Integrative functional linear model for genome-wide association studies with multiple traits

Abstract

In recent biomedical research, genome-wide association studies (GWAS) have demonstrated great success in investigating the genetic architecture of human diseases. For many complex diseases, multiple correlated traits have been collected. However, most of the existing GWAS are still limited because they analyze each trait separately without considering their correlations and suffer from a lack of sufficient information. Moreover, the high dimensionality of single nucleotide polymorphism (SNP) data still poses tremendous challenges to statistical methods, in both theoretical and practical aspects. In this article, we innovatively propose an integrative functional linear model for GWAS with multiple traits. This study is the first to approximate SNPs as functional objects in a joint model of multiple traits with penalization techniques. It effectively accommodates the high dimensionality of SNPs and correlations among multiple traits to facilitate information borrowing. Our extensive simulation studies demonstrate the satisfactory performance of the proposed method in the identification and estimation of disease-associated genetic variants, compared to four alternatives. The analysis of type 2 diabetes data leads to biologically meaningful findings with good prediction accuracy and selection stability.

Keywords: Functional data analysis; Genome-wide association studies; Joint analysis of multiple traits; Penalization.

Fig. 1.

A simple example: true coefficient signals (grey solid line), estimated signals using the regression model with the smoothly clipped absolute deviation (SCAD) penalty (Fan and Li, 2001) (blue points), and estimated signals using the functional data analysis method fSCAD developed in Lin and others (2017) (orange dashed line). Upper right small plot: zoomed-in version with y-axis from 0.01 to 0.01.

Fig. 2.

Simulation: true coefficient functions under scenario of Case I (20% signal region). Blue solid line: ; Pink dashed line: . Left: and ; Middle: and ; Right: and .

Fig. 3.

Simulation: true and estimated coefficient functions under scenario of Case I with , correlation 0.9 and . Blue solid line (thin): ; Blue solid line (thick): ; Orange dashed line (thin): ; Orange dashed line (thick): .

Fig. 4.

Data analysis: estimated coefficient functions. Blue solid line: ; Orange dashed line: .