Smoothed functional principal component analysis for testing association of the entire allelic spectrum of genetic variation

Abstract

Fast and cheaper next-generation sequencing technologies will generate unprecedentedly massive and highly dimensional genetic variation data that allow nearly complete evaluation of genetic variation including both common and rare variants. There are two types of association tests: variant-by-variant test and group test. The variant-by-variant test is designed to test the association of common variants, while the group test is suitable to collectively test the association of multiple rare variants. We propose here a smoothed functional principal component analysis (SFPCA) statistic as a general approach for testing association of the entire allelic spectrum of genetic variation (both common and rare variants), which utilizes the merits of both variant-by-variant analysis and group tests. By intensive simulations, we demonstrate that the SFPCA statistic has the correct type 1 error rates and much higher power than the existing methods to detect association of (1) common variants, (2) rare variants, (3) both common and rare variants and (4) variants with opposite directions of effects. To further evaluate its performance, the SFPCA statistic is applied to ANGPTL4 sequence and six continuous phenotypes data from the Dallas Heart Study as an example for testing association of rare variants and a GWAS of schizophrenia data as an example for testing association of common variants. The results show that the SFPCA statistic has much smaller P-values than many existing statistics in both real data analysis examples.

Functional Linear Models for Association Analysis of Quantitative Traits

“…The basic idea of the functional data analysis approach is different from those of either burden tests or kernel-based approaches [Luo et al, 2011, 2012a, b]. Instead of collapsing genetic variants as burden tests or building a kernel matrix as SKAT, multiple genetic variants of an individual in a human population are treated in our approach as a realization of a stochastic process in the functional data analysis [de Boor, 2001; Ferraty and Romain, 2010; Horváth and Kokoszka, 2012; Ramsay and Silverman, 1996; Ramsay et al, 2009].…”

Meta-analysis of Complex Diseases at Gene Level with Generalized Functional Linear Models

“…The high dimensionality of modern genetic data does not necessarily imply that traditional population genetics theory is not correct because the number of causal variants may not be large. A fixed model should be fine to analyze the major gene locus data in most cases if the dimension of the genetic data can be properly reduced.By viewing genetic variant data as realizations of an underlying stochastic process, functional regression models were proposed to reduce the dimensionality and to perform a gene-based association analysis of quantitative, qualitative, and survival traits (Luo et al 2011(Luo et al , 2012(Luo et al , 2013Fan et al 2013Fan et al , 2014Fan et al , 2015Fan et al , 2016Vsevolozhskaya et al 2014;Zhang et al 2014;Wang et al 2015). For quantitative traits, functional linear models lead to both F-and chi-squared-distributed test statistics that are almost always more powerful than SKAT and SKAT-O (Luo et al 2012;Fan et al 2013Fan et al , 2015Wang et al 2015).…”

“…For quantitative traits, functional linear models lead to both F-and chi-squared-distributed test statistics that are almost always more powerful than SKAT and SKAT-O (Luo et al 2012;Fan et al 2013Fan et al , 2015Wang et al 2015). For dichotomous and survival traits, functional regression models lead to test statistics that are more powerful than SKAT and SKAT-O except in some cases where the causal variants are all rare (Luo et al 2011(Luo et al , 2013Fan et al 2014Fan et al , 2016Vsevolozhskaya et al 2014). Therefore, functional regression models are found to outperform other methods and potentially to be useful in gene-based association analysis of complex traits.…”

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

“…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.…”