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Table 7 Simulation Results (Normal Distribution, 2:1 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

14/6

5

-1

-5

0

0

-5

0

94

97

94

90

92

90

15

10

11

14

12

12

59

44

54

  

10

1

-4

-1

2

-4

-1

94

97

93

92

93

91

25

18

18

18

16

14

60

44

55

  

30

0

-5

-1

1

-6

-1

94

97

91

93

94

93

59

53

44

36

35

27

60

44

55

MD = 8

134/66

5

0

0

0

0

-1

0

96

97

97

88

88

88

78

77

76

21

21

21

92

91

91

RoM = 1.08

 

10

0

0

0

0

-1

0

96

96

96

92

91

91

98

98

97

27

27

27

92

91

91

  

30

0

0

0

0

-1

0

96

96

96

94

94

94

100

100

100

56

57

57

92

91

91

SMD = 0.5

14/6

5

0

-4

-1

0

-5

0

94

97

94

90

92

90

57

50

50

41

37

36

59

44

54

  

10

0

-5

-1

1

-5

-1

94

97

93

92

93

91

86

83

79

62

61

56

60

44

55

  

30

0

-5

-1

0

-6

-1

94

96

91

93

93

92

100

100

100

96

97

94

60

43

56

MD = 20

134/66

5

0

0

0

0

-1

1

96

96

97

88

88

88

100

100

100

60

61

60

92

91

91

RoM = 1.2

 

10

0

0

0

0

-1

0

96

96

96

92

92

91

100

100

100

85

86

85

92

91

91

  

30

0

0

0

0

-1

0

96

96

95

94

94

94

100

100

100

100

100

100

92

91

91

SMD = 0.8

14/6

5

0

-4

-1

0

-5

0

94

97

93

90

92

90

91

89

87

71

69

66

59

43

54

  

10

0

-5

-1

0

-5

-1

94

96

92

92

93

91

100

100

99

93

93

91

60

43

55

  

30

0

-5

-2

0

-6

-1

94

94

90

93

92

92

100

100

100

100

100

100

60

42

56

MD = 32

134/66

5

0

0

0

0

-1

1

96

96

96

88

88

88

100

100

100

91

91

91

92

91

91

RoM = 1.32

 

10

0

0

0

0

-1

0

96

96

96

92

92

91

100

100

100

100

100

100

92

91

91

  

30

0

0

0

0

-1

0

96

96

95

94

94

93

100

100

100

100

100

100

92

91

91

  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 (14/6 and 134/66 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.