ACAT: A Fast and Powerful p Value Combination Method for Rare-Variant Analysis in Sequencing Studies

Abstract

Set-based analysis that jointly tests the association of variants in a group has emerged as a popular tool for analyzing rare and low-frequency variants in sequencing studies. The existing set-based tests can suffer significant power loss when only a small proportion of variants are causal, and their powers can be sensitive to the number, effect sizes, and effect directions of the causal variants and the choices of weights. Here we propose an aggregated Cauchy association test (ACAT), a general, powerful, and computationally efficient p value combination method for boosting power in sequencing studies. First, by combining variant-level p values, we use ACAT to construct a set-based test (ACAT-V) that is particularly powerful in the presence of only a small number of causal variants in a variant set. Second, by combining different variant-set-level p values, we use ACAT to construct an omnibus test (ACAT-O) that combines the strength of multiple complimentary set-based tests, including the burden test, sequence kernel association test (SKAT), and ACAT-V. Through analysis of extensively simulated data and the whole-genome sequencing data from the Atherosclerosis Risk in Communities (ARIC) study, we demonstrate that ACAT-V complements the SKAT and the burden test, and that ACAT-O has a substantially more robust and higher power than those of the alternative tests.

Keywords: omnibus test; rare-variant analysis; variant set test; whole-genome sequencing.

Figure 1

Summary of the Proposed Methods ACAT, ACAT-V, and ACAT-O and the Relationship Among Them

Figure 2

Power Comparisons of ACAT-O, ACAT-V, SKAT, and the Burden Test for Continuous Traits Each bar represents the empirical power estimated as the proportion of p values less than $\text{α}={10}^{-6}$. The proportion of causal variants is set to be 5%, 20%, and 50%, which correspond to the three rows of each panel. The left panel assumes the effects of the causal variants to have the same direction, whereas the right panel assumes the effect directions are randomly determined with an equal probability. The effect sizes $\left(\left|{\beta }_i\right|\text{s}\right)$ of the causal variants either are all the same as $\left|{\beta }_i\right|=\text{b}$ (left column in each panel) or have a decreasing relationship with MAF (right column in each panel) as $\left|{\beta }_i\right|=\text{c}\left|{\log }_{10}MA{F}_i\right|$, where constants $\text{b}$ and $\text{c}$ depend on the proportions of causal variants and their values are presented in Table S1. For each configuration, the total sample sizes considered are 2,500, 5,000, 7,500, and 10,000. Seven methods are compared: ACAT-V(1,25), ACAT-V(1,1), SKAT(1,25), SKAT(1,1), burden(1,25), burden(1,1), and the omnibus test ACAT-O that combines the other six tests, where the two numbers in the parentheses indicate the choice of the beta(MAF) weight parameters $a_1$ and $a_2$ in the test.

Figure 3

Power Comparisons of ACAT-O, ACAT-V, SKAT, and the Burden Test for Dichotomous Traits Each bar represents the empirical power estimated as the proportion of p values less than $\text{α}={10}^{-6}$. The proportion of causal variants is set to be 5%, 20%, and 50%, which correspond to the three rows of each panel. The left panel assumes the effects of the causal variants to have the same direction, whereas the right panel assumes the effect directions are randomly determined with an equal probability. The effect sizes $\left(\left|{\beta }_i\right|\text{s}\right)$ of the causal variants either are all the same as $\left|{\beta }_i\right|=\text{b}$ (left column in each panel) or have a decreasing relationship with MAF (right column in each panel) as $\left|{\beta }_i\right|=\text{c}\left|{\log }_{10}MA{F}_i\right|$, where constants $\text{b}$ and $\text{c}$ depend on the proportions of causal variants; their values are presented in Table S1. For each configuration, the total sample sizes considered are 2,500, 5,000, 7,500, and 10,000. Seven methods are compared: ACAT-V(1,25), ACAT-V(1,1), SKAT(1,25), SKAT(1,1), burden(1,25), burden(1,1), and the omnibus test ACAT-O that combines the other six tests, where the two numbers in the parentheses indicate the choice of the beta(MAF) weight parameters $a_1$ and $a_2$ in the test.