A Powerful and Adaptive Association Test for Rare Variants

Abstract

This article focuses on conducting global testing for association between a binary trait and a set of rare variants (RVs), although its application can be much broader to other types of traits, common variants (CVs), and gene set or pathway analysis. We show that many of the existing tests have deteriorating performance in the presence of many nonassociated RVs: their power can dramatically drop as the proportion of nonassociated RVs in the group to be tested increases. We propose a class of so-called sum of powered score (SPU) tests, each of which is based on the score vector from a general regression model and hence can deal with different types of traits and adjust for covariates, e.g., principal components accounting for population stratification. The SPU tests generalize the sum test, a representative burden test based on pooling or collapsing genotypes of RVs, and a sum of squared score (SSU) test that is closely related to several other powerful variance component tests; a previous study has demonstrated good performance of one, but not both, of the Sum and SSU tests in many situations. The SPU tests are versatile in the sense that one of them is often powerful, although its identity varies with the unknown true association parameters. We propose an adaptive SPU (aSPU) test to approximate the most powerful SPU test for a given scenario, consequently maintaining high power and being highly adaptive across various scenarios. We conducted extensive simulations to show superior performance of the aSPU test over several state-of-the-art association tests in the presence of many nonassociated RVs. Finally we applied the SPU and aSPU tests to the GAW17 mini-exome sequence data to compare its practical performance with some existing tests, demonstrating their potential usefulness.T HE recent advances in sequencing technologies have made it feasible to conduct global testing for association between complex traits and rare variants (RVs) (Bansal et al. 2010). The most popular approach in genome-wide association studies (GWASs) is to test on each single nucleotide variant (SNV) one by one and then select the SNVs meeting a stringent significance level after adjusting for multiple testing. However, such a strategy may be low powered due to the weak signal contained within each individual RV for its extremely low minor allele frequency (MAF). Hence, developing new association tests tailored to RVs has been an active research area in the past few years. Due to low MAFs of RVs, to achieve practically meaningful power, the majority of existing approaches focus on testing on a group of RVs, rather than on each individual RV (Capanu et al. 2011); the main idea is to boost power through aggregating information across multiple RVs in an analysis unit, such as a gene (e.g., Morgenthaler and Thilly 2007;Li and Leal 2008;Madsen and Browning 2009;Liu and Leal 2010;Han and Pan 2010;Hoffmann et al. 2010;Li et al. 2010;Price et al. 2010;Zhang et al. 2010;Zhu et al. 2010;Luo et al. 2011;Neale et al. 2011;Ionita-Laza et al....

An Adaptive Test on High-dimensional Parameters in Generalized Linear Models

“…Inspired by Pan et al (2014), we would use U to construct some weights to upweight more informative components of the score vector, proposing a sum of powered score (SPU) test statistic with power index…”

“…Taking the minimum p-value is a simple and effective way to approximate the most powerful test (Pan et al, 2014). Note that T aSPU is no longer a genuine p-value and we need to derive its asymptotic null distribution to facilitate calculating its p-value.…”

“…Our proposed test is an extension of the original aSPU test (Pan et al, 2014) to high-dimensional GLMs; the original aSPU test was proposed for analysis of rare variants with large n and small p. For simplicity, we use the same name "aSPU" for our proposed test here. Since the asymptotic properties of the adaptive aSPU test for GLMs have not been studied, we derive its asymptotic null distribution in a high-dimensional setting, based on which the asymptotic p-values of L(γ, µ 0 ) and T aSPU can be calculated.…”

“…, p}, and their values were constant at c. We varied s, c, n and p to evaluate the performance of the new method under various situations. We used the parametric bootstrap (Pan et al, 2014) to obtain a 'bronze-standard' (slightly inferior to a 'gold standard', where the true p-value is known) analysis, to which we compared the asymptotic results based on Theorem 2. In all simulations, we treated Σ as unknown and thus estimated Σ, then calculated the means and covariances of the SPU test statistics according to Propositions 1-3.…”

Assessing Gene-Environment Interactions for Common and Rare Variants with Binary Traits Using Gene-Trait Similarity Regression

“…However, the presence of many null variants can still unfavorably affect the test performance. For main-effect collapsing tests, efforts have been made to boost power when the signal sparsity is low by adaptively focusing on the subsets enriched with causal variants (e.g., Barnett 2014;Pan et al 2014). Their extensions to G3E tests will be helpful to further optimize the power to detect G3E effects.…”