On Efficient and Accurate Calculation of Significance P‐Values for Sequence Kernel Association Testing of Variant Set

Abstract

Summary The objective of this paper is to discuss and develop alternative computational methods to accurately and efficiently calculate significance p-values for the commonly used sequence kernel association test (SKAT) and adaptive sum of SKAT and burden test (SKAT-O) for variant set association. We show that the existing software can lead to either conservative or inflated type I errors. We develop alternative and efficient computational algorithms that quickly compute the SKAT p-value and have well-controlled type I errors. In addition, we derive an alternative and simplified formula for calculating the significance p-value of SKAT-O, which sheds light on the development of efficient and accurate numerical algorithms. We implement the proposed methods in the publicly available R package that can be readily used or adapted to large-scale sequencing studies. Given that more and more large-scale exome and whole genome sequencing or re-sequencing studies are being conducted, the proposed methods are practically very important. We conduct extensive numerical studies to investigate the performance of the proposed methods. We further illustrate their usefulness with application to associations between rare exonic variants and fasting glucose levels in the Atherosclerosis Risk in Communities (ARIC) Study.

Gene‐based genetic association test with adaptive optimal weights

“…It can be shown that under the null hypothesis, the above statistic in asymptotically follows a linear combination of chi‐square distributions (Chen, Han et al., ), where is independently and identically distributed chi‐square distribution with degree of freedom ( df ) 1. Therefore, the P ‐value for SKAT can be estimated by the Davis’ approach or other methods (Davies, ; Wu, Guan, & Pankow, ). From , we know that the performance of SKAT depends on the weight matrix W .…”

“…where 2 ,1 is independently and identically distributed chisquare distribution with degree of freedom (df) 1. Therefore, the P-value for SKAT can be estimated by the Davis' approach or other methods (Davies, 1980;Wu, Guan, & Pankow, 2016). From (3), we know that the performance of SKAT depends on the weight matrix .…”

A review of kernel methods for genetic association studies

“…This entails computing the first two moments of under the null hypothesis and using these moments to estimate the degrees of freedom and a factor to rescale the χ 2 distribution. Liu et al () and Kwee et al () both applied the same Satterthwaite approximation, although this can be anticonservative at the extreme tail and higher moment‐matching methods have been proposed to improve accuracy (B. Wu & Pankow, ; B. Wu, Guan, & Pankow, ). For the sequence kernel association test (SKAT), M. C. Wu et al () considered a more accurate asymptotic approximation of the distribution of Q , recognizing that its distribution is a linear combination of i.i.d.…”

“…A challenge is computing reliable P ‐values for SKAT‐O when evaluating a range of values for the parameter . It has been shown that the SKAT‐O P ‐values are less reliable than the SKAT P ‐values, and the performance of current SKAT‐O implementations depends on the set size of genetic markers and their correlation (B. Wu et al, ).…”

“…Liu et al (2007) and Kwee et al (2008) both applied the same Satterthwaite approximation, although this can be anticonservative at the extreme tail and higher momentmatching methods have been proposed to improve accuracy (B. Wu & Pankow, 2016a;B. Wu, Guan, & Pankow, 2016).…”