title: Standardizing effect size from linear regression models with log-transformed variables for meta-analysis.
abstract: Meta-analysis is very useful to summarize the effect of a treatment or a risk factor for a given disease. Often studies report results based on log-transformed variables in order to achieve the principal assumptions of a linear regression model. If this is the case for some, but not all studies, the effects need to be homogenized.
  
  
  
  We derived a set of formulae to transform absolute changes into relative ones, and vice versa, to allow including all results in a meta-analysis. We applied our procedure to all possible combinations of log-transformed independent or dependent variables. We also evaluated it in a simulation based on two variables either normally or asymmetrically distributed.
  
  
  
  In all the scenarios, and based on different change criteria, the effect size estimated by the derived set of formulae was equivalent to the real effect size. To avoid biased estimates of the effect, this procedure should be used with caution in the case of independent variables with asymmetric distributions that significantly differ from the normal distribution. We illustrate an application of this procedure by an application to a meta-analysis on the potential effects on neurodevelopment in children exposed to arsenic and manganese.
  
  
  
  The procedure proposed has been shown to be valid and capable of expressing the effect size of a linear regression model based on different change criteria in the variables. Homogenizing the results from different studies beforehand allows them to be combined in a meta-analysis, independently of whether the transformations had been performed on the dependent and/or independent variables.
authors.affiliation: Andalusian School of Public Health (EASP), Campus Universitario de Cartuja, c/Cuesta del Observatorio 4, 18080, Granada, Spain. miguel.rodriguez.barranco.easp@juntadeandalucia.es.|Instituto de Investigación Biosanitaria ibs.GRANADA, University Hospitals of Granada/University of Granada, Granada, Spain. miguel.rodriguez.barranco.easp@juntadeandalucia.es.|CIBERESP, Madrid, Spain. miguel.rodriguez.barranco.easp@juntadeandalucia.es.
authors.forename: Miguel
authors.initials: M
authors.lastname: Rodríguez-Barranco
authors.affiliation: Institute of Environmental Assessment and Water Research (IDAEA), Spanish Council for Scientific Research (CSIC), Barcelona, Spain.
authors.forename: Aurelio
authors.initials: A
authors.lastname: Tobías
authors.affiliation: Andalusian School of Public Health (EASP), Campus Universitario de Cartuja, c/Cuesta del Observatorio 4, 18080, Granada, Spain.|Instituto de Investigación Biosanitaria ibs.GRANADA, University Hospitals of Granada/University of Granada, Granada, Spain.|CIBERESP, Madrid, Spain.
authors.forename: Daniel
authors.initials: D
authors.lastname: Redondo
authors.affiliation: Andalusian School of Public Health (EASP), Campus Universitario de Cartuja, c/Cuesta del Observatorio 4, 18080, Granada, Spain.|Instituto de Investigación Biosanitaria ibs.GRANADA, University Hospitals of Granada/University of Granada, Granada, Spain.|CIBERESP, Madrid, Spain.
authors.forename: Elena
authors.initials: E
authors.lastname: Molina-Portillo
authors.affiliation: Andalusian School of Public Health (EASP), Campus Universitario de Cartuja, c/Cuesta del Observatorio 4, 18080, Granada, Spain.|Instituto de Investigación Biosanitaria ibs.GRANADA, University Hospitals of Granada/University of Granada, Granada, Spain.|CIBERESP, Madrid, Spain.
authors.forename: María José
authors.initials: MJ
authors.lastname: Sánchez
mesh_terms: D001151:Arsenic / Q000633:toxicity* / Q000652:urine; D003198:Computer Simulation; D006197:Hair / Q000737:chemistry; D006801:Humans; D016014:Linear Models; D008345:Manganese / Q000633:toxicity*; D015201:Meta-Analysis as Topic; D065886:Neurodevelopmental Disorders / Q000139:chemically induced*
chemical_list: D008345:Manganese; D001151:Arsenic
keywords: Effect size; Linear regression; Log-transformation; Meta-analysis; Regression coefficients; Systematic review