A comprehensive comparison of multilocus association methods with summary statistics in genome-wide association studies

Table 1 An overview of 22 SNP-set methods and their corresponding modeling characteristics

No	Year	Method	Input					Calculate P value		References
No	Year	Method	P	Z	W	R	Other	Analytical	Simulation	References
1	1960	MLR		√	√	√	N	√		[76]
2	2008	FLM		√	√	√	N	√		[45, 77]
3	2004	HC		√	√			√		[66]
4	2017	GHC		√	√	√		√		[49]
5	2019	BJ		√	√			√		[51]
6	2019	GBJ		√	√	√		√		[51]
7	2020	DOT		√	√	√		√		[67]
8	2017	BT		√	√	√		√		[45]
9	2013	SKATO		√	√	√		√		[45]
10	2018	SKAT		√	√	√		√		[45]
11	1986	Simes	√					√		[68]
12	1992	FCP	√					√		[69]
13	2002	TPM	√				τ	√		[70]
14	2003	RTP	√				k	√		[71]
15	2007	minP	√			√		√		[72]
16	2019	ART	√				k	√		[78]
17	2019	ART-A	√		√		k	√	√	[78]
18	2007	GM	√				a	√		[73]
19	2008	SimpleM	√			√		√		[74]
20	2011	GATES	√			√			√	[79]
21	2019	HMP	√		√			√		[75]
22	2020	ACAT	√		√			√		[54]

P denotes a vector of P values, Z denotes a vector of Z scores, W is a vector of weights, R denotes the SNP-by-SNP correlation matrix, τ indicates a fixed value that P is less than in TPM, with the default being 0.2; k is the number of P values to be combined in RTP, ARTP, ART, ART-A, with the default value being 2/M, where M is the number of SNPs for a given gene; a is a shape parameter in GM, with the default being 0.0383; N is the sample size
MLR Multiple linear regression, FLM Functional multiple linear regression model, HC Higher criticism test, GHC Generalized higher criticism test, BJ Berk–Jones test, GBJ Generalized Berk–Jones test, DOT Decorrelation by orthogonal transformation, BT Burden test, SKATO Optimal sequence kernel association test, SKAT Sequence kernel association test, Simes Simes’s test, FCP Fisher combined probability, TPM Truncated product method, RTP Rank truncated product, ART Augmented rank truncation, ART-A Adaptive augmented rank truncation, GM Gamma method, GATES Gene-based association test that uses extended Simes procedure, HMP The harmonic mean P value test, ACAT Aggregated Cauchy association test

ISSN: 1471-2105