TRIO LOGIC REGRESSION - DETECTION OF SNP - SNP INTERACTIONS IN CASE-PARENT TRIOS

Statistical approaches to evaluate higher order SNP-SNP and SNP-environment interactions are critical in genetic association studies, as susceptibility to complex disease is likely to be related to the interaction of multiple SNPs and environmental factors. Logic regression (Kooperberg et al., 2001; Ruczinski et al., 2003) is one such approach, where interactions between SNPs and environmental variables are assessed in a regression framework, and interactions become part of the model search space. In this manuscript we extend the logic regression methodology, originally developed for cohort and case-control studies, for studies of trios with affected probands. Trio logic regression accounts for the linkage disequilibrium (LD) structure in the genotype data, and accommodates missing genotypes via haplotype-based imputation. We also derive an efficient algorithm to simulate case-parent trios where genetic risk is determined via epistatic interactions.

Semiparametric Latent Variable Regression Models for Spatio-temporal Modeling of Mobile Source Particles in the Greater Boston Area

Traffic particle concentrations show considerable spatial variability within a metropolitan area. We consider latent variable semiparametric regression models for modeling the spatial and temporal variability of black carbon and elemental carbon concentrations in the greater Boston area. Measurements of these pollutants, which are markers of traffic particles, were obtained from several individual exposure studies conducted at specific household locations as well as 15 ambient monitoring sites in the city. The models allow for both flexible, nonlinear effects of covariates and for unexplained spatial and temporal variability in exposure. In addition, the different individual exposure studies recorded different surrogates of traffic particles, with some recording only outdoor concentrations of black or elemental carbon, some recording indoor concentrations of black carbon, and others recording both indoor and outdoor concentrations of black carbon. A joint model for outdoor and indoor exposure that specifies a spatially varying latent variable provides greater spatial coverage in the area of interest. We propose a penalised spline formation of the model that relates to generalised kringing of the latent traffic pollution variable and leads to a natural Bayesian Markov Chain Monte Carlo algorithm for model fitting. We propose methods that allow us to control the degress of freedom of the smoother in a Bayesian framework. Finally, we present results from an analysis that applies the model to data from summer and winter separately