Distributed mediation analysis with communication efficiency

We study the mediation analysis under the distributed framework, where data are stored and processed across different worker machines due to storage limitations or privacy concerns. Building upon the classic Sobel's test and MaxP test, we introduce the distributed Sobel's test and distributed MaxP test, respectively. These tests are both communication-efficient and easy to implement. Theoretical analysis and numerical experiments show that, compared to the global test obtained by pooling all data together, the proposed tests achieve nearly identical power, independent of the number of machines. Furthermore, based on these two distributed test statistics, many enhanced mediation tests derived from the Sobel's or MaxP tests can be easily adapted to the distributed system. We apply our method to an educational study, testing whether the effect of high school mathematics on college-level Probability and Mathematical Statistics courses is mediated by Calculus. Our method successfully detects the mediation effect, which would not be identifiable using data from only the first or second class, highlighting the advantage of our approach.