A random effects meta-analysis model with Box-Cox transformation

Table 4 Posterior median and 95 percent credible interval of: I ² from the normal random effects model, ratio of IQR squares from the proposed model; 95 percent prediction intervals from each model

NRE		BC		BC-SI
		Ratio of IQR		Ratio of IQR
I ² (%)	95%	squares^a (%)	95%	squares^a (%)	95%
Post. (s.d.)	prediction	Post. (s.d.)	prediction	Post. (s.d.)	prediction
(95% CI)	interval	(95% CI)	interval	(95% CI)	interval
Example 1: Teacher expectancy on pupil IQ
44.9 (24.0)	(−0.284,0.500)	20.9 (21.9)	(−0.179,0.393)	n/a	n/a
(0.5,81.9)		(0.1,73.6)
Example 2: Antidepressants for reducing pain in fibromyalgia syndrome
39.1 (22.7)	(−0.879,−0.001)	17.3 (19.1)	(−0.732,−0.118)	18.4 (19.8)	(−0.753,−0.112)
(0.4,78.0)		(0.1,65.7)		(0.1,67.9)

^aRatio of IQR squares =(ξ ₇₅−ξ ₂₅)²/(ν ₇₅−ν ₂₅)²
Post.: posterior median, s.d.: standard deviation, CI: credible interval
NRE: normal random effects model, BC: proposed model using Box-Cox transformation
BC-SI: proposed model using Box-Cox transformation with the sign inversion for negatively skewed data

ISSN: 1471-2288