Privacy-Preserving Statistical Analysis by Exact Logistic Regression

Logistic regression is the method of choice in most genome-wide association studies (GWAS). Due to the heavy cost of performing iterative parameter updates when training such a model, existing methods have prohibitive communication and computational complexities that make them unpractical for real-life usage. We propose a new sampling-based secure protocol to compute exact statistics, that requires a constant number of communication rounds and a much lower number of computations. The publicly available implementation of our protocol (and its many optional optimisations adapted to different security scenarios) can, in a matter of hours, perform statistical testing of over 600 SNP variables across thousands of patients while accounting for potential confounding factors in the clinical data.