM, which do not use these restrictions, introduce the unnecessary noise as compared to the analysis with the proper logic regression model. This results in a larger number of degrees of freedom for the corresponding likelihood ratio statistics and a lower power of detection of the influence of the group of genes. Also, when using GLM, the natural logic predictors are projected both on the main effects and classical interactions, what additionally leads to a loss of power of detection of interacting effects. In this article we discuss the properties of the logic regression in the context of localizing quantitative trait loci (QTL) in experimental populations. We will present some theoretical results as well as the results of the simulation study and real data analysis comparing the performance of the classical methods of localizing QTL, based on the standard GLM models, with two versions of logic regression : logicFS of SCHWENDER et. al. 2008, and a new version of Bayesian Logic Regression, based on the Monte Carlo Logic Regression of KOOPERBERG and RUCZINSKI 2005. In the real data analysis methods based on logic regression pointed at some strong gene-gene interactions, which were missed by classical methods of QTL mapping.

This is a joint work with Magdalena Malina from Wroclaw University and Katja Ickstadt and Holger Schwender from TU Dortmund University.

Associated Reading:

1. Kooperberg C. and I. Ruczinski, 2005 Identifying Interacting SNPs Using Monte Carlo Logic Regression. Genetic Epidemiology 28: 157-170.
2. Ruczinski, I., C. Kooperberg, M. LeBlanc, 2003 Logic regression. J. Comput. Graphical Statist. 12(3): 474-511.
3. Schwender, H. and K. Ickstadt, 2008 Identification of SNP interactions using logic regression. Biostatistics 9: 187-198.

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