Risk classification with an adaptive naive bayes kernel machine model

Genetics play a major and complex role in many types of diseases. The complexity of the genetic architecture of human health and disease makes it difficult to identify genomic markers associated with disease risk or to construct accurate genetic risk prediction models. Accurate risk assessment is further complicated by the availability of a large number of markers that may be predominately unrelated to the outcome or may explain small amounts of genetic variation. Standard prediction models often rely on additive or marginal relationships between markers and the phenotype of interest. Marginal association based analysis has limited power to detect associations, while simple additive modeling performs poorly when underlying associations involve interactions and other nonlinear effects. Additionally, these methods do not utilize information regarding genetic pathways or gene structure. We propose a multi-stage method relating markers to disease risk through gene-sets identified from biological criteria. With a naive bayes kernel machine model, we estimate gene-set specific risk models that relate each gene-set to the outcome. Second, we aggregate across gene-sets by adaptively estimating weights for each set. The KM framework models the potentially non-linear effects of predictors without specifying a particular functional form. Estimation and predictive accuracy are improved with kernel PCA in the first stage and adaptive regularization in the second stage to remove non-informative regions from the final model. Prediction accuracy is assessed with ROC curves and AUC statistics. Numerical studies suggest that the model performs well in the presence of non-informative regions and both linear and non-linear effects.