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Table 4 Results of comparison of various methods, including Zhao et. al. [12] (Zhao), Spinka et al. [9] using grid-search (Spinka, grid) or supplementary information on Pr(D = 1) (Spinka, suppl.), and the proposed multinomial logistic regression method (Proposed)

From: Multinomial logistic regression approach to haplotype association analysis in population-based case-control studies

  Zhao Spinka, grid Spinka, suppl. Proposed
  β X β hap β int β X β hap β int β X β hap β int β X β hap β int
α = -3, β X = 0.3, β hap = 0.1, β int = 0
biasa 0.002 0.025 0.028 0.002 -0.010 0.015 0.002 -0.020 -0.005 0.002 -0.021 -0.016
SEb 0.066 0.269 0.254 0.065 0.188 0.155 0.060 0.189 0.155 0.059 0.170 0.142
SE _ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeGabaaQgmaaHaaabiqaaGQbcqqGtbWucqqGfbqraiaawkWaaaaa@310E@ c 0.064 0.260 0.268 0.063 0.187 0.159 0.063 0.183 0.153 0.063 0.175 0.143
coverd 0.948 0.958 0.975 0.955 0.957 0.965 0.943 0.947 0.952 0.970 0.947 0.955
sizee - - 0.025 - - 0.035 - - 0.048 - - 0.045
α = -3, β X = 0.3, β hap = 0.1,β int = 0.3
biasa 0.001 0.022 0.029 0.000 -0.009 0.029 -0.006 -0.017 0.005 0.001 -0.028 -0.019
SEb 0.064 0.269 0.289 0.063 0.197 0.182 0.061 0.193 0.152 0.064 0.187 0.137
SE _ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeGabaaQgmaaHaaabiqaaGQbcqqGtbWucqqGfbqraiaawkWaaaaa@310E@ c 0.064 0.265 0.277 0.063 0.193 0.161 0.063 0.189 0.154 0.063 0.181 0.137
coverd 0.950 0.952 0.936 0.948 0.958 0.923 0.954 0.948 0.950 0.954 0.948 0.956
powerf - - 0.198 - - 0.524 - - 0.480 - - 0.513
  1. aSimulation mean of the parameter estimates minus the true value.
  2. bSimulation standard error of the parameter estimates.
  3. cSimulation mean of the estimated standard errors.
  4. dCoverage probability of 95% confidence interval.
  5. eSize of Wald test for testing H0 : β int = 0.
  6. fPower of Wald test for testing H0 : β int = 0.