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Table 4 Empirical power at the 0.05 significance level for Ω0 + I + II in the homogenous population

From: Rare variant association analysis in case-parents studies by allowing for missing parental genotypes

  Causal variants have different effects with the same direction Causal variants have opposite effects
Non-causal variants Sample size (N)a \( {TDT}_{\mathrm{BRV}} \) \( {\tilde{Z}}_C \) \( {TDT}_{\mathrm{BRV}} \) \( {\tilde{Z}}_C \)
80% N0 0.602 0.408 0.226 0.140
+ \( \frac{1}{10} \) N0 0.709(17.8%) 0.560(37.3%) 0.271(19.9%) 0.224(60.0%)
+ \( \frac{1}{5} \) N0 0.740(22.9%) 0.668(63.7%) 0.282(24.8%) 0.250(78.6%)
+ \( \frac{1}{2} \) N0 0.778(29.2%) 0.749(83.6%) 0.311(37.6%) 0.304(117%)
60% N0 0.828 0.776 0.364 0.164
+ \( \frac{1}{10} \) N0 0.930(12.3%) 0.918(18.3%) 0.456(25.3%) 0.302(84.1%)
+ \( \frac{1}{5} \) N0 0.949(14.6%) 0.941(21.3%) 0.490(34.6%) 0.410(150%)
+ \( \frac{1}{2} \) N0 0.971(17.3%) 0.972(25.3%) 0.581(59.6%) 0.551(236%)
40% N0 1.00 0.982 0.264 0.178
+ \( \frac{1}{10} \) N0 1.00 1.00 0.279(5.7%) 0.230(29.2%)
+ \( \frac{1}{5} \) N0 1.00 1.00 0.308(16.7%) 0.290(62.9%)
+ \( \frac{1}{2} \) N0 1.00 1.00 0.345(30.7%) 0.340(91.0%)
20% N0 1.00 1.00 0.278 0.166
+ \( \frac{1}{10} \) N0 1.00 1.00 0.292(5.04%) 0.210(26.5%)
+ \( \frac{1}{5} \) N0 1.00 1.00 0.315(13.3%) 0.260(56.6%)
+ \( \frac{1}{2} \) N0 1.00 1.00 0.370(33.1%) 0.321(93.3%)
  1. Note: aThe sample size N = N0++NI + NII, denoted by + \( \frac{1}{10} \) N0, + \( \frac{1}{5} \) N0, and + \( \frac{1}{2} \) N0, where there are N0 (=500) complete case-parents trios (Ω0) and NI case-parents trios of ΩI and NII case-parents trios of ΩII with NI = NII = \( \frac{1}{20} \) N0, \( \frac{1}{10} \) N0, and \( \frac{1}{4} \) N0, respectively. Shown in parentheses is the proportion of power improvement