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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