Federated Statistical Analysis: Non-parametric Testing and Quantile Estimation

The age of big data has fueled expectations for accelerating learning. The availability of large data sets enables researchers to achieve more powerful statistical analyses and enhances the reliability of conclusions, which can be based on a broad collection of subjects. Often such data sets can be assembled only with access to diverse sources; for example, medical research that combines data from multiple centers in a federated analysis. However these hopes must be balanced against data privacy concerns, which hinder sharing raw data among centers. Consequently, federated analyses typically resort to sharing data summaries from each center. The limitation to summaries carries the risk that it will impair the efficiency of statistical analysis procedures. In this work we take a close look at the effects of federated analysis on two very basic problems, nonparametric comparison of two groups and quantile estimation to describe the corresponding distributions. We also propose a specific privacy-preserving data release policy for federated analysis with the $K$-anonymity criterion, which has been adopted by the Medical Informatics Platform of the European Human Brain Project. Our results show that, for our tasks, there is only a modest loss of statistical efficiency.