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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.