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%) | |