Table 7 

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

% 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 



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/(k1) was close to unity as expected, corresponding to I^{2 }= 0 [data not shown].) Abbreviations for Table and Legend: contr – control, exp – experimental, I^{2 }– I^{2 }heterogeneity measure, k – number of trials in each metaanalysis, 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. 

Friedrich et al. BMC Medical Research Methodology 2008 8:32 doi:10.1186/14712288832 