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Table 1 Type I error rate of \( {\tilde{Z}}_C \) and \( {TDT}_{\mathrm{BRV}} \)

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

  \( {\tilde{Z}}_C \) \( {TDT}_{\mathrm{BRV}} \)
α = 0.05 α = 0.001 α = 0.05 α = 0.001
Sample size (N) Sample size (N) Sample size (N) Sample size (N)
Homogeneous population N0 + \( \frac{1}{10} \) N0 N0 + \( \frac{1}{5} \) N0 N0 + \( \frac{1}{2} \) N0 N0 + \( \frac{1}{10} \) N0 N0 + \( \frac{1}{5} \) N0 N0 + \( \frac{1}{2} \) N0 N0 + \( \frac{1}{10} \) N0 N0 + \( \frac{1}{5} \) N0 N0 + \( \frac{1}{2} \)N0 N0 + \( \frac{1}{10} \) N0 N0 + \( \frac{1}{5} \) N0 N0 + \( \frac{1}{2} \) N0
 Ω0 + Ι 0.057 0.045 0.052 0.0012 0.0014 0.0009 0.053 0.046 0.051 0.0011 0.0012 0.0010
 Ω0 + ΙΙ 0.055 0.055 0.050 0.0011 0.0008 0.0014 0.054 0.055 0.052 0.0012 0.0009 0.0014
 Ω0 + Ι + ΙΙ 0.048 0.049 0.046 0.0009 0.0013 0.0012 0.048 0.049 0.049 0.0009 0.0013 0.0013
Population stratification
 Ω0 + Ι 0.055 0.051 0.050 0.0013 0.0012 0.0010 0.055 0.047 0.054 0.0013 0.0012 0.0012
 Ω0 + ΙΙ 0.053 0.056 0.053 0.0014 0.0009 0.0014 0.056 0.054 0.051 0.0012 0.0009 0.0011
 Ω0 + Ι + ΙΙ 0.049 0.049 0.051 0.0009 0.0013 0.0014 0.048 0.050 0.047 0.0009 0.0010 0.0014
  1. Note: The sample size N = N0 + NI, N = N0 + NII, N = N0 + NI + NII for Ω0 + Ι, Ω0 + ΙΙ, and Ω0+Ι+ΙΙ, respectively, with N0 (=500) complete case-parents trios (Ω0). There are NI case-parents trios of ΩI forΩ0 + Ιand NII case-parents trios of ΩII for Ω0 + ΙΙ with NI, NII=\( \frac{1}{10} \)N0, \( \frac{1}{5} \)N0, and \( \frac{1}{2} \)N0, respectively. For Ω0+Ι+ΙΙ, NI = NII, and NI + NII = \( \frac{1}{10} \)N0, \( \frac{1}{5} \)N0, and \( \frac{1}{2} \)N0, respectively