Haplotype-based association analysis via variance-components score test

Abstract

Haplotypes provide a more informative format of polymorphisms for genetic association analysis than do individual single-nucleotide polymorphisms. However, the practical efficacy of haplotype-based association analysis is challenged by a trade-off between the benefits of modeling abundant variation and the cost of the extra degrees of freedom. To reduce the degrees of freedom, several strategies have been considered in the literature. They include (1) clustering evolutionarily close haplotypes, (2) modeling the level of haplotype sharing, and (3) smoothing haplotype effects by introducing a correlation structure for haplotype effects and studying the variance components (VC) for association. Although the first two strategies enjoy a fair extent of power gain, empirical evidence showed that VC methods may exhibit only similar or less power than the standard haplotype regression method, even in cases of many haplotypes. In this study, we report possible reasons that cause the underpowered phenomenon and show how the power of the VC strategy can be improved. We construct a score test based on the restricted maximum likelihood or the marginal likelihood function of the VC and identify its nontypical limiting distribution. Through simulation, we demonstrate the validity of the test and investigate the power performance of the VC approach and that of the standard haplotype regression approach. With suitable choices for the correlation structure, the proposed method can be directly applied to unphased genotypic data. Our method is applicable to a wide-ranging class of models and is computationally efficient and easy to implement. The broad coverage and the fast and easy implementation of this method make the VC strategy an effective tool for haplotype analysis, even in modern genomewide association studies.

Figure 1.

The 10 largest eigenvalues of matrix W^-1/2P₀SP₀W^-1/2. The eigenvalues are dominated by the first few and decrease rapidly to 0. The eigenvalues are averages across the 1,000 replications in the simulation scenario of high haplotype diversity and an allele frequency of 0.1 for binary traits.

Figure 2.

QQ-plots of the test statistic T_τ. We defined the standardized T_τ as and the scaled T_τ,i as T_τ,i/b_i, where b_i is the scale parameter of the Gamma approximation. The left panels show the standardized T_τ against the expected quantiles from Normal(0,1). The right panels show the scaled T_τ against the expected quantiles from the Gamma(,1). The upper panels are for quantitative traits, and the lower panels are for binary traits. These QQ-plots suggest that, for both trait types, T_τ values deviate from the normal distribution, as predicted by the usual asymptotic theory, and the empirical distribution of T_τ values can be approximated by a Gamma (a_i,b_i) distribution appropriately.

Figure 3.

P values from the ALS data analysis around the most promising SNP reported by Schymick et al. (i.e., SNP rs4363506, with location indicated by the arrows). The P values are presented on the scale of negative logarithm of base 10. A, P values of the three-SNP haplotype test by use of the VC-score method (solid line) and P values of a single-SNP genotypic test (dotted dashed line). B, P values of the three-SNP haplotype test by use of the VC-score method (solid line) and P values of the three-SNP haplotype test by use of the fixed-effect method (dashed line). C, P values of the four-SNP haplotype test by use of the VC-score method (solid line) and P values of the four-SNP haplotype test by use of the fixed-effect method (dashed line).