PEA: Practical Private Epistasis Analysis Using MPC

Abstract

Due to the significant drop in prices for genome sequencing in the last decade, genome databases were constantly growing. This enabled genome analyses such as Genome-Wide Association Studies (GWAS) that study associations between a gene and a disease and allow to improve medical treatment. However, GWAS fails at the analysis of complex diseases caused by non-linear gene-gene interactions such as sporadic breast cancer or type 2 diabetes. Epistasis Analysis (EA) is a more powerful approach that complements GWAS and considers non-linear interactions between multiple parts of the genome and environment. Statistical genome analyses require large, well-curated genomic datasets, which are difficult to obtain. Hence, the aggregation of multiple databases is often necessary, but the sharing of genomic data raises severe privacy concerns and is subject to extensive regulations (e.g., GDPR or HIPAA), requiring further privacy protection for collaborative analyses. Although there has been work on private GWAS, there was a lack of attention to Private EA (PEA). In this work, we design the first secure and accurate PEA protocol, with security against passive adversaries. Our efficient PEA protocol consists of two subprotocols: (1) (optional) feature selection for filtering noisy features to reduce the input size for better efficiency and (2) finding relevant associations. For feature selection, we design two protocols based on Secure Multi-Party Computation (MPC) for Relief-F and TuRF. For finding associations, we design an MPC protocol for Multifactor Dimensionality Reduction (MDR). Our private MDR protocol is based on two novel, efficient building blocks, arithmetic greater than and arithmetic swap, which may be of independent interest. This approach omits the need for expensive conversions between sharing types in private MDR and reduces the communication by two orders of magnitude compared to a naïve design using garbled circuits. Our private MDR protocol runs in (extrapolated) three days on a practical database with 10,000 features for all two mutually combined features, i.e., considering about 50 million combinations.