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

ABSTRACT Objectives We developed and evaluated a privacy-preserving O ne-shot D istributed A lgorithm to fit a multi-center C ox proportional hazard model ( ODAC ) without sharing patient-level information across sites. 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 four datasets from the Observational Health Data Sciences and Informatics (OHDSI) network. Results 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 (i.e., the pooled estimator). The relative bias was less than 0.1% across all scenarios. The accuracy of ODAC remained high across different sample sizes and event rates. On the other hand, the metaanalysis estimator, which was obtained by the inverse variance weighted average of the sitespecific estimates, had substantial bias when the event rate is less than 5%, with the relative bias reaching 20% when the event rate is 1%. In the OHDSI network application, the ODAC estimates have a relative bias less than 5% for 15 out of 16 log hazard ratios; while the meta-analysis estimates had substantially higher bias than ODAC. Conclusions ODAC is a privacy-preserving and non-iterative 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.