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Table 3 The empirical Type I error rates (× 100) and power (× 100) for the six tests when methylation values generated from mixtures of two normal 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 2.4 3.8 4.9 9.4 5.4 12.3
(Type I error) No 1 0.4 0.7 0.8 3.2 1.3 4.5
  No 0.5 0.2 0.4 0.4 2.0 0.8 2.8
diffM&eqV No 5 16.6 58.4 74.9 56.2 87.0 53.6
  No 1 4.0 30.8 55.1 26.6 65.8 25.5
  No 0.5 2.3 25.5 45.1 17.8 53.9 19.6
eqM&diffV No 5 34.5 98.1 55.1 88.8 57.8 69.9
  No 1 10.5 81.1 36.1 71.6 32.4 47.7
  No 0.5 6.4 72.7 28.9 62.5 23.6 40.5
diffM&diffV No 5 37.7 98.7 61.1 92.0 68.3 76.4
  No 1 12.0 85.2 41.5 77.2 42.6 54.3
  No 0.5 7.8 78.1 34.0 68.3 32.2 46.7
eqM&eqV Yes 5 25.0 3.9 2.8 6.5 4.8 8.1
(Type I error) Yes 1 6.8 0.7 0.4 1.4 1.0 2.1
  Yes 0.5 3.7 0.4 0.2 0.7 0.6 1.3
diffM&eqV Yes 5 4.2 59.4 16.3 21.5 78.1 34.9
  Yes 1 1.1 32.1 5.1 5.2 55.7 9.8
  Yes 0.5 0.5 26.5 3.3 3.5 44.7 5.2
eqM&diffV Yes 5 0.6 97.4 14.4 80.2 49.6 63.3
  Yes 1 0.1 79.5 5.1 59.8 27.4 39.4
  Yes 0.5 0.0 71.2 3.5 54.1 19.7 31.5
diffM&diffV Yes 5 1.0 98.1 19.5 84.6 61.0 71.1
  Yes 1 0.2 83.6 7.5 65.7 37.5 47.0
  Yes 0.5 0.1 76.8 5.6 60.1 27.9 38.1