Table 3.

Simulation Results (Normal Distribution, Equal Experimental and Control Groups, Standard Deviation 40% of Control Mean Value).

			% Bias						% Coverage						% Statistical Power						I2(%)
			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

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 I² 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 I² = 0 [data not shown].)

Abbreviations for Table and Legend: contr – control, exp – experimental, I² – I² 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.