Expectile Neural Networks for Genetic Data Analysis of Complex Diseases

Abstract

The genetic etiologies of common diseases are highly complex and heterogeneous. Classic methods, such as linear regression, have successfully identified numerous variants associated with complex diseases. Nonetheless, for most diseases, the identified variants only account for a small proportion of heritability. Challenges remain to discover additional variants contributing to complex diseases. Expectile regression is a generalization of linear regression and provides complete information on the conditional distribution of a phenotype of interest. While expectile regression has many nice properties, it has rarely been used in genetic research. In this paper, we develop an expectile neural network (ENN) method for genetic data analyses of complex diseases. Similar to expectile regression, ENN provides a comprehensive view of relationships between genetic variants and disease phenotypes, which can be used to discover variants predisposing to sub-populations. We further 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 genotype-phenotype relationships. We also applied the proposed method to the data from the Study of Addiction: Genetics and Environment (SAGE), investigating the relationships of candidate genes with smoking quantity.

Fig. 1.

A graphical representation of expectile neural network with one hidden layer

Fig. 2.

Performance comparison between ENN and ER under various non-linear relationships between genotypes and phenotypes and different expectiles (i.e., 0.1, 0.25, 0.5, 0.75, and 0.9) ENN: expectile neural network; ER: expectile regression; TR: training; TS: testing

Fig. 3.

Performance comparison between ENN and ER for different types of interactions and different expectiles (i.e., 0.1, 0.25, 0.5, 0.75, and 0.9) ENN: expectile neural network; ER: expectile regression; TR: training; TS: testing

Fig. 4.

An alternative architecture, a non-fully connected architecture, for gene-gene interaction analysis

Fig. 5.

Performance comparison between ENN with a fully connected architecture and ENN with a non-fully connected architecture for gene-gene interaction analysis FUL: ENN with a fully connected architecture; NONFUL: ENN with a non-fully connected architecture;TR: training; TS: testing

Fig. 6.

Performance comparison between ENN and QRNN under asymmetric, normal and heteroscedastic settings ENN: expectile neural network; TR: training; TS: testing

Fig. 7.

The conditional distribution of smoking quantity for five expectile levels (i.e., 0.1, 0.25, 0.5, 0.75, and 0.9)

Fig. 8.

The conditional distribution of CPD considering the interaction between CHRNA5 and CHRNA3

Fig. 9.

The conditional distribution of CPD considering the interaction between CHRNA5 and CHRNB4

Fig. 10.

The conditional distribution of CPD considering the interaction between CHRNB4 and CHRNA3