Communication-efficient federated learning of temporal effects on opioid use disorder with data from distributed research networks

Objective: To develop a distributed algorithm to fit multi-center Cox regression models with time-varying coefficients to facilitate privacy-preserving data integration across multiple health systems. Materials and Methods: The Cox model with time-varying coefficients relaxes the proportional hazards assumption of the usual Cox model and is particularly useful to model time-to-event outcomes. We proposed a One-shot Distributed Algorithm to fit multi-center Cox regression models with Time varying coefficients (ODACT). This algorithm constructed a surrogate likelihood function to approximate the Cox partial likelihood function, using patient-level data from a lead site and aggregated data from other sites. The performance of ODACT was demonstrated by simulation and a real-world study of opioid use disorder (OUD) using decentralized data from a large clinical research network across 5 sites with 69 163 subjects. Results: The ODACT method precisely estimated the time-varying effects over time. In the simulation study, ODACT always achieved estimation close to that of the pooled analysis, while the meta-estimator showed considerable amount of bias. In the OUD study, the bias of the estimated hazard ratios by ODACT are smaller than those of the meta-estimator for all 7 risk factors at almost all of the time points from 0 to 2.5 years. The greatest bias of the meta-estimator was for the effects of age ≥65 years, and smoking. Conclusion: ODACT is a privacy-preserving and communication-efficient method for analyzing multi-center time-to-event data which allows the covariates' effects to be time-varying. ODACT provides estimates close to the pooled estimator and substantially outperforms the meta-analysis estimator. Discussion: The proposed ODACT is a privacy-preserving distributed algorithm for fitting Cox models with time-varying coefficients. The limitations of ODACT include that privacy-preserving via aggregate data does rely on relatively large number of data at each individual site, and rigorous quantification of the risk of privacy leaks requires further investigation.