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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