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.

Model Evaluation Based on the Distribution of Estimated Absolute Prediction Error

The construction of a reliable, practically useful prediction rule for future response is heavily dependent on the "adequacy" of the fitted regression model. In this article, we consider the absolute prediction error, the expected value of the absolute difference between the future and predicted responses, as the model evaluation criterion. This prediction error is easier to interpret than the average squared error and is equivalent to the mis-classification error for the binary outcome. We show that the distributions of the apparent error and its cross-validation counterparts are approximately normal even under a misspecified fitted model. When the prediction rule is "unsmooth", the variance of the above normal distribution can be estimated well via a perturbation-resampling method. We also show how to approximate the distribution of the difference of the estimated prediction errors from two competing models. With two real examples, we demonstrate that the resulting interval estimates for prediction errors provide much more information about model adequacy than the point estimates alone.