text: For precision medicine and personalized treatment, we need to identify predictive markers of disease. We focus on Alzheimer's disease (AD), where magnetic resonance imaging scans provide information about the disease status. By combining imaging with genome sequencing, we aim at identifying rare genetic markers associated with quantitative traits predicted from convolutional neural networks (CNNs), which traditionally have been derived manually by experts. Kernel-based tests are a powerful tool for associating sets of genetic variants, but how to optimally model rare genetic variants is still an open research question. We propose a generalized set of kernels that incorporate prior information from various annotations and multi-omics data. In the analysis of data from the Alzheimer's Disease Neuroimaging Initiative (ADNI), we evaluate whether (i) CNNs yield precise and reliable brain traits, and (ii) the novel kernel-based tests can help to identify loci associated with AD. The results indicate that CNNs provide a fast, scalable and precise tool to derive quantitative AD traits and that new kernels integrating domain knowledge can yield higher power in association tests of very rare variants.
  @cite_4: SUMMARY With development of massively parallel sequencing technologies, there is a substantial need for developing powerful rare variant association tests. Common approaches include burden and non-burden tests. Burden tests assume all rare variants in the target region have effects on the phenotype in the same direction and of similar magnitude. The recently proposed sequence kernel association test (SKAT) (Wu, M. C., and others, 2011. Rare-variant association testing for sequencing data with the SKAT.The American Journal of HumanGenetics89,82–93],anextensionoftheC-alphatest(Neale,B.M.,andothers,2011.Testingforan unusual distribution of rare variants. PLoS Genetics 7, 161–165], provides a robust test that is particularly powerful in the presence of protective and deleterious variants and null variants, but is less powerful than burden tests when a large number of variants in a region are causal and in the same direction. As the underlying biological mechanisms are unknown in practice and vary from one gene to another across the genome,itisofsubstantialpracticalinteresttodevelopatestthatisoptimalforbothscenarios.Inthispaper, we propose a class of tests that include burden tests and SKAT as special cases, and derive an optimal test within this class that maximizes power. We show that this optimal test outperforms burden tests and SKAT in a wide range of scenarios. The results are illustrated using simulation studies and triglyceride data from the Dallas Heart Study. In addition, we have derived sample size power calculation formula for SKAT with a new family of kernels to facilitate designing new sequence association studies.
  @cite_7: Motivation: Set-based variance component tests have been identified as a way to increase power in association studies by aggregating weak individual effects. However, the choice of test statistic has been largely ignored even though it may play an important role in obtaining optimal power. We compared a standard statistical test— a score test—with a recently developed likelihood ratio (LR) test. Further, when correction for hidden structure is needed, or gene– gene interactions are sought, state-of-the art algorithms for both the score and LR tests can be computationally impractical. Thus we develop new computationally efficient methods. Results: After reviewing theoretical differences in performance between the score and LR tests, we find empirically on real data that the LR test generally has more power. In particular, on 15 of 17 real datasets, the LR test yielded at least as many associations as the score test—up to 23 more associations—whereas the score test yielded at most one more association than the LR test in the two remaining datasets. On synthetic data, we find that the LR test yielded up to 12 more associations, consistent with our results on real data, but also observe a regime of extremely small signal where the score test yielded up to 25 more associations than the LR test, consistent with theory. Finally, our computational speedups now enable (i) efficient LR testing when the background kernel is full rank, and (ii) efficient score testing when the background kernel changes with each test, as for gene–gene interaction tests. The latter yielded a factor of 2000 speedup on a cohort of size 13 500. Availability: Software available at http: research.microsoft.com enus um redmond projects MSCompBio Fastlmm .
  @cite_8: 
  @cite_0: Motivation: Approaches for testing sets of variants, such as a set of rare or common variants within a gene or pathway, for association with complex traits are important. In particular, set tests allow for aggregation of weak signal within a set, can capture interplay among variants and reduce the burden of multiple hypothesis testing. Until now, these approaches did not address confounding by family relatedness and population structure, a problem that is becoming more important as larger datasets are used to increase power. Results: We introduce a new approach for set tests that handles confounders. Our model is based on the linear mixed model and uses two random effects—one to capture the set association signal and one to capture confounders. We also introduce a computational speedup for two random-effects models that makes this approach feasible even for extremely large cohorts. Using this model with both the likelihood ratio test and score test, we find that the former yields more power while controlling type I error. Application of our approach to richly structured Genetic Analysis Workshop 14 data demonstrates that our method successfully corrects for population structure and family relatedness, whereas application of our method to a 15 000 individual Crohn’s disease case–control cohort demonstrates that it additionally recovers genes not recoverable by univariate analysis. Availability: A Python-based library implementing our approach is available at http: mscompbio.codeplex.com. Contact:jennl@microsoft.com or lippert@microsoft.com or heckerma@microsoft.com Supplementary information:Supplementary data are available at Bioinformatics online.
  @cite_19: 
  @cite_17: Analysis of rare genetic variants has focused on region-based analysis wherein a subset of the variants within a genomic region is tested for association with a complex trait. Two important practical challenges have emerged. First, it is difficult to choose which test to use. Second, it is unclear which group of variants within a region should be tested. Both depend on the unknown true state of nature. Therefore, we develop the Multi-Kernel SKAT (MK-SKAT) which tests across a range of rare variant tests and groupings. Specifically, we demonstrate that several popular rare variant tests are special cases of the sequence kernel association test which compares pair-wise similarity in trait value to similarity in the rare variant genotypes between subjects as measured through a kernel function. Choosing a particular test is equivalent to choosing a kernel. Similarly, choosing which group of variants to test also reduces to choosing a kernel. Thus, MK-SKAT uses perturbation to test across a range of kernels. Simulations and real data analyses show that our framework controls type I error while maintaining high power across settings: MK-SKAT loses power when compared to the kernel for a particular scenario but has much greater power than poor choices.
summary: Popular kernel-based tests include FaST-LMM-Set @cite_0 @cite_19 , the sequence kernel association test (SKAT, @cite_7 ) and optimal SKAT (SKAT-O, @cite_4 ), which are based on weighted linear kernels @math @cite_7 @cite_8 @cite_19 , or a linear combination of weighted linear and collapsing kernels @cite_4 . Newer approaches @cite_17 derive further data-adaptive combinations of linear, quadratic, IBS, and collapsing kernels. However, all these kernels provide suboptimal performance for the analysis of very rare genetic variants. Here, linear and quadratic kernels yield uninformative similarity measures (i.e., diagonal kernel matrices for singletons, which are variants with only one observed copy of the minor allele) and collapsing kernels often yield unspecific signals and aggregate noise.