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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.