An R Program for Synthesizing Mediation Analysis Across Multiple Trials

Title:  An R Program for Synthesizing Mediation Analyses Across Multiple Trials

ABSTRACT BODY: 

Introduction: Mediation analyses can require larger sample sizes than main effect analyses to achieve the same statistical power. Combining the findings across similar trials may be the only practical option for increasing the statistical power needed for mediation analyses. By utilizing pooled results across multiple trials, the synthesis of mediation information provides a way to assess the overall strength of mediation across trials.

Methods: In this paper, we present the statistical theory and an R code to combine

regression coefficients from multiple research trials to estimate a combined mediated effect and a bootstrapped confidence interval under a random effects model. Values of a and b, along with their standard errors from each trial are used as input. The set-up is as follows. For each of K trials, let ai be the ith trial’s regression coefficient of the mediator on independent variable, and bi the ith trial’s regression coefficient of the outcome on the mediator, adjusted for independent variable. In large samples the regression coefficients’ distributions have approximately independent normal distributions, conditional on trial level means αi and β i..  αi and β I in turn are independently bivariate normally distributed across trials with marginal mean vector (μ) and the unknown trial-level variance-covariance matrix (Sigma). The log likelihood function was defined and we work directly with vector differentials (for μ) and matrix differentials (for Sigma), to obtain Maximum Likelihood Estimates for μ and for Sigma.

Finally, the ML estimate of the mediated effect is just the product of the estimates for μ. We then apply the Bootstrap method to obtain 1 –α confidence intervals.

Discussion: In this study, we proposed a method to estimate marginal means for mediation path a and b coefficients across multi-trials and between-trial level variance-covariance matrix based on bivariate normal distribution. It is worth noting that this program also allows researchers to evaluate mediation effects in clustered data, such as studies conducted in multiple schools and classrooms, where mediation effects usually are estimated for each cluster. Future extensions to this program include incorporating missing data on path a and path b issues, as well as including an interaction term of X and M jointly affecting Y.