Concealed correlations meta-analysis: A new method for synthesizing standardized regression coefficients

Belén Fernández-Castilla, Ariel M. Aloe, Lies Declercq, Laleh Jamshidi, Patrick Onghena, S. Natasha Beretvas, Wim Van den Noortgate

The synthesis of standardized regression coefficients is still a controversial issue in the field of meta-analysis. The difficulty lies in the fact that the standardized regression coefficients belonging to regression models that include different sets of covariates do not represent the same parameter, and thus their direct combination is meaningless. In the present study, a new approach called concealed correlations meta-analysis is proposed that allows for using the common information that standardized regression coefficients from different regression models contain to improve the precision of a combined focal standardized regression coefficient estimate. The performance of this new approach was compared with that of two other approaches: (1) carrying out separate meta-analyses for standardized regression coefficients from studies that used the same regression model, and (2) performing a meta-regression on the focal standardized regression coefficients while including an indicator variable as a moderator indicating the regression model to which each standardized regression coefficient belongs. The comparison was done through a simulation study. The results showed that, as expected, the proposed approach led to more accurate estimates of the combined standardized regression coefficients under both random- and fixed-effect models.