Table 3

The validation of the theoretical results from Table 2.a

Average formulation

95% probability formulation



Univariate method

Binomial method

Permutation


π1

λ0

nb

q

λ

ϕλ0

nc

q

λ

ϕλ0

nd


5%

60%

9

0.0505

0.69

0.937

9

0.0505

0.69

0.937

11.3(0.453)

70%

9

0.0505

0.69

0.497

10

0.0502

0.80

0.983

12.5(0.507)

80%

10

0.0502

0.80

0.506

11

0.0494

0.87

0.961

14.2(0.485)

90%

12

0.0492

0.91

0.730

13

0.0484

0.95

0.965

17.1(0.568)

10%

60%

8

0.0490

0.71

0.997

8

0.0490

0.71

0.997

9.8(0.361)

70%

8

0.0490

0.71

0.589

9

0.0506

0.81

1.000

10.8(0.368)

80%

9

0.0506

0.81

0.688

10

0.0503

0.88

0.999

12.1(0.291)

90%

11

0.0497

0.93

0.921

11

0.0497

0.93

0.921

14.6(0.491)

20%

60%

7

0.0498

0.73

1.000

7

0.0498

0.73

1.000

8.0(0.089)

70%

7

0.0498

0.73

0.901

7

0.0498

0.73

0.901

9.0(0.045)

80%

8

0.0491

0.84

0.966

8

0.0491

0.84

0.966

10.1(0.224)

90%

9

0.0501

0.90

0.627

10

0.0497

0.94

0.999

12.2(0.384)


a. Empirical estimates of FDR q, average sensitivity λ, and probability ϕλ0 of the univariate method for the average formulation and of the binomial method for the 95% probability formulation. The parameters used in the calculation were: m = 2,000, δ0 = 2, and q* = 0.05.

b. Sample size n is computed by the univariate method from Equation (1) to achieve sensitivity λ0 on average.

c. Sample size n is calculated using Tsai et al. [7] method to ensure sensitivity λ0 with 95% probability.

d. Sample size n (standard deviation) is calculated using the proposed permutation method to ensure sensitivity λ0 with 95% probability with pilot study of group size 4 under the independent model.

Lin et al. BMC Bioinformatics 2010 11:48   doi:10.1186/1471-2105-11-48

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