Table 3 

The validation of the theoretical results from Table 2.^{a} 

Average formulation 
95% probability formulation 




Univariate method 
Binomial method 
Permutation 



π_{1} 
λ_{0} 
n^{b} 
q 
λ 
ϕ_{λ0} 
n^{c} 
q 
λ 
ϕ_{λ0} 
n^{d} 


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 ϕ_{λ0 }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, δ_{0 }= 2, and q* = 0.05. b. Sample size n is computed by the univariate method from Equation (1) to achieve sensitivity λ_{0 }on average. c. Sample size n is calculated using Tsai et al. [7] method to ensure sensitivity λ_{0 }with 95% probability. d. Sample size n (standard deviation) is calculated using the proposed permutation method to ensure sensitivity λ_{0 }with 95% probability with pilot study of group size 4 under the independent model. 

Lin et al. BMC Bioinformatics 2010 11:48 doi:10.1186/147121051148 