Gene Level Meta-Analysis of Quantitative Traits by Functional Linear Models

Abstract

Meta-analysis of genetic data must account for differences among studies including study designs, markers genotyped, and covariates. The effects of genetic variants may differ from population to population, i.e., heterogeneity. Thus, meta-analysis of combining data of multiple studies is difficult. Novel statistical methods for meta-analysis are needed. In this article, functional linear models are developed for meta-analyses that connect genetic data to quantitative traits, adjusting for covariates. The models can be used to analyze rare variants, common variants, or a combination of the two. Both likelihood-ratio test (LRT) and F-distributed statistics are introduced to test association between quantitative traits and multiple variants in one genetic region. Extensive simulations are performed to evaluate empirical type I error rates and power performance of the proposed tests. The proposed LRT and F-distributed statistics control the type I error very well and have higher power than the existing methods of the meta-analysis sequence kernel association test (MetaSKAT). We analyze four blood lipid levels in data from a meta-analysis of eight European studies. The proposed methods detect more significant associations than MetaSKAT and the P-values of the proposed LRT and F-distributed statistics are usually much smaller than those of MetaSKAT. The functional linear models and related test statistics can be useful in whole-genome and whole-exome association studies.KEYWORDS meta-analysis; rare variants; common variants; association mapping; quantitative trait loci; complex traits; functional data analysis M ETA-ANALYSIS is a statistical method to combine multiple studies for a unified analysis and it plays an important role in genetic studies (de Bakker et al. 2008;Zeggini and Ioannidis 2009;Cantor et al. 2010;Evangelou and Ioannidis 2013). One obvious advantage of meta-analysis is that the sample size is large (Liu et al. 2014). Therefore, metaanalysis should lead to more significant results. It is argued that most of the reported complex disease associations came from large-scale meta-analysis of genome-wide association studies (GWASs) (Zeggini and Ioannidis 2009;Evangelou and Ioannidis 2013;Liu et al. 2014). Therefore, there has been great interest in developing novel statistical methods to perform GWAS meta-analysis (Ioannidis et al. 2007; Hu et al. 2013;Liu et al. 2014). Meta-analysis combines studies with different study designs. The genotype data and covariates may vary from study to study. Moreover, the effects of genetic variants in different populations may not be the same, i.e., the heterogeneity (Tang and Lin 2014). Thus, meta-analysis of combining data of multiple studies is difficult. Novel statistical methods for meta-analysis are needed.The statistical methods for meta-analysis fall into two classes: (1) single genetic variant-based approaches and (2) gene-based variant analysis approaches. The single genetic variant approaches only use one genetic variant at a time and are usually based ...

Meta-analysis of quantitative pleiotropic traits for next-generation sequencing with multivariate functional linear models

“…If we only have one quantitative trait, ie, J = 1, the three approximate F-distribution tests based on Pillai-Bartlett trace, Hotelling-Lawley trace, and Wilks's Lambda are equivalent to the F-test statistics of the standard multiple linear regression. The models proposed in this article and the related approximate F-distribution tests extend the models and the F-test statistics in Fan et al 18 In practice, we find that the results of the three approximate F-distribution tests based on Pillai-Bartlett trace, Hotelling-Lawley trace, and Wilks's Lambda are similar to each other. 10 In this article, we only report the results of approximate F-distribution tests based on Pillai-Bartlett trace.…”

“…To estimate the GVFs X ci ðtÞ from the genotypes G ci , we use an ordinary linear square smoother. [16][17][18][19][20]42,43 Let ϕ k (t), k = 1, ⋯, K, be a series of K basis functions, such as the B-spline basis and Fourier basis functions. Denote ϕ(t) = (ϕ 1 (t), ⋯, ϕ K (t))′.…”

“…10,[16][17][18][19][20][21][22][23][24][25][26][27][28][29] In most cases, it was shown that the functional regression test statistics perform better than sequence kernel association test (SKAT), its optimal unified test (SKAT-O), and a combined sum test of rare and common variant effect (SKAT-C) of mixed models. 4,[16][17][18][19][20][21][22][23][24][25][26][27][30][31][32][33] Specifically, mixed model-based SKAT/SKATO/ SKAT-C performs well when (a) the number of causal variants is large and (b) each causal variant contributes a small amount to the traits, as the assumption of mixed models is satisfied under these circumstances. 7,21,34 In most cases, however, fixed models perform better since the causal variants of complex disorders can be common or rare or a combination of the two and some causal variants may have relatively large effects.…”

“…7,21,34 In most cases, however, fixed models perform better since the causal variants of complex disorders can be common or rare or a combination of the two and some causal variants may have relatively large effects. 10,[16][17][18][19][20][21][22][23][24][25][26][27] If the number of causal variants is large and each causal variant contributes a small amount to the traits, it would be hard to show association as the power of a test can be low. 35 One may want to note that SKAT and SKAT-O were shown to have higher power than burden tests, which is another main method to analyze rare variants.…”

“…For individual studies, MFLM were built to perform pleiotropy analysis between multiple genetic variants and multiple quantitative traits adjusting for covariates in Wang et al 10 Similarly, functional linear models were developed to perform meta-analysis of a univariate quantitative trait in Fan et al 18 In this paper, we build MFLM to analyze multiple traits of multiple studies and introduce related approximate F-distributed test statistics to test for association based on multivariate analysis theory. The proposed methods are applied to analyze lipid traits in eight European cohorts.…”