Likelihood Ratio Tests in Rare Variant Detection for Continuous Phenotypes

Abstract

SummaryIt is believed that rare variants play an important role in human phenotypes; however, the detection of rare variants is extremely challenging due to their very low minor allele frequency. In this paper, the likelihood ratio test (LRT) and restricted likelihood ratio test (ReLRT) are proposed to test the association of rare variants based on the linear mixed effects model, where a group of rare variants are treated as random effects. Like the sequence kernel association test (SKAT), a state-of-the-art method for rare variant detection, LRT and ReLRT can effectively overcome the problem of directionality of effect inherent in the burden test in practice. By taking full advantage of the spectral decomposition, exact finite sample null distributions for LRT and ReLRT are obtained by simulation. We perform extensive numerical studies to evaluate the performance of LRT and ReLRT, and compare to the burden test, SKAT and SKAT-O. The simulations have shown that LRT and ReLRT can correctly control the type I error, and the controls are robust to the weights chosen and the number of rare variants under study. LRT and ReLRT behave similarly to the burden test when all the causal rare variants share the same direction of effect, and outperform SKAT across various situations. When both positive and negative effects exist, LRT and ReLRT suffer from few power reductions compared to the other two competing methods; under this case, an additional finding from our simulations is that SKAT-O is no longer the optimal test, and its power is even lower than that of SKAT. The exome sequencing SNP data from Genetic Analysis Workshop 17 were employed to illustrate the proposed methods, and interesting results are described.

The Weighting is the Hardest Part: On the Behavior of the Likelihood Ratio Test and the Score Test Under a Data-Driven Weighting Scheme in Sequenced Samples

“…These results are consistent with those reported by Zeng et al [53] and by Lippert et al [30], who found the LRT to be generally more powerful than the score test across their simulated settings. Although Lippert et al did not consider the behavior of the two tests under misspecified weights, they reported the same pattern of results in real data analysis, where the LRT yielded consistently more associations than the score test.…”

Bootstrap Restricted Likelihood Ratio Test for the Detection of Rare Variants

“…In the bootstrap ReLRT algorithm, B was set to 2000, and for the approximation mixture in we selected L = 2000, 1500, 1000, 800, 500, 300 and 100. We also implemented the simulation-based algorithm for the finite sample null distribution of ReLRT [ 20 , 35 , 36 ], and the number of runs in this algorithm is set to 10000. Besides ReLRT, the burden test, the optimal SKAT (SKAT-O) [ 37 , 38 ], SKAT [ 12 ], the genetic random field (GenRF) model [ 39 , 40 ] and the mixed effects score test (MiST) [ 41 ] were conducted together for comparisons.…”

Jackknife model averaging prediction methods for complex phenotypes with gene expression levels by integrating external pathway information

“…For example, it is well known that single nucleotide polymorphisms (SNPs) can be divided into groups in terms of functional annotations or genes, and genes in turn can be grouped into pathways due to the shared biological function. It has been shown that incorporating such useful group/functional information into model fitting can substantially boost statistical power in genetic association studies and can facilitate our understanding of the genetic architecture of disease variation by heritability partition [25][26][27][28][29][30][31][32][33]. One widely-used group source is the pathway information in the Kyoto Encyclopedia of Genes and Genomes (KEGG) [34,35], which integrates information on genomic, chemical and system functions and groups genes with highly related sequences by analyzing the sequence similarity of genes.…”