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Table 3 Empirical power at the 0.05 significance level for Ω0 + 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 0.702(16.6%) 0.551(35.1%) 0.269(19.0%) 0.218(55.7%)
+ \( \frac{1}{5} \) N0 0.732(21.6%) 0.660(61.8%) 0.278(23.0%) 0.241(72.1%)
+ \( \frac{1}{2} \) N0 0.770(27.9%) 0.745(82.6%) 0.309(36.7%) 0.300(114%)
60% N0 0.828 0.776 0.364 0.164
+ \( \frac{1}{10} \) N0 0.920(9.20%) 0.911(17.4%) 0.454(24.7%) 0.310(89.0%)
+ \( \frac{1}{5} \) N0 0.941(13.6%) 0.936(20.6%) 0.482(32.4%) 0.406(147%)
+ \( \frac{1}{2} \) N0 0.963(16.3%) 0.960(23.7%) 0.575(58.0%) 0.542(230%)
40% N0 1.00 0.980 0.264 0.178
+ \( \frac{1}{10} \) N0 1.00 1.00 0.277(4.92%) 0.231(29.8%)
+ \( \frac{1}{5} \) N0 1.00 1.00 0.300(13.6%) 0.286(60.7%)
+ \( \frac{1}{2} \) N0 1.00 1.00 0.348(31.8%) 0.339(90.4%)
20% N0 1.00 1.00 0.278 0.166
+ \( \frac{1}{10} \) N0 1.00 1.00 0.289(3.96%) 0.204(22.9%)
+ \( \frac{1}{5} \) N0 1.00 1.00 0.310(11.5%) 0.262(57.8%)
+ \( \frac{1}{2} \) N0 1.00 1.00 0.368(32.4%) 0.320(92.8%)
  1. Note: aThe sample size N = N0 + 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 NII case-parents trios of ΩII with NII = \( \frac{1}{10} \) N0, \( \frac{1}{5} \) N0, and \( \frac{1}{2} \) N0, respectively. Shown in parentheses is the proportion of power improvement