Table 2. The proportion of individual with different status of disease/SNP1/SNP2 could be calculated by p_baseline, MAF₁, MAF₂, OR_y,SNP1, OR_y,SNP2 and OR_interaction.

SNP1	SNP2	Disease	Proportion in total population
Major homozygous	Major homozygous	Control	(1-MAF1)2(1-MAF2)2(1-q1)
Major homozygous	Major homozygous	Case	(1-MAF1)2(1-MAF2)2q1
Major homozygous	Heterogeneous	Control	2(1-MAF1)2(1-MAF2)p6(1-q2)
Major homozygous	Heterogeneous	Case	2(1-MAF1)2(1-MAF2)p6q2
Major homozygous	Minor homozygous	Control	(1-MAF1)2(1-MAF2)2(1-q3)
Major homozygous	Minor homozygous	Case	(1-MAF1)2(1-MAF2)2q3
Heterogeneous	Major homozygous	Control	2MAF1(1-MAF1)(1-MAF2)2(1-q4)
Heterogeneous	Major homozygous	Case	2MAF1(1-MAF1)(1-MAF2)2q4
Heterogeneous	Heterogeneous	Control	4MAF1(1-MAF1)(1-MAF2)p6(1-q5)
Heterogeneous	Heterogeneous	Case	4MAF1(1-MAF1)(1-MAF2)p6q5
Heterogeneous	Minor homozygous	Control	2MAF1(1-MAF1)(1-MAF2)2(1-q6)
Heterogeneous	Minor homozygous	Case	2MAF1(1-MAF1)(1-MAF2)2q6
Minor homozygous	Major homozygous	Control	MAF12(1-MAF2)2(1-q7)
Minor homozygous	Major homozygous	Case	MAF12(1-MAF2)2q7
Minor homozygous	Heterogeneous	Control	2MAF12(1-MAF2)p6(1-q8)
Minor homozygous	Heterogeneous	Case	2MAF12(1-MAF2)p6q8
Minor homozygous	Minor homozygous	Control	MAF12(1-MAF2)2(1-q9)
Minor homozygous	Minor homozygous	Case	MAF12(1-MAF2)2q9

p_baseline: the disease risk in subjects with major homozygous genotype of SNP1 and SNP2 in each simulated population; MAF₁: the minor allele frequency of SNP1; MAF₂: the minor allele frequency of SNP2; OR_y,SNP1: the main effect of SNP1; OR_y,SNP2: the main effect of SNP2; OR_interaction: gene–gene interaction effect between SNP1 and SNP2.

q₁ to q₉: the disease prevalence of individuals with different genotype.

• q₁ = p_baseline = (1 + exp(−ln(p_baseline /(1 − p_baseline))))⁻¹
• $q_2={\left(1+\text{exp}\left(-\text{ln}\left(p_{baseline}O{R}_{y,SN{P}_2}/\left(1-p_{baseline}\right)\right)\right)\right)}^{-1}$
• $q_3={\left(1+\text{exp}\left(-\text{ln}\left(p_{baseline}O{R}_{y,SN{P}_2}{}^2/\left(1-p_{baseline}\right)\right)\right)\right)}^{-1}$
• $q_4={\left(1+\text{exp}\left(-\text{ln}\left(p_{baseline}O{R}_{y,SN{P}_1}/\left(1-p_{baseline}\right)\right)\right)\right)}^{-1}$
• $q_5={\left(1+\text{exp}\left(-\text{ln}\left(p_{baseline}O{R}_{y,SN{P}_1}O{R}_{y,SN{P}_2}/\left(1-p_{baseline}\right)\right)\right)\right)}^{-1}$
• $q_6={\left(1+\text{exp}\left(-\text{ln}\left(p_{baseline}O{R}_{y,SN{P}_1}O{R}_{y,SN{P}_2}{}^2/\left(1-p_{baseline}\right)\right)\right)\right)}^{-1}$
• $q_7={\left(1+\text{exp}\left(-\text{ln}\left(p_{baseline}O{R}_{y,SN{P}_1}{}^2/\left(1-p_{baseline}\right)\right)\right)\right)}^{-1}$
• $q_8={\left(1+\text{exp}\left(-\text{ln}\left(p_{baseline}O{R}_{y,SN{P}_1}{}^{2}O{R}_{y,SN{P}_2}/\left(1-p_{baseline}\right)\right)\right)\right)}^{-1}$
• $q_9={\left(1+\text{exp}\left(-\text{ln}\left(p_{baseline}O{R}_{y,SN{P}_1}{}^{2}O{R}_{y,SN{P}_2}{}^2/\left(1-p_{baseline}\right)\right)\right)\right)}^{-1}$