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. 2021 Feb 1;51(3):237–249. doi: 10.1007/s10519-020-10035-7

Table 1.

Statistical power to reject the null hypothesis that A–C covariance is zero (alpha = 0.05)

prPRS prPh σ2A σ2C σ2E σAC rAC σ2Ph pr2σAC Power N (0.80)
1 0.2 0.054 0.3 (0.27) 0.2 (0.18) 0.5 (0.45) 0.048 0.2 1.09 0.088 0.216 11,420
2 0.2 0.052 0.3 (0.26) 0.2 (0.17) 0.5 (0.43) 0.073 0.3 1.14 0.128 0.415 5158
3 0.2 0.053 0.3 (0.27) 0.3 (0.26) 0.4 (0.36) 0.060 0.2 1.12 0.107 0.323 6971
4 0.2 0.050 0.3 (0.25) 0.3 (0.25) 0.4 (0.34) 0.090 0.3 1.18 0.153 0.606 3161
5 0.4 0.109 0.3 (0.27) 0.2 (0.18) 0.5 (0.45) 0.048 0.2 1.09 0.088 0.402 5352
6 0.4 0.104 0.3 (0.26) 0.2 (0.17) 0.5 (0.43) 0.073 0.3 1.14 0.128 0.724 2408
7 0.4 0.107 0.3 (0.27) 0.3 (0.26) 0.4 (0.36) 0.060 0.2 1.12 0.107 0.595 3241
8 0.4 0.101 0.3 (0.25) 0.3 (0.25) 0.4 (0.34) 0.090 0.3 1.18 0.153 0.906 1462
9 0.2 0.088 0.5 (0.44) 0.2 (0.18) 0.3 (0.27) 0.063 0.2 1.12 0.112 0.238 10,107
10 0.2 0.084 0.5 (0.42) 0.2 (0.17) 0.3 (0.25) 0.094 0.3 1.18 0.159 0.455 4594
11 0.2 0.086 0.5 (0.43) 0.3 (0.26) 0.2 (0.17) 0.077 0.2 1.15 0.134 0.362 6084
12 0.2 0.081 0.5 (0.40) 0.3 (0.24) 0.2 (0.16) 0.116 0.3 1.23 0.189 0.661 2784
13 0.4 0.177 0.5 (0.44) 0.2 (0.18) 0.3 (0.26) 0.063 0.2 1.12 0.112 0.465 4481
14 0.4 0.168 0.5 (0.42) 0.2 (0.17) 0.3 (0.25) 0.094 0.3 1.18 0.158 0.794 2028
15 0.4 0.173 0.5 (0.43) 0.3 (0.26) 0.2 (0.17) 0.077 0.2 1.15 0.133 0.682 2650
16 0.4 0.162 0.5 (0.41) 0.3 (0.24) 0.2 (0.16) 0.116 0.3 1.23 0.188 0.950 1206

Given σ2A = σ2Ap + σ2Aq, prPRS equals σ2Ap/σ2A, i.e., the proportion of additive genetic variance attributable to the PRS, and prPh is the proportion of phenotypic variance attributable to the PRS, σ2Ap/σ2Ph; rAC and σAC are the correlation and covariance of A and C, σ2Ph is the phenotypic variance; pr2*σAC is the proportion of phenotypic variance due to 2*σAC

The standardized A, C, E variance components are given in parentheses. For instance, in setting 16, the raw variance is 0.5 + 0.3 + 0.2 + 0.116*2 = 1.23, and the standardized variance is 0.41 + 0.24 + 0.16 + 0.188 =  ~ 1

The power is given for Nmz = Ndz = 1000, given α = 0.05; N(0.80) is the sample size (N = Nmz + Ndz, where Nmz = Ndz) associated with a power of 0.80, given α = 0.05