Time-to-Event Modeling with Pseudo-Observations in Federated Settings

In multi-center clinical research, privacy regulations often prohibit pooling individual-level records, complicating the analysis of time-to-event data. Current federated survival methods frequently require iterative communication or rely strictly on proportional hazards (PH) assumptions or require sensitive survival information. We propose a one-shot federated framework using pseudo-observations derived from a sequentially updated Kaplan-Meier estimator and fitted via a renewable generalized estimating equation. Unlike traditional methods, our approach allows flexible link functions tailored to the target estimand and accommodates non-proportional hazards. To address site-level heterogeneity, we introduce a covariate-wise debiasing procedure that shrinks noise-driven local deviations toward the global estimate while preserving genuine site-specific effects. Simulation studies demonstrate that our framework achieves inferential accuracy comparable to pooled Cox regression and the privacy-preserving One-shot Distributed Algorithm to fit a multicenter Cox proportional hazards model (ODAC) under PH assumptions, while recovering time-varying coefficient trajectories when PH is violated. Furthermore, simulations confirm that the debiasing procedure optimizes the bias-variance trade-off, adaptively balancing global stability with the preservation of genuine site-specific deviations. Applied to pediatric obesity data from the Chicago Area Patient-Centered Outcomes Research Network (CAPriCORN) network ($N=45,865$), the model produced robust estimates of time-invariant and time-varying hazard ratios, offering a flexible, privacy-preserving alternative for collaborative survival research.