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Table 2 Empirical power at the 0.05 significance level for Ω0 + I 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 0.712(18.3%) 0.566(38.7%) 0.272(20.4%) 0.228(62.9%)
+ \( \frac{1}{5} \) N0 0.748(24.3%) 0.674(65.2%) 0.290(28.3%) 0.257(83.6%)
+ \( \frac{1}{2} \) N0 0.784(30.2%) 0.752(84.3%) 0.312(38.1%) 0.304(117%)
60% N0 0.828 0.776 0.364 0.164
+ \( \frac{1}{10} \) N0 0.938(13.3%) 0.922(18.8%) 0.458(25.8%) 0.310(89.0%)
+ \( \frac{1}{5} \) N0 0.956(15.5%) 0.946(21.9%) 0.506(39.0%) 0.414(152%)
+ \( \frac{1}{2} \) N0 0.980(18.4%) 0.982(26.5%) 0.587(61.3%) 0.556(239%)
40% N0 1.00 0.980 0.264 0.178
+ \( \frac{1}{10} \) N0 1.00 1.00 0.284(7.58%) 0.242(34.0%)
+ \( \frac{1}{5} \) N0 1.00 1.00 0.308(16.7%) 0.296(66.3%)
+ \( \frac{1}{2} \) N0 1.00 1.00 0.360(36.4%) 0.350(96.6%)
20% N0 1.00 1.00 0.278 0.166
+ \( \frac{1}{10} \) N0 1.00 1.00 0.294(5.76%) 0.218(31.3%)
+ \( \frac{1}{5} \) N0 1.00 1.00 0.315(13.3%) 0.275(65.7%)
+ \( \frac{1}{2} \) N0 1.00 1.00 0.376(35.2%) 0.330(98.7%)
  1. Note: a The sample size N = N0 + NI, 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 with NI = \( \frac{1}{10} \) N0, \( \frac{1}{5} \) N0, and \( \frac{1}{2} \) N0, respectively. Shown in parentheses is the proportion of power improvement