A Sequential Bayes Approach to Combining Information Across Mediation Studies

Introduction: Bayesian analysis is useful because it allows researchers to use information from one data set in the process of analyzing a subsequent data set.  Bayesian analysis uses prior knowledge (in the form of chosen prior distributions for parameters) along with the observed data (the likelihood of the data) to create an estimated posterior distribution of a parameter.  Data from a set of eight experimentson the use of mental imagery in word recall were used to demonstrate how information could be combined sequentially across time using Bayesian analysis.  Mediation path estimates from a maximum likelihood analysis of Study 1 were used as prior information for a Bayesian mediation analysis of Study 2. Results from Study 2 were used as prior information for Study 3, and so on. Therefore, each subsequent study incorporated increasingly more information, and the analysis for the final study incorporated information from all previous studies.

Methods: All models were estimated in Mplus7 for traditional and potential outcomes estimators of mediation effects. Maximum likelihood point estimates and standard errors of the mediation paths in the first Study 1 were specified as the means and variances of normal prior distributions for the mediation paths in a Bayesian analysis of the Study 2 data. The posterior median estimates of the mediation paths from this analysis of the Study 2 data were then specified as the means of normal prior distributions for the mediation paths in a Bayesian analysis of the Study 3 data, and so on for all eight studies. The variance of the normal prior for each mediation path estimate was specified as the variance of the posterior distribution for that parameter from the previous study. This reflected the increasing precision of the expectations of the path estimates. The method will also be applied to a prevention research data set.

Results:The maximum likelihood estimate of the mediated effect in Study 1 was  = 1.457, 95% Confidence Interval [.252, 2.663] for the mediated effect in Study 8.  Using this sequential Bayesian method yielded a posterior median estimate of  = 2.171, 95% Credibility Interval [1.507, 3.127] for the mediated effect in Study 8.

Conclusions: Using Bayesian analysis to combine information across studies can increase precision for mediation parameter estimates. Applications in synthesis of prevention studies are discussed.