High-dimensional Bayesian mediation analysis with adaptive Laplace priors

The mediation analysis method is used to investigate effects of mediators that intervene in the pathways between an exposure variable and an outcome variable. Bayesian methods are naturally used in mediation analysis due to the hierarchical structure of Bayesian models. This paper introduces an innovative adaptive Bayesian mediation analysis method that incorporates adaptive Laplace priors into the predictive model to account for high-dimensional mediators. This approach introduces a penalization function on the estimated direct and indirect effects rather than solely on the coefficients of predictive models. Consequently, estimated effects that lack statistical significance may shrink to zero, facilitating a more robust analysis. We demonstrate the efficacy of our adaptive mediation analysis method on simulations and on a Louisiana triple negative breast cancer (TNBC) dataset to examine racial disparity in diagnosed stage among TNBC patients diagnosed between 2010 and 2017. The dataset is linked to the 2017 hazardous air pollutant emissions burden estimation database using patients' residential address. We effectively explain a portion of the disparity using currently collected variables. The analysis identifies crucial mediators and confounders, highlighting the significance of variables such as age of diagnosis, insurance status, tumor grades, and the concentration of Naphtha in the air.