Bayesian Mediation Analysis with Power Prior Distributions

Bayesian methods are often suggested as a solution for issues encountered in small sample research, however, Bayesian methods often require informative priors to outperform classical methods in these settings. Specifying accurate priors with respect to the true value of the parameter of interest is challenging and inaccurate informative priors can have detrimental effects on conclusions from the statistical analysis. This paper proposes an objective procedure for creating informative priors for mediation analysis based on a historical data set; the only requirements for implementing the procedure are that the data from the current study constitute a representative sample from the population of interest, and that the historical and current data sets contain measures of the same covariates and independent variable, mediator, and outcome. The simulation study findings show that the proposed method leads to appropriate amount of borrowing from the historical data set, which leads to increases in precision and power when the historical data and current data are exchangeable, and does not induce bias when the historical and current studies are not exchangeable. The proposed method is illustrated using data from the project PROsetta Stone, and we provide rstan code for implementing the proposed method.