Learning from local to global: An efficient distributed algorithm for modeling time-to-event data

Rui Duan, Chongliang Luo, Martijn J. Schuemie, Jiayi Tong, C. Jason Liang, Howard H. Chang, Mary Regina Boland, Jiang Bian, Hua Xu, John H. Holmes, Christopher B. Forrest, Sally C. Morton, Jesse A. Berlin, Jason H. Moore, Kevin B. Mahoney, Yong Chen

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


Objective: We developed and evaluated a privacy-preserving One-shot Distributed Algorithm to fit a multicenter Cox proportional hazards model (ODAC) without sharing patient-level information across sites. Materials and Methods: Using patient-level data from a single site combined with only aggregated information from other sites, we constructed a surrogate likelihood function, approximating the Cox partial likelihood function obtained using patient-level data from all sites. By maximizing the surrogate likelihood function, each site obtained a local estimate of the model parameter, and the ODAC estimator was constructed as a weighted average of all the local estimates. We evaluated the performance of ODAC with (1) a simulation study and (2) a real-world use case study using 4 datasets from the Observational Health Data Sciences and Informatics network. Results: On the one hand, our simulation study showed that ODAC provided estimates nearly the same as the estimator obtained by analyzing, in a single dataset, the combined patient-level data from all sites (ie, the pooled estimator). The relative bias was <0.1% across all scenarios. The accuracy of ODAC remained high across different sample sizes and event rates. On the other hand, the meta-analysis estimator, which was obtained by the inverse variance weighted average of the site-specific estimates, had substantial bias when the event rate is <5%, with the relative bias reaching 20% when the event rate is 1%. In the Observational Health Data Sciences and Informatics network application, the ODAC estimates have a relative bias <5% for 15 out of 16 log hazard ratios, whereas the meta-analysis estimates had substantially higher bias than ODAC. Conclusions: ODAC is a privacy-preserving and noniterative method for implementing time-to-event analyses across multiple sites. It provides estimates on par with the pooled estimator and substantially outperforms the meta-analysis estimator when the event is uncommon, making it extremely suitable for studying rare events and diseases in a distributed manner.

Original languageEnglish
Pages (from-to)1028-1036
Number of pages9
JournalJournal of the American Medical Informatics Association
Issue number7
StatePublished - Jul 1 2020


  • Cox proportional hazards model
  • data integration
  • distributed algorithm
  • electronic health record
  • meta-analysis


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