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Table 1 Two hundred thirty four disease scenarios considered in the simulations

From: Performance of epistasis detection methods in semi-simulated GWAS

Epistasis model ρ

MAF (f a ,f b )

LD r2

Main effect (r a ,r b )

Interaction ρ

# scenarios

\(M_{0} = \left (\begin {array}{lll} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1\\ \end {array}\right)\)

(0.15,0.15) (0.3,0.3)

0,0.2,0.5

(1,1) (1.5,1.5) (1,1.5)

1

18

\(M_{1} = \left (\begin {array}{lll} 1 & 1 & 1 \\ 1 & \rho & \rho \\ 1 & \rho & \rho \end {array}\right)\)

(0.15,0.15) (0.3,0.3)

0,0.2,0.5

(1,1) (1.5,1.5) (1,1.5)

2, 3, 5

54

\(M_{2} = \left (\begin {array}{lll} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & \rho \\ \end {array}\right)\)

(0.15,0.15) (0.3,0.3)

0,0.2,0.5

(1,1) (1.5,1.5) (1,1.5)

2, 5, 10

54

\(M_{3} = \left (\begin {array}{lll} 1 & 1 & 1 \\ 1 & \rho & \rho ^{2} \\ 1 & \rho ^{2} & \rho ^{4} \end {array}\right)\)

(0.15,0.15) (0.3,0.3)

0,0.2,0.5

(1,1) (1.5,1.5) (1,1.5)

2, 3, 5

54

\(M_{4} = \left (\begin {array}{lll} 1 & 1 & 1 \\ 1 & 1 & \rho \\ \rho & \rho & \rho \\ \end {array}\right)\)

(0.15,0.15) (0.3,0.3)

0,0.2,0.5

(1,1) (1.5,1.5) (1,1.5)

2, 3, 5

54

     

234

  1. Each scenario includes two causal SNPs a and b with MAF f a and f b respectively, and with a LD r2. The relative risk of genotype (a,b)=(i,j) vs genotype (0,0) is given by Ri,j=ra,irb,jρi,j. The matrix ρi,j is given by the epistasis model (null, dominant-dominant, recessive-recessive, multiplicative or alternative from top to bottom) and the scalar interaction parameter ρ. The main effect for SNP a is ra,i=r a if a≠0, and ra,0=1, and similarly for SNP b. For each epistasis model we consider all the combination of MAF, LD, main effect and interaction parameter