The ratio of means method as an alternative to mean differences for analyzing continuous outcome variables in meta-analysis: A simulation study

Friedrich, Jan O; Adhikari, Neill KJ; Beyene, Joseph

doi:10.1186/1471-2288-8-32

Table 5 Simulation Results (Normal Distribution, Equal Experimental and Control Groups, Standard Deviation 70% 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	-1	-5	0	95	97	96	90	92	91	15	11	12	15	13	12	59	48	45
		10	0	-5	-1	0	-5	-1	95	97	96	92	93	93	27	22	23	19	18	16	60	48	45
		30	0	-5	-1	0	-6	-1	94	96	95	94	94	93	66	61	60	38	38	34	60	47	46
MD = 14	100/100	5	0	0	0	0	-1	2	96	97	96	88	88	87	82	82	82	21	21	22	93	92	91
RoM = 1.14		10	0	0	0	0	0	1	96	96	96	92	92	90	99	99	99	27	27	31	93	92	91
		30	0	0	0	0	0	1	96	96	96	94	94	92	100	100	100	56	58	62	93	92	91
SMD = 0.5	10/10	5	0	-4	-1	0	-5	-1	95	97	95	90	92	91	64	57	58	43	40	38	59	48	47
		10	0	-5	-2	0	-5	-2	95	97	95	92	93	92	91	89	88	66	64	61	60	47	47
		30	0	-5	-2	0	-6	-3	94	96	92	94	93	91	100	100	100	98	97	97	60	47	48
MD = 35	100/100	5	0	0	0	0	0	2	96	97	96	88	88	87	100	100	100	61	61	63	93	92	91
RoM = 1.35		10	0	0	0	0	0	1	96	96	96	92	92	90	100	100	100	85	86	88	93	92	91
		30	0	0	0	0	-1	1	96	96	95	94	94	92	100	100	100	100	100	100	93	92	91
SMD = 0.8	10/10	5	0	-4	-1	0	-5	-2	95	97	95	90	92	90	95	94	93	74	72	71	59	47	48
		10	0	-5	-2	0	-5	-3	95	96	94	92	92	91	100	100	100	95	95	94	60	46	48
		30	0	-5	-3	0	-6	-4	94	94	90	94	92	89	100	100	100	100	100	100	60	46	49
MD = 56	100/100	5	0	0	0	0	0	2	96	96	96	88	88	87	100	100	100	91	91	92	93	92	91
RoM= 1.56		10	0	0	0	0	0	2	96	96	96	92	92	90	100	100	100	100	100	100	93	91	91
		30	0	0	0	0	-1	1	96	96	95	94	94	92	100	100	100	100	100	100	93	91	91

Results of 10,000 simulations per scenario with a standard deviation equal to 70% 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].)
Abbreviations for Table and Legend: contr – control, exp – experimental, I ² – I 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.

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ISSN: 1471-2288

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