The genetic etiologies of common diseases are highly complex and heterogeneous. Classic statistical methods, such as linear regression, have successfully identified numerous genetic variants associated with complex diseases. Nonetheless, for most complex diseases, the identified variants only account for a small proportion of heritability. Challenges remain to discover additional variants contributing to complex diseases. In this dissertation, we developed an expectile neural network (ENN) method and applied the method to genetic data analysis. ENN provides a comprehensive view of relationships between genetic variants and disease phenotypes and can be used to discover genetic variants predisposing to sub-populations (e.g., high-risk groups). We integrate the idea of neural networks into ENN, making it capable of capturing non-linear and non-additive genetic effects (e.g., gene-gene interactions). Through simulations, we showed that the proposed method outperformed an existing expectile regression when there exist complex relationships between genetic variants and disease phenotypes. We also applied the proposed method to the genetic data from the Study of Addiction: Genetics and Environment(SAGE), investigating the relationships of candidate genes with smoking quantity. Neural networks have been widely used in applications. However, few studies have been focused on the statistical properties of neural networks. We further investigate the Asymptotic properties of ENN (e.g., consistency). Simulations have been conducted to test the validity of the theory.
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