Kernel Machine SNP‐Set Testing Under Multiple Candidate Kernels

Abstract

Joint testing for the cumulative effect of multiple single nucleotide polymorphisms grouped on the basis of prior biological knowledge has become a popular and powerful strategy for the analysis of large scale genetic association studies. The kernel machine (KM) testing framework is a useful approach that has been proposed for testing associations between multiple genetic variants and many different types of complex traits by comparing pairwise similarity in phenotype between subjects to pairwise similarity in genotype, with similarity in genotype defined via a kernel function. An advantage of the KM framework is its flexibility: choosing different kernel functions allows for different assumptions concerning the underlying model and can allow for improved power. In practice, it is difficult to know which kernel to use a priori since this depends on the unknown underlying trait architecture and selecting the kernel which gives the lowest p-value can lead to inflated type I error. Therefore, we propose practical strategies for KM testing when multiple candidate kernels are present based on constructing composite kernels and based on efficient perturbation procedures. We demonstrate through simulations and real data applications that the procedures protect the type I error rate and can lead to substantially improved power over poor choices of kernels and only modest differences in power versus using the best candidate kernel.

Unified Sequence-Based Association Tests Allowing for Multiple Functional Annotations and Meta-analysis of Noncoding Variation in Metabochip Data

“…We additionally compared our methods with our Fisher's unified statistic and the weighted summation method proposed by Wu et al and present the results and additional simulation scenarios in Tables S1 and S2. 21 In…”

“…Wu et al and Minica et al proposed practical strategies for combining multiple weights or kernels in SKAT by using perturbation-and permutation-based approaches. 20,21 However, these approaches, based on standard perturbation and permutation procedures, are often time consuming, and analytical p values are not available, which limits their use in a genome-wide analysis, where extreme p values at the genome-wide level are needed.…”

A generalized association test based on U statistics

“…Nevertheless, its performance may not guaranteed to be optimal. In this case, we can perform kernel selection, for example, by using the procedure proposed by Wu et al (2013). Besides the choice of kernel, different choices of weights can also influence the power of GSU for multivariate phenotype.…”

Identifying individual risk rare variants using protein structure-guided local tests (POINT)

“…Therefore, associations involving rare 4 variants are typically discerned using "global" or variant-set tests, which aggregate 5 information across variants to gain sufficient power. These aggregation tests can be 6 done in a burden-based fashion (i.e., modeling phenotype as a function of a weighted 7 sum of genetic markers) [1][2][3][4], or using kernel tests (i.e., examining association between 8 pairwise trait similarity and pairwise genetic similarity) [5][6][7][8][9]. Global aggregation tests 9 substantially improve the power for detecting set-level association with phenotypes; 10 however, they are not able to identify individual rare risk variants responsible for the 11 set-level significance.…”

“…As shown in the variant-borrowing maps (Fig 3, S1 Fig -441 S12 Fig, and important open problem in general kernel machine regression. One way to ensure the 461 use of a "near optimal" kernel is to apply the composite kernel of Wu et al [9], which 462 can yield performance similar to the optimal kernel with substantial improvement over 463 "wrong" kernels.…”