An Efficient Nonlinear Regression Approach for Genome-Wide Detection of Marginal and Interacting Genetic Variations

Genome-wide association studies have revealed individual genetic variants associated with phenotypic traits such as disease risk and gene expressions. However, detecting pairwise interaction effects of genetic variants on traits still remains a challenge due to a large number of combinations of variants (

$$\sim 10^{11}$$

SNP pairs in the human genome), and relatively small sample sizes (typically

$$< 10^{4}$$

). Despite recent breakthroughs in detecting interaction effects, there are still several open problems, including: (1) how to quickly process a large number of SNP pairs, (2) how to distinguish between true signals and SNPs/SNP pairs merely correlated with true signals, (3) how to detect non-linear associations between SNP pairs and traits given small sample sizes, and (4) how to control false positives? In this paper, we present a unified framework, called SPHINX, which addresses the aforementioned challenges. We first propose a piecewise linear model for interaction detection because it is simple enough to estimate model parameters given small sample sizes but complex enough to capture non-linear interaction effects. Then, based on the piecewise linear model, we introduce randomized group lasso under stability selection, and a screening algorithm to address the statistical and computational challenges mentioned above. In our experiments, we first demonstrate that SPHINX achieves better power than existing methods for interaction detection under false positive control. We further applied SPHINX to late-onset Alzheimer’s disease dataset, and report 16 SNPs and 17 SNP pairs associated with gene traits. We also present a highly scalable implementation of our screening algorithm which can screen

$$\sim $$

118 billion candidates of associations on a 60-node cluster in

$$<{}5.5$$

hours. SPHINX is available at http://www.cs.cmu.edu/

$$\sim $$

seunghak/SPHINX/.