Bayesian Mediation Analysis with an Application to Explore Racial Disparities in the Diagnostic Age of Breast Cancer.

A mediation effect refers to the effect transmitted by a mediator intervening in the relationship between an exposure variable and a response variable. Mediation analysis is widely used to identify significant mediators and to make inferences on their effects. The Bayesian method allows researchers to incorporate prior information from previous knowledge into the analysis, deal with the hierarchical structure of variables, and estimate the quantities of interest from the posterior distributions. This paper proposes three Bayesian mediation analysis methods to make inferences on mediation effects. Our proposed methods are the following: (1) the function of coefficients method; (2) the product of partial difference method; and (3) the re-sampling method. We apply these three methods to explore racial disparities in the diagnostic age of breast cancer patients in Louisiana. We found that African American (AA) patients are diagnosed at an average of 4.37 years younger compared with Caucasian (CA) patients (57.40 versus 61.77, < 0.0001). We also found that the racial disparity can be explained by patients' insurance (12.90%), marital status (17.17%), cancer stage (3.27%), and residential environmental factors, including the percent of the population under age 18 (3.07%) and the environmental factor of intersection density (9.02%).