Table 2.

Biases, root mean squared errors (RMSEs), and 95% confidence interval coverage probabilities (CPs, in percentage, %) of the estimated overall median proportions (in percentage, %) based on 1000 simulated meta-analyses with N=30 studies under various simulation settings.

	p=1%								p=20%
Method	τ=0.1				τ=0.5				τ=0.1				τ=0.5
	Bias	RMSE	CP		Bias	RMSE	CP		Bias	RMSE	CP		Bias	RMSE	CP
Sample sizes ranging in 100–500
Generalized linear mixed model:
Log	−0.01	0.11	96		0.01	0.16	93		0.01	0.53	94		−0.26	1.56	92
Logit	−0.01	0.11	96		0.01	0.16	93		0.01	0.53	94		0.07	1.59	92
Probit	−0.01	0.11	96		0.01	0.16	93		0.02	0.53	94		0.26	1.61	93
Cauchit	−0.01	0.11	96		0.02	0.15	90		−0.01	0.53	94		−0.99	1.86	87
Complementary log-log	−0.01	0.11	96		0.01	0.16	93		0.01	0.53	94		−0.09	1.56	92
Two-step method:
Log	0.31	0.33	22		0.43	0.46	15		0.19	0.55	93		0.01	1.52	93
Logit	0.30	0.32	24		0.43	0.46	15		0.10	0.52	93		0.23	1.57	93
Arcsine	0.09	0.14	90		0.17	0.23	81		−0.05	0.52	94		0.55	1.67	92
Double-arcsine (harmonic)	0.04	0.11	96		0.13	0.20	87		−0.07	0.52	93		0.55	1.67	92
Double-arcsine (geometric)	0.07	0.13	93		0.16	0.23	83		−0.05	0.52	93		0.57	1.67	92
Double-arcsine (arithmetic)	0.09	0.14	91		0.19	0.24	78		−0.04	0.52	94		0.59	1.68	92
Double-arcsine (IV)	0.24	0.27	41		0.34	0.37	32		0.06	0.52	94		0.64	1.69	92
Sample sizes ranging in 1000–5000
Generalized linear mixed model:
Log	0.00	0.04	92		0.01	0.09	96		0.00	0.34	93		−0.38	1.48	93
Logit	0.00	0.04	92		0.01	0.09	96		0.01	0.34	93		0.00	1.48	93
Probit	0.00	0.04	92		0.02	0.10	95		0.02	0.34	93		0.22	1.50	94
Cauchit	0.00	0.04	92		−0.06	0.11	89		−0.04	0.34	93		−1.42	2.06	85
Complementary log-log	0.00	0.04	92		0.01	0.09	96		0.00	0.34	93		−0.18	1.47	93
Two-step method:
Log	0.02	0.05	89		0.03	0.10	93		0.02	0.33	91		−0.34	1.48	93
Logit	0.02	0.05	89		0.03	0.10	93		0.02	0.33	91		0.02	1.49	94
Arcsine	0.00	0.04	92		0.05	0.11	93		0.03	0.33	92		0.55	1.60	93
Double-arcsine (harmonic)	−0.01	0.04	92		0.05	0.11	93		0.02	0.33	91		0.56	1.60	93
Double-arcsine (geometric)	−0.01	0.04	92		0.06	0.12	92		0.03	0.33	92		0.56	1.60	92
Double-arcsine (arithmetic)	0.00	0.04	92		0.06	0.12	92		0.03	0.33	92		0.56	1.60	92
Double-arcsine (IV)	0.01	0.04	91		0.07	0.12	90		0.04	0.33	91		0.53	1.59	93

Note: p denotes the true overall median proportion, and τ denotes the between-study standard deviation (of proportions on the logit scale). For the double-arcsine transformation used by the two-step method, the “harmonic,” “geometric,” and “arithmetic” denote the harmonic, geometric, and arithmetic means of sample sizes, and the “IV” denotes the inverse of variance.