VERTICOX: Vertically Distributed Cox Proportional Hazards Model Using the Alternating Direction Method of Multipliers

• Published in: IEEE transactions on knowledge and data engineering Vol. 34; no. 2; pp. 996 - 1010
• Main Authors: Dai, Wenrui, Jiang, Xiaoqian, Bonomi, Luca, Li, Yong, Xiong, Hongkai, Ohno-Machado, Lucila
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.02.2022; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; alternating direction method of multipliers; Analytical models; Computational modeling; cox proportional hazards model; Data models; Data privacy; Distributed databases; Estimation; Exchanging; Federated survival analysis; Hazards; Multipliers; Parameter estimation; privacy protection; Source code; Statistical models; Survival; Survival analysis; vertically partitioned data; Federated survival analysis; alternating direction method of multipliers; privacy protection; vertically partitioned data; Cox proportional hazards model
• ISSN: 1041-4347; 1558-2191
• DOI: 10.1109/TKDE.2020.2989301

The Cox proportional hazards model is a popular semi-parametric model for survival analysis. In this paper, we aim at developing a federated algorithm for the Cox proportional hazards model over vertically partitioned data (i.e., data from the same patient are stored at different institutions). We propose a novel algorithm, namely VERTICOX, to obtain the global model parameters in a distributed fashion based on the Alternating Direction Method of Multipliers (ADMM) framework. The proposed model computes intermediary statistics and exchanges them to calculate the global model without collecting individual patient-level data. We demonstrate that our algorithm achieves equivalent accuracy for the estimation of model parameters and statistics to that of its centralized realization. The proposed algorithm converges linearly under the ADMM framework. Its computational complexity and communication costs are polynomially and linearly associated with the number of subjects, respectively. Experimental results show that VERTICOX can achieve accurate model parameter estimation to support federated survival analysis over vertically distributed data by saving bandwidth and avoiding exchange of information about individual patients. The source code for VERTICOX is available at: https://github.com/daiwenrui/VERTICOX .