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Table 6 Simulation Results (Skewed 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 -2 0 -1 -5 1 95 97 95 89 92 90 16 12 16 15 13 15 60 50 60
   10 0 -3 0 0 -4 0 94 97 94 92 93 92 29 22 28 19 17 19 61 49 61
   30 0 -4 0 0 -5 0 94 96 94 94 94 94 68 62 67 38 37 36 61 49 61
MD = 8 100/100 5 0 0 0 1 0 1 96 96 96 88 88 88 82 81 82 21 21 21 93 92 92
RoM = 1.08   10 0 -1 0 0 0 0 96 96 96 92 92 91 99 99 99 27 28 28 93 92 92
   30 0 0 0 0 0 0 96 96 96 94 93 93 100 100 100 56 58 59 93 92 92
SMD = 0.5 10/10 5 0 -2 1 -1 -4 1 95 97 95 89 92 90 65 59 64 43 40 42 60 49 60
   10 0 -3 0 0 -4 0 94 97 94 92 93 92 92 90 91 65 63 63 61 49 61
   30 0 -4 0 0 -5 0 94 96 94 94 94 94 100 100 100 98 98 98 61 48 61
MD = 20 100/100 5 0 0 0 0 0 1 96 96 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 91 91 100 100 100 85 86 86 93 92 92
   30 0 0 0 0 0 0 96 96 96 94 93 93 100 100 100 100 100 100 93 92 92
SMD = 0.8 10/10 5 0 -2 1 0 -3 1 95 97 95 89 92 90 95 94 95 74 72 73 60 48 60
   10 0 -3 1 0 -4 0 94 96 94 92 92 92 100 100 100 95 95 95 61 48 61
   30 0 -4 0 0 -5 0 94 95 94 94 93 94 100 100 100 100 100 100 61 48 62
MD = 32 100/100 5 0 0 0 0 0 1 96 96 96 88 88 88 100 100 100 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 92 92
   30 0 0 0 0 0 0 96 96 96 94 93 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) assuming a skewed distribution described in the Methods. 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.