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

Abstract

Figure S1The genomic landscape of sliding windows significantly associated with Lp(a) levels among AAs on chromosome 6. Seven methods are compared: ACAT-V(1,1), ACAT-V(1,25), SKAT(1,1), SKAT(1,25), Burden(1,1), Burden(1,25) 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 and in the test. A dot means that the sliding window at this location is significant by the method that the color of the dot represents. The numbers on the left of the plot show the number of significant windows identified by each method. Figure S2The genomic landscape of sliding windows significantly associated with Lp(a) levels among EAs on chromosome 6. Seven methods are compared: ACAT-V(1,1), ACAT-V(1,25), SKAT(1,1), SKAT(1,25), Burden(1,1), Burden(1,25) 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 and in the test. A dot means that the sliding window at this location is significant by the method that the color of the dot represents. The numbers on the left of the plot show the number of significant windows identified by each method.

Methods for combining multiple correlated biomarkers with application to the study of low-grade inflammation and muscle mass in senior horses

“…In this article, we studied the problem of combining multiple correlated summary statistics. This problem has recently become increasingly important in multiple areas, including problems of pleiotropy in complex traits (Solovieff et al, 2013;Zhu et al, 2015), gene and pathway scores from SNP-phenotype association summary statistics (Lamparter et al, 2016;Liu et al, 2019), prediction of individual's diagnostic outcome based on combination of multiple biomarkers (Mamtani et al, 2006;Yan et al, 2018), etc. We studied analytical properties of the traditional approach for combining summary statistics, TQ, which includes popular methods for association analysis of genetic variants with a disease (Pasaniuc and Price, 2017), and derived the distribution of the TQstatistic under the alternative hypothesis.…”

Statistical Analysis of Spatial Expression Pattern for Spatially Resolved Transcriptomic Studies

“…With parameter estimates from the PQL-based algorithm, we computed a p-value for each of the ten kernels using the Satterthwaite Method 69 based on score statistics, which follow a mixture of chi-square distributions. Afterwards, we combined these ten p-values through the recently developed Cauchy p-value combination rule 21 . To apply the Cauchy combination rule, we converted each of the ten p-values into a Cauchy statistic, aggregated the ten Cauchy statistics through summation, and converted the summation back to a single p-value based on the standard Cauchy distribution.…”

“…To apply the Cauchy combination rule, we converted each of the ten p-values into a Cauchy statistic, aggregated the ten Cauchy statistics through summation, and converted the summation back to a single p-value based on the standard Cauchy distribution. The Cauchy rule takes advantage of the fact that combination of Cauchy random variables also follows a Cauchy distribution regardless whether these random variables are correlated or not 21,22 . Therefore, the Cauchy combination rule allows us to combine multiple potentially correlated p-values into a single p-value without loss of type I error control.…”

“…With a newly developed penalized quasi-likelihood (PQL) algorithm 19,20 , SPARK is scalable to analyzing tens of thousands genes across tens of thousands samples. Importantly, SPARK relies on a mixture of Chi-square distributions to serve as the exact test statistics distribution and further takes advantage of a recently developed Cauchy combination rule 21,22 to combine information across multiple spatial kernels for calibrated p-value calculation. As a result, SPARK properly controls for type I error at the transcriptome-wide level and is more powerful for identifying SE genes than existing approaches.…”

DOT: Gene-set analysis by combining decorrelated association statistics

“…proposed method "ACAT" by Liu and colleagues,21 where association P-values for individual SNPs are transformed to Cauchy-distributed random variables, then added up to obtain the overall P-value. ACAT was included into comparisons because it has robust power across different models of association.…”