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Table 4 The empirical Type I error rates (× 100) and power (× 100) for the six tests when methylation values generated from chi-squared 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 13.8 4.2 5.0 6.3 5.3 5.2
(Type I errror) No 1 6.3 0.7 0.9 1.5 1.3 1.2
  No 0.5 4.4 0.4 0.4 0.8 0.5 0.5
diffM&eqV No 5 90.2 99.7 99.8 99.6 99.9 99.9
  No 1 53.8 97.1 99.0 97.1 99.4 99.4
  No 0.5 40.9 95.9 98.1 94.9 99.2 99.0
eqM&diffV No 5 18.6 10.2 29.2 29.6 35.4 34.6
  No 1 5.8 2.1 10.3 11.4 14.7 15.0
  No 0.5 3.9 1.3 6.9 7.0 11.1 10.4
diffM&diffV No 5 18.4 42.2 59.9 54.9 70.6 69.0
  No 1 3.7 17.9 35.7 27.5 45.5 43.8
  No 0.5 2.1 13.9 27.9 18.9 38.9 35.6
eqM&eqV Yes 5 20.1 4.0 4.8 6.7 5.5 5.3
(Type I error) Yes 1 10.3 0.7 0.7 1.7 1.1 1.1
  Yes 0.5 7.8 0.5 0.2 0.8 0.5 0.5
diffM&eqV Yes 5 67.9 99.5 99.9 99.4 99.9 99.9
  Yes 1 23.7 96.5 99.1 96.4 99.4 99.3
  Yes 0.5 12.9 95.0 98.7 94.0 99.0 98.8
eqM&diffV Yes 5 27.5 9.5 34.0 39.7 41.0 41.5
  Yes 1 9.9 1.8 11.9 16.6 19.3 19.0
  Yes 0.5 6.1 1.1 7.3 11.2 14.0 13.7
diffM&diffV Yes 5 21.9 39.8 65.2 60.4 73.2 72.1
  Yes 1 6.3 16.3 39.9 31.7 49.7 47.7
  Yes 0.5 3.4 12.2 32.5 23.9 41.8 39.7