Privacy-preserving model evaluation for logistic and linear regression using homomorphically encrypted genotype data

Linear and logistic regression are widely used statistical techniques in population genetics for analyzing genetic data and uncovering patterns and associations in large genetic datasets, such as identifying genetic variations linked to specific diseases or traits. However, obtaining statistically significant results from these studies requires large amounts of sensitive genotype and phenotype information from thousands of patients, which raises privacy concerns. Although cryptographic techniques such as homomorphic encryption offers a potential solution to the privacy concerns as it allows computations on encrypted data, previous methods leveraging homomorphic encryption have not addressed the confidentiality of shared models, which can leak information about the training data. In this work, we present a secure model evaluation method for linear and logistic regression using homomorphic encryption for six prediction tasks, where input genotypes, output phenotypes, and model parameters are all encrypted. Our method ensures no private information leakage during inference and achieves high accuracy (≥93% for all outcomes) with each inference taking less than ten seconds for ∼200 genomes. Our study demonstrates that it is possible to perform linear and logistic regression model evaluation while protecting patient confidentiality with theoretical security guarantees. Our implementation and test data are available at https://github.com/G2Lab/privateML/.