FedGMMAT: Federated generalized linear mixed model association tests

Abstract

Increasing genetic and phenotypic data size is critical for understanding the genetic determinants of diseases. Evidently, establishing practical means for collaboration and data sharing among institutions is a fundamental methodological barrier for performing high-powered studies. As the sample sizes become more heterogeneous, complex statistical approaches, such as generalized linear mixed effects models, must be used to correct for the confounders that may bias results. On another front, due to the privacy concerns around Protected Health Information (PHI), genetic information is restrictively protected by sharing according to regulations such as Health Insurance Portability and Accountability Act (HIPAA). This limits data sharing among institutions and hampers efforts around executing high-powered collaborative studies. Federated approaches are promising to alleviate the issues around privacy and performance, since sensitive data never leaves the local sites. Motivated by these, we developed FedGMMAT, a federated genetic association testing tool that utilizes a federated statistical testing approach for efficient association tests that can correct for confounding fixed and additive polygenic random effects among different collaborating sites. Genetic data is never shared among collaborating sites, and the intermediate statistics are protected by encryption. Using simulated and real datasets, we demonstrate FedGMMAT can achieve the virtually same results as pooled analysis under a privacy-preserving framework with practical resource requirements.

Fig 1. Scatter plot on -log10 scale of P-values of Synthetic data in FedGMMAT and GMMAT (Experimental Setup 3).

Fig 2. Scatter plot on -log10 scale of P-values in FedGMMAT and GMMAT.

(A) Heterogeneity; (B) Homogeneity.

Fig 3. Scatter plot on -log10 scale of P-values in FedGMMAT and GMMAT on real data.

Fig 4. The comparison of computation time with different numbers of SNPs per batch in minutes between HE and Non-HE protection of FedGMMAT.

Fig 5. The total run-time per site (y-axis) in second with respect to the number of subjects on each site (x-axis).

Fig 6. Matrix Splitting at the Central Server and aggregation among local data repositories.

In the FedGMMAT framework, each local data repository will maintain its unique dataset locally and gather intermediate model information from Global updates. The vertical splitting of Σ⁻1 among local repositories is illustrated in the figure as an example. Each site receives n_j × n sized covariate matrices (X_j), which are multiplied locally with n_j × p sized matrices. The resulting n × p matrices are encrypted and aggregated among sites via round-robin schedule and sent to the server. Splitting and aggregation of other matrices is accomplished with similar protocol.

Fig 7. Key setup and aggregation via round-robin schedule.

The central server initiates the public/private key pair at the initialization and broadcasts the public key to all sites. Aggregation of split matrices are performed among sites by taking turns in aggregation. Each site encrypts their matrix “share” before aggregation. Symmetric keys (secret seeds) for OTP-like encryption is sent to all sites at the scoring stage whenever an aggregation is performed (S2 and S3 Figs).