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Table 8 Simulation Results (Normal Distribution, 1:2 Experimental to Control Group Sizes, Standard Deviation 40% of Control Mean Value).

From: The ratio of means method as an alternative to mean differences for analyzing continuous outcome variables in meta-analysis: A simulation study

   

% Bias

% Coverage

% Statistical Power

I 2(%)

   

τ = 0s

τ = 0.5s

τ = 0s

τ = 0.5s

τ = 0s

τ 0.5s

τ 0.5s

Δ

n(exp/contr)

k

MD

SMD

RoM

MD

SMD

RoM

MD

SMD

RoM

MD

SMD

RoM

MD

SMD

RoM

MD

SMD

RoM

MD

SMD

RoM

SMD = 0.2

6/14

5

1

-3

1

1

-3

2

94

97

94

90

93

90

15

10

17

14

12

16

59

44

55

MD = 8

 

10

0

-4

1

2

-4

1

94

97

94

92

94

92

25

18

30

18

16

22

60

44

56

RoM = 1.08

 

30

0

-5

1

1

-5

1

93

97

93

94

94

93

59

53

69

36

35

44

60

44

56

 

66/134

5

0

0

0

0

-1

1

96

96

96

88

88

87

77

77

79

20

20

21

92

91

92

  

10

0

-1

0

0

-1

0

96

96

96

92

92

91

98

98

98

26

27

28

92

91

92

  

30

0

0

0

0

-1

0

96

96

96

94

94

94

100

100

100

56

57

59

92

91

92

SMD = 0.5

6/14

5

0

-3

1

1

-4

1

94

97

95

90

92

90

57

50

61

41

37

43

59

44

56

MD = 20

 

10

0

-4

1

1

-5

1

94

97

94

92

93

92

86

83

89

62

60

66

60

44

57

RoM = 1.2

 

30

0

-5

1

0

-6

1

93

96

94

94

94

94

100

100

100

96

97

98

60

43

57

 

66/134

5

0

0

0

0

-1

1

96

96

96

88

88

88

100

100

100

61

61

61

92

91

92

  

10

0

0

0

0

-1

0

96

96

96

92

92

91

100

100

100

84

85

86

92

91

92

  

30

0

0

0

0

-1

0

96

96

96

94

94

94

100

100

100

100

100

100

92

91

92

SMD = 0.8

6/14

5

0

-4

0

0

-4

1

94

97

95

90

92

90

91

89

93

72

69

74

59

43

56

MD = 32

 

10

0

-5

0

0

-5

1

94

96

95

92

93

92

100

100

100

93

93

94

60

43

57

RoM = 1.32

 

30

0

-5

0

0

-6

0

93

95

94

94

92

94

100

100

100

100

100

100

60

42

57

 

66/134

5

0

0

0

0

-1

1

96

96

96

88

88

88

100

100

100

90

91

91

92

91

92

  

10

0

0

0

0

-1

1

96

96

96

92

92

92

100

100

100

100

100

100

92

91

92

  

30

0

0

0

0

-1

0

96

96

96

94

94

94

100

100

100

100

100

100

92

91

92

  1. Results of 10,000 simulations per scenario with a standard deviation equal to 40% of the control mean, for each combination of effect size (0.2, 0.5, and 0.8 standard deviation units), number of patients (6/14 and 66/134 experimental/control patients per trial), and number of trials (5, 10, and 30). The "% Bias" columns show the bias of each effect measure (MD, SMD, RoM) expressed as percentages of the expected values (negative sign denotes less than expected value), with and without heterogeneity. The "% coverage" columns show the percentage of cases that the true value falls within the 95% confidence interval of the simulated result, with and without heterogeneity. The "% statistical power" columns show the percentage of cases that the 95% confidence interval of the simulated result yields a significant treatment effect (i.e. excluding zero for MD and SMD, and one for RoM), with and without heterogeneity. The I 2 column shows the degree of heterogeneity only for the scenarios in which heterogeneity was introduced. (For all the scenarios without heterogeneity, the ratio of Q/(k-1) was close to unity as expected, corresponding to I 2 = 0 [data not shown].)
  2. Abbreviations for Table and Legend: contr – control, exp – experimental, I 2I 2 heterogeneity measure, k – number of trials in each meta-analysis, n – number of experimental or number of control patients per trial, Q – Cochran's Q statistic for heterogeneity, MD – mean difference, RoM – ratio of means, s – standard deviation units, SMD – standardized mean difference.