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This paper mainly utilizes likelihood-based tests to detect rare variants associated with a continuous phenotype under the framework of kernel machine learning. Both the likelihood ratio test (LRT) and the restricted likelihood ratio test (ReLRT) are investigated. The relationship between the kernel machine learning and the mixed effects model is discussed. By using the eigenvalue representation of LRT and ReLRT, their exact finite sample distributions are obtained in a simulation manner. Numerical studies are performed to evaluate the performance of the proposed approaches under the contexts of standard mixed effects model and kernel machine learning. The results have shown that the LRT and ReLRT can control the type I error correctly at the given  α  level. The LRT and ReLRT consistently outperform the SKAT, regardless of the sample size and the proportion of the negative causal rare variants, and suffer from fewer power reductions compared to the SKAT when both positive and negative effects of rare variants are present. The LRT and ReLRT performed under the context of kernel machine learning have slightly higher powers than those performed under the context of standard mixed effects model. We use the Genetic Analysis Workshop 17 exome sequencing SNP data as an illustrative example. Some interesting results are observed from the analysis. Finally, we give the discussion.

Rare Variants Detection with Kernel Machine Learning Based on Likelihood Ratio Test