Re-expressing coefficients from regression models for inclusion in a meta-analysis

Abstract

Meta-analysis poses a challenge when original study results have been expressed in a non-uniform manner, such as when regression results from some original studies were based on a log-transformed key independent variable while in others no transformation was used. Methods of re-expressing regression coefficients to generate comparable results across studies regardless of data transformation have recently been developed. We examined the relative bias of three re-expression methods using simulations and 15 real data examples where the independent variable had a skewed distribution. Regression coefficients from models with log-transformed independent variables were re-expressed as though they were based on an untransformed variable. We compared the re-expressed coefficients to those from a model fit to the untransformed variable. In the simulated and real data, all three reexpression methods usually gave biased results, and the skewness of the independent variable predicted the amount of bias. Meta-analyses stratified by whether the key independent variable was log-transformed and synthesis of the stratified results without meta-analysis appear to be preferable to use of the re-expression methods examined.