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Table 4 Performance on simulated data for scenario I

From: Statistical tools for synthesizing lists of differentially expressed features in related experiments

Parameters

Rules

q

R

CI 95

O 11

O 1+

O +1

FP (%)

TP (%)

FN (%)

TN (%)

Global error

Independence case: n= 3000, common = 0, DE1 = 1000, DE2 = 800

            

   Independence: signal to noise

 

0.55

1*

0.98-1.02

0†

0†

0†

0

0

0

3,000 (100.0)

0

   ratio = 0.4‡

            

A: n = 3000, common = 700, DE1 = 1000, DE2 = 800

            

   Case A1: signal to noise ratio = 9.6‡

Max

0.01

2.60

2.50-2.72

619

975

730

4 (0.2)

615 (87.8)

85 (12.2)

2,296 (99.8)

89

 

Double

0.06

2.04

1.97-2.19

676

1,095

877

29 (1.3)

647 (92.4)

53 (7.6)

2,271 (98.7)

82

            

Min§ = 81

   Case A2: signal to noise ratio = 1.6‡

Max

0.01

4.72

4.19-5.29

86

346

157

1 (0.0)

85 (12.1)

615 (87.9)

2,299 (100.0)

616

 

Double

0.08

2.01

1.90-2.20

212

677

459

28 (1.2)

184 (26.3)

516 (73.7)

2,272 (98.8)

544

            

Min§ = 535

B: n = 3000, common = 200, DE1 = 700, DE2 = 500

            

   Case B1: signal to noise ratio = 9.6‡

Max¶

0.01

1.72

1.58-1.86

185

691

467

8 (0.3)

177 (88.5)

23 (11.5)

2,792 (99.7)

31

            

Min§ = 31

   Case B2: signal to noise ratio = 1.6‡

Max

0.01

2.98

2.38-3.71

36

250

145

3 (0.1)

33 (16.7)

167 (83.3)

2,797 (99.9)

170

 

Double

0.03

2.03

1.67-2.40

57

355

236

11 (0.4)

46 (23.0)

154 (77.1)

2,789 (99.6)

165

            

Min§ = 165

C: n = 3000, common = 100, DE1 = 500, DE2 = 400

            

   Case C1: signal to noise ratio = 9.6‡

Max¶

0.01

1.48

1.30-1.67

95

500

383

7 (0.2)

88 (88.4)

12 (11.6)

2,893 (99.8)

19

            

Min§ = 19

   Case C2: signal to noise ratio = 1.6‡

Max

0.01

2.93

2.16-3.83

20

214

96

3 (0.1)

17 (16.6)

83 (83.4)

2,897 (99.9)

86

 

Double

0.02

2.16

1.63-2.81

26

262

134

5 (0.2)

21 (21.0)

79 (79.0)

2,895 (99.8)

84

            

Min§ = 84

  1. Average simulation results: we show the results from the joint model on one case of simulated data for independent experiments and six cases of simulated data for two associated experiments. The simulation scenario consists of four groups of genes: differentially expressed DE in both experiments, differentially expressed in only one experiment (DE1 and DE2 respectively), and differentially expressed in neither experiment. For the Independence case, the number of genes differentially expressed in both experiments was set to 0. We present two decision rules: the threshold associated with the maximum R(q) is q max and the threshold associated with the R(q) ≥ 2 is q2 (called 'double' in the table). We define q max = arg max{Median(R(q) | O, n) over the set of values of q for which CI95(q) excludes 1} and q2 = max{over the set of values of q for which CI95(q) excludes 1 and Median(R(q) | O, n) ≥ 2}. We averaged the results over 50 repeats for each case. *In case of independence it is still possible to calculate he maximum of R(q), but it is not significant, so there is no associated list of common genes. †All the CIs contain 1, so no genes are called in common; thus, there are no FP. ‡The signal to ratio is calculated as E(Ga(shape, 1/scale))/(r1/2 + r2/2). §Minimum global error (observed). ¶There is no ratio larger than 2 and only the maximum rule has been reported.