Center for Statistical Sciences Seminar
Abstract: An important follow-up step after genetic markers are found to be associated with a disease outcome is a more detailed analysis investigating how the implicated gene or chromosomal region and an established environment risk factor interact to influence the disease risk. The standard approach to this study of gene- environment interaction considers one genetic marker at a time, and therefore could misrepresent and underestimate the genetic contribution to the joint effect when one or more functional loci, some of which might not be genotyped, exist in the region and interact with the environment risk factor in a complex way. We develop a more global approach based on a Bayesian model that uses a latent genetic profile variable to capture all of the genetic variation in the entire targeted region and allows the environment effect to vary across different genetic profile categories. We also propose a resampling-based test derived from the developed Bayesian model for the detection of gene-environment interaction. Using data collected in the Environment and Genetics in Lung Cancer Etiology (EAGLE) Study, we apply the Bayesian model to evaluate the joint effect of smoking intensity and genetic variants in the 15q25.1 region, which contains a cluster of nicotinic acetylcholine receptor genes and has been shown to be associated with both lung cancer and smoking behavior. We find evidence for gene-environment interaction (P-value=0.016), with the smoking effect appearing to be stronger in subjects with a genetic profile associated with a higher lung cancer risk; the conventional test of gene-environment interaction based on the single-marker approach is far from significant.
Lefschetz Center for Dynamical Systems Seminar
Abstract: Glimm's theorem (1965) established existence of global-in-time weak solutions to the Cauchy problem for 1-dimensional hyperbolic systems of conservation laws, provided the data have small total variation. The key ingredient is a uniform bound on the spatial variation of the solution. There are counter examples showing that no naive extension of Glimm's theorem is available for ``large'' data in 1-d, nor for systems in several space dimensions. We outline these obstructions and consider two questions related to a priori bounds for (a) 1-d isentropic gas flow, and (b) multi-d, linear parabolic equations. The results for (a) are in collaboration with Geng Chen (post-doc, PSU).
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