Standardizing effect size from linear regression models with log-transformed variables for meta-analysis

Table 6 Original regression coefficients and transformed effect size for studies included in the meta-analysis

Author (Year)	Mean of X	Units	Transf. on X	β	SE(β)	θ	SE(θ)
As in urine
Hamadani (2011)-Girls [7]		μg/L	Ln	−1.40	0.66	−0.57	0.27
Hamadani (2011)-Boys [7]		μg/L	Ln	0.70	0.56	0.28	0.23
Rocha-Amador (2007) [8]		μg/gr crea	Ln	−5.72	1.93	−2.32	0.78
von Ehrenstein (2007) [9]	78	μg/L	None	−0.0007	0.0008	−0.03	0.03
Wasserman (2007) [10]		μg/gr crea	Ln	−1.78	1.42	−0.72	0.58
Wasserman (2004) [11]		μg/gr crea	Ln	−2.90	1.71	−1.18	0.69
As in water
Rocha-Amador (2007) [8]		μg/L	Ln	−6.15	1.87	−2.49	0.76
von Ehrenstein (2007) [9]	147	μg/L	None	−0.0002	0.0004	−0.01	0.03
Wasserman (2007) [10]		μg/L	Ln	−1.06	0.57	−0.43	0.23
Wasserman (2004) [11]		μg/L	Ln	−1.64	0.64	−0.66	0.26
Mn in hair
Bouchard (2011) [12]		μg/g	log10	−3.30	1.43	−0.58	0.25
Menezes-Filho (2011) [13]		μg/g	log10	−5.78	2.84	−1.02	0.50
Riojas-Rodríguez (2010) [14]	6.35	μg/g	None	−0.20	0.11	−0.64	0.36
Wright (2006) [15]	0.47	μg/g	None	−10.00	5.00	−2.35	1.18

As, arsenic, Mn manganese, θ transformed effect size for k = 1.5, Ln natural logarithm, log10 base 10 logarithm, gr crea grams of creatinine