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Table 2 The empirical Type I error rates (× 100) and power (× 100) of the six tests when methylation values were generated from Beta distributions. The numbers of non-diseased and diseased samples are (100, 100)

From: Robust joint score tests in the application of DNA methylation data analysis

Scenarios Outlier α(%) jointLRT KS AW iAW.Lev iAW.BF iAW.TM
eqM&eqV No 5 5.7 3.5 5.4 5.4 5.4 5.5
(Type I error) No 1 1.5 0.5 1.0 1.1 1.2 1.1
  No 0.5 0.8 0.3 0.5 0.5 0.5 0.5
diffM&eqV No 5 96.8 94.7 97.5 97.2 97.4 97.4
  No 1 88.4 86.7 91.7 90.5 91.0 90.9
  No 0.5 83.1 77.5 87.8 86.6 87.9 87.4
eqM&diffV No 5 88.1 18.9 86.8 83.1 82.7 83.0
  No 1 68.6 6.2 65.8 62.2 60.6 61.3
  No 0.5 60.4 2.5 55.6 53.5 52.6 53.2
diffM&diffV No 5 83.5 64.5 88.6 84.9 85.8 85.9
  No 1 58.1 42.8 70.4 63.0 64.5 64.8
  No 0.5 48.9 30.2 60.6 54.6 57.6 56.8
eqM&eqV Yes 5 11.0 3.6 3.8 5 4.9 4.9
(Type I error) Yes 1 3.3 0.6 0.7 1.0 1.0 1.0
  Yes 0.5 1.8 0.3 0.3 0.5 0.5 0.5
diffM&eqV Yes 5 97.6 95.9 98.8 98.6 98.8 98.7
  Yes 1 89.2 87.7 94.8 93.4 94.0 93.7
  Yes 0.5 82.6 79.6 91.6 89.3 89.9 89.8
eqM&diffV Yes 5 31.9 15.7 24.9 61.2 59.8 60.6
  Yes 1 11.5 5.1 6.7 33.0 31.3 32.1
  Yes 0.5 6.6 2.0 4.0 23.2 21.3 22.0
diffM&diffV Yes 5 26.4 59.9 36.6 52.6 53.4 53.6
  Yes 1 8.4 38.3 15.4 24.9 25.7 25.5
  Yes 0.5 4.5 26.0 10.6 16.5 17.2 17.2