Learning from vertically distributed data across multiple sites: An efficient privacy-preserving algorithm for Cox proportional hazards model with variable selection.

OBJECTIVE: To develop a lossless distributed algorithm for regularized Cox proportional hazards model with variable selection to support federated learning for vertically distributed data. METHODS: We propose a novel distributed algorithm for fitting regularized Cox proportional hazards model when data sharing among different data providers is restricted. Based on cyclical coordinate descent, the proposed algorithm computes intermediary statistics by each site and then exchanges them to update the model parameters in other sites without accessing individual patient-level data. We evaluate the performance of the proposed algorithm with (1) a simulation study and (2) a real-world data analysis predicting the risk of Alzheimer's dementia from the Religious Orders Study and Rush Memory and Aging Project (ROSMAP). Moreover, we compared the performance of our method with existing privacy-preserving models. RESULTS: Our algorithm achieves privacy-preserving variable selection for time-to-event data in the vertically distributed setting, without degradation of accuracy compared with a centralized approach. Simulation demonstrates that our algorithm is highly efficient in analyzing high-dimensional datasets. Real-world data analysis reveals that our distributed Cox model yields higher accuracy in predicting the risk of Alzheimer's dementia than the conventional Cox model built by each data provider without data sharing. Moreover, our algorithm is computationally more efficient compared with existing privacy-preserving Cox models with or without regularization term. CONCLUSION: The proposed algorithm is lossless, privacy-preserving and highly efficient to fit regularized Cox model for vertically distributed data. It provides a suitable and convenient approach for modeling time-to-event data in a distributed manner.

The vertical partitioning between denitrification and dissimilatory nitrate reduction to ammonium of coastal mangrove sediment microbiomes.

Mangrove aquatic ecosystems receive substantial nitrogen (N) inputs from both land and sea, playing critical roles in modulating coastal N fluxes. The microbially-mediated competition between denitrification and dissimilatory nitrate reduction to ammonium (DNRA) in mangrove sediments significantly impacts the N fate and transformation processes. Despite their recognized role in N loss or retention in surface sediments, how these two processes vary with sediment depths and their influential factors remain elusive. Here, we employed a comprehensive approach combining 15N isotope tracer, quantitative PCR (qPCR) and metagenomics to verify the vertical dynamics of denitrification and DNRA across five 100-cm mangrove sediment cores. Our results revealed a clear vertical partitioning, with denitrification dominated in 0-30 cm sediments, while DNRA played a greater role with increasing depths. Quantification of denitrification and DNRA functional genes further explained this phenomenon. Taxonomic analysis identified Pseudomonadota as the primary denitrification group, while Planctomycetota and Pseudomonadota exhibited high proportion in DNRA group. Furthermore, genome-resolved metagenomics revealed multiple salt-tolerance strategies and aromatic compound utilization potential in denitrification assemblages. This allowed denitrification to dominate in oxygen-fluctuating and higher-salinity surface sediments. However, the elevated C/N in anaerobic deep sediments favored DNRA, tending to generate biologically available NH4+. Together, our results uncover the depth-related variations in the microbially-mediated competition between denitrification and DNRA, regulating N dynamics in mangrove ecosystems.