Table 1.

Population structure settings in simulation I.

Population structure setting*	Group	Population 1	Population 2	Population 3	Population 4
S1 (a, b)	Case	500a	500b
	Control	500(1 − a)	500(1 − b)
S2 (p₁, p₀)	Case	500p₁	500(1 − p₁)
	Control	500p₀	500(1 − p₀)
S3 (p₁₁, p₁₂, p₀₁, p₀₂)	Case	500p₁₁	500p₁₂	500(1 − p₁₁ − p₁₂)
	Control	500p₀₁	500p₀₂	500(1 − p₀₁ − p₀₂)
S4 (p₁₁, p₁₂, p₁₃, p₀₁, p₀₂, p₀₃)	Case	500p₁₁	500p₁₂	500p₁₃	500(1 − p₁₁ − p₁₂ − p₁₃)
	Control	500p₀₁	500p₀₂	500p₀₃	500(1 − p₀₁ − p₀₂ − p₀₃)

Population structure S1 has two subpopulations with each having 500 samples. Population structure S2–S4 each has 500 cases and 500 controls. In S1, the parameters a and b take values in Table 2. S2 contains two subpopulations, where p₁ and p₀ denote the proportions of cases and controls from subpopulation 1, respectively. We consider two levels of population stratification: the moderate ancestral difference is defined as (p₁, p₀) = (0.4, 0.6), and the extreme ancestral difference is defined as (p₁, p₀) = (0.5, 0). S3 contains three subpopulations. Moderate and extreme ancestral differences are defined as (p₁₁, p₁₂, p₀₁, p₀₂) = (0.45, 0.35, 0.35, 0.20) and (0.33, 0.67, 0.0, 0.33), respectively. S4 contains four subpopulations. Parameters (p₁₁, p₁₂, p₁₃, p₀₁, p₀₂, p₀₃) take values (0.35, 0.3, 0.2, 0.15, 0.2, 0.3) and (0.25, 0.25, 0.5, 0.0, 0.5, 0.25), which correspond to moderate and extreme ancestral differences between cases and controls, respectively.