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Table 5 Simulation Results (Normal Distribution, Equal Experimental and Control Groups, Standard Deviation 70% 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 10/10 5 0 -4 0 -1 -5 0 95 97 96 90 92 91 15 11 12 15 13 12 59 48 45
   10 0 -5 -1 0 -5 -1 95 97 96 92 93 93 27 22 23 19 18 16 60 48 45
   30 0 -5 -1 0 -6 -1 94 96 95 94 94 93 66 61 60 38 38 34 60 47 46
MD = 14 100/100 5 0 0 0 0 -1 2 96 97 96 88 88 87 82 82 82 21 21 22 93 92 91
RoM = 1.14   10 0 0 0 0 0 1 96 96 96 92 92 90 99 99 99 27 27 31 93 92 91
   30 0 0 0 0 0 1 96 96 96 94 94 92 100 100 100 56 58 62 93 92 91
SMD = 0.5 10/10 5 0 -4 -1 0 -5 -1 95 97 95 90 92 91 64 57 58 43 40 38 59 48 47
   10 0 -5 -2 0 -5 -2 95 97 95 92 93 92 91 89 88 66 64 61 60 47 47
   30 0 -5 -2 0 -6 -3 94 96 92 94 93 91 100 100 100 98 97 97 60 47 48
MD = 35 100/100 5 0 0 0 0 0 2 96 97 96 88 88 87 100 100 100 61 61 63 93 92 91
RoM = 1.35   10 0 0 0 0 0 1 96 96 96 92 92 90 100 100 100 85 86 88 93 92 91
   30 0 0 0 0 -1 1 96 96 95 94 94 92 100 100 100 100 100 100 93 92 91
SMD = 0.8 10/10 5 0 -4 -1 0 -5 -2 95 97 95 90 92 90 95 94 93 74 72 71 59 47 48
   10 0 -5 -2 0 -5 -3 95 96 94 92 92 91 100 100 100 95 95 94 60 46 48
   30 0 -5 -3 0 -6 -4 94 94 90 94 92 89 100 100 100 100 100 100 60 46 49
MD = 56 100/100 5 0 0 0 0 0 2 96 96 96 88 88 87 100 100 100 91 91 92 93 92 91
RoM= 1.56   10 0 0 0 0 0 2 96 96 96 92 92 90 100 100 100 100 100 100 93 91 91
   30 0 0 0 0 -1 1 96 96 95 94 94 92 100 100 100 100 100 100 93 91 91
  1. Results of 10,000 simulations per scenario with a standard deviation equal to 70% of the control mean, for each combination of effect size (0.2, 0.5, and 0.8 standard deviation units), number of patients (10/10 and 100/100 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.