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Table 3 Simulation Results (Normal Distribution, Equal Experimental and Control Groups, 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 10/10 5 0 -4 0 0 -5 1 95 97 95 90 92 90 15 11 14 15 13 14 59 48 55
   10 0 -5 0 1 -5 0 95 97 95 92 93 92 27 22 26 19 18 19 60 48 56
   30 0 -5 0 1 -6 0 94 96 95 94 94 94 66 61 64 39 38 38 60 48 56
MD = 8 100/100 5 0 0 0 0 0 1 96 97 96 88 88 87 82 82 82 21 21 21 93 92 92
RoM = 1.08   10 0 0 0 0 0 0 96 96 96 92 92 91 99 99 99 27 27 28 93 92 92
   30 0 0 0 0 0 0 96 96 96 94 94 94 100 100 100 56 58 59 93 92 92
SMD = 0.5 10/10 5 0 -4 0 0 -5 0 95 97 95 90 92 90 64 57 62 43 40 42 59 48 56
   10 0 -5 0 0 -5 0 95 97 95 92 93 92 91 89 90 66 64 65 60 48 56
   30 0 -5 0 0 -6 0 94 96 94 94 93 93 100 100 100 98 97 97 60 47 57
MD = 20 100/100 5 0 0 0 0 0 1 96 97 96 88 88 88 100 100 100 61 61 61 93 92 92
RoM = 1.2   10 0 0 0 0 0 0 96 96 96 92 92 91 100 100 100 85 86 86 93 92 92
   30 0 0 0 0 -1 0 96 96 96 94 94 93 100 100 100 100 100 100 93 92 92
SMD = 0.8 10/10 5 0 -4 0 0 -5 0 95 97 95 90 92 90 95 94 95 75 72 73 59 47 56
   10 0 -5 0 0 -5 0 95 96 95 92 92 92 100 100 100 95 95 95 60 47 57
   30 0 -5 -1 0 -6 0 94 94 94 94 92 93 100 100 100 100 100 100 60 46 57
MD = 32 100/100 5 0 0 0 0 0 1 96 96 96 88 88 87 100 100 100 91 91 91 93 92 92
RoM = 1.32   10 0 0 0 0 0 1 96 96 96 92 92 91 100 100 100 100 100 100 93 91 92
   30 0 0 0 0 -1 0 96 96 96 94 94 93 100 100 100 100 100 100 93 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 (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.