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Table 8 Simulation Results (Normal Distribution, 1:2 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 6/14 5 1 -3 1 1 -3 2 94 97 94 90 93 90 15 10 17 14 12 16 59 44 55
MD = 8   10 0 -4 1 2 -4 1 94 97 94 92 94 92 25 18 30 18 16 22 60 44 56
RoM = 1.08   30 0 -5 1 1 -5 1 93 97 93 94 94 93 59 53 69 36 35 44 60 44 56
  66/134 5 0 0 0 0 -1 1 96 96 96 88 88 87 77 77 79 20 20 21 92 91 92
   10 0 -1 0 0 -1 0 96 96 96 92 92 91 98 98 98 26 27 28 92 91 92
   30 0 0 0 0 -1 0 96 96 96 94 94 94 100 100 100 56 57 59 92 91 92
SMD = 0.5 6/14 5 0 -3 1 1 -4 1 94 97 95 90 92 90 57 50 61 41 37 43 59 44 56
MD = 20   10 0 -4 1 1 -5 1 94 97 94 92 93 92 86 83 89 62 60 66 60 44 57
RoM = 1.2   30 0 -5 1 0 -6 1 93 96 94 94 94 94 100 100 100 96 97 98 60 43 57
  66/134 5 0 0 0 0 -1 1 96 96 96 88 88 88 100 100 100 61 61 61 92 91 92
   10 0 0 0 0 -1 0 96 96 96 92 92 91 100 100 100 84 85 86 92 91 92
   30 0 0 0 0 -1 0 96 96 96 94 94 94 100 100 100 100 100 100 92 91 92
SMD = 0.8 6/14 5 0 -4 0 0 -4 1 94 97 95 90 92 90 91 89 93 72 69 74 59 43 56
MD = 32   10 0 -5 0 0 -5 1 94 96 95 92 93 92 100 100 100 93 93 94 60 43 57
RoM = 1.32   30 0 -5 0 0 -6 0 93 95 94 94 92 94 100 100 100 100 100 100 60 42 57
  66/134 5 0 0 0 0 -1 1 96 96 96 88 88 88 100 100 100 90 91 91 92 91 92
   10 0 0 0 0 -1 1 96 96 96 92 92 92 100 100 100 100 100 100 92 91 92
   30 0 0 0 0 -1 0 96 96 96 94 94 94 100 100 100 100 100 100 92 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 (6/14 and 66/134 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.