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Table 1 The empirical Type I error rates (× 100) and power (× 100) for the six tests when methylation values were generated from normal distributions without (Outlier=No) or with an outlier (Outlier =Yes). 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 5.1 3.4 5.1 5.1 5.0 5.1
(Type I error) No 1 1.0 0.5 1.1 1.0 1.0 1.1
  No 0.5 0.5 0.4 0.6 0.6 0.5 0.6
diffM&eqV No 5 97.3 95.5 97.1 97.1 97.2 97.2
  No 1 90.2 84.9 89.4 89.8 90.0 89.7
  No 0.5 85.3 75.0 84.3 83.1 83.8 83.6
eqM&diffV No 5 90.0 25.1 87.3 84.1 83.8 83.8
  No 1 74.3 6.1 65.7 63.5 62.9 62.6
  No 0.5 66.3 2.4 55.2 51.6 52.0 52.5
diffM&diffV No 5 83.2 63.9 81.0 79.3 79.2 79.3
  No 1 63.7 36.8 59.9 56.9 56.8 56.3
  No 0.5 53.9 24.5 48.8 45.5 46.3 46.2
eqM&eqV Yes 5 12.2 3.2 3.7 4.8 4.8 4.8
(Type I error) Yes 1 3.7 0.5 0.5 0.9 0.9 1.0
  Yes 0.5 2.3 0.4 0.3 0.4 0.4 0.4
diffM&eqV Yes 5 95.6 94.9 98.4 98.1 98.1 98.1
  Yes 1 83.0 86.6 94.5 92.3 92.7 92.4
  Yes 0.5 77.5 76.9 91.0 89.4 90.0 89.3
eqM&diffV Yes 5 46.3 16.7 54.3 69.3 68.8 68.9
  Yes 1 20.3 5.3 31.5 43.0 43.5 43.2
  Yes 0.5 15.1 2.2 22.8 36.0 36.8 36.1
diffM&diffV Yes 5 54.6 58.4 75.5 78.4 78.5 78.7
  Yes 1 26.5 38.2 56.9 56.1 57.2 57.0
  Yes 0.5 20.3 25.8 47.5 48.4 50.4 49.1