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Communication-Efficient Federated Risk Difference Estimation for Time-to-Event Clinical Outcomes

Ziwen Wang, Siqi Li, Marcus Eng Hock Ong, Nan Liu

TL;DR

This work tackles privacy-preserving estimation of absolute time-to-event risk differences across multiple sites by introducing FedRD, a server-independent federated framework. It develops two estimators: FedRD-U for homogeneous baselines (3 communication rounds) and FedRD-S for heterogeneous baselines (1 round), both with theoretical guarantees of asymptotic equivalence to pooled analysis and valid inference via sandwich covariance. Through simulations and real-world data (MIMIC and SGH), FedRD achieves RD estimates and predictive performance comparable to pooled analyses and consistently outperforms local and meta-analytic baselines, while requiring minimal inter-site communication. The approach enables robust absolute risk assessment in privacy-restricted, multi-site clinical studies, offering a practical alternative to traditional FL architectures that rely on central servers. This work thus advances privacy-preserving survival analysis by delivering accurate, inference-enabled RD estimates in a communication-efficient, architecture-friendly framework.

Abstract

Privacy-preserving model co-training in medical research is often hindered by server-dependent architectures incompatible with protected hospital data systems and by the predominant focus on relative effect measures (hazard ratios) which lack clinical interpretability for absolute survival risk assessment. We propose FedRD, a communication-efficient framework for federated risk difference estimation in distributed survival data. Unlike typical federated learning frameworks (e.g., FedAvg) that require persistent server connections and extensive iterative communication, FedRD is server-independent with minimal communication: one round of summary statistics exchange for the stratified model and three rounds for the unstratified model. Crucially, FedRD provides valid confidence intervals and hypothesis testing--capabilities absent in FedAvg-based frameworks. We provide theoretical guarantees by establishing the asymptotic properties of FedRD and prove that FedRD (unstratified) is asymptotically equivalent to pooled individual-level analysis. Simulation studies and real-world clinical applications across different countries demonstrate that FedRD outperforms local and federated baselines in both estimation accuracy and prediction performance, providing an architecturally feasible solution for absolute risk assessment in privacy-restricted, multi-site clinical studies.

Communication-Efficient Federated Risk Difference Estimation for Time-to-Event Clinical Outcomes

TL;DR

This work tackles privacy-preserving estimation of absolute time-to-event risk differences across multiple sites by introducing FedRD, a server-independent federated framework. It develops two estimators: FedRD-U for homogeneous baselines (3 communication rounds) and FedRD-S for heterogeneous baselines (1 round), both with theoretical guarantees of asymptotic equivalence to pooled analysis and valid inference via sandwich covariance. Through simulations and real-world data (MIMIC and SGH), FedRD achieves RD estimates and predictive performance comparable to pooled analyses and consistently outperforms local and meta-analytic baselines, while requiring minimal inter-site communication. The approach enables robust absolute risk assessment in privacy-restricted, multi-site clinical studies, offering a practical alternative to traditional FL architectures that rely on central servers. This work thus advances privacy-preserving survival analysis by delivering accurate, inference-enabled RD estimates in a communication-efficient, architecture-friendly framework.

Abstract

Privacy-preserving model co-training in medical research is often hindered by server-dependent architectures incompatible with protected hospital data systems and by the predominant focus on relative effect measures (hazard ratios) which lack clinical interpretability for absolute survival risk assessment. We propose FedRD, a communication-efficient framework for federated risk difference estimation in distributed survival data. Unlike typical federated learning frameworks (e.g., FedAvg) that require persistent server connections and extensive iterative communication, FedRD is server-independent with minimal communication: one round of summary statistics exchange for the stratified model and three rounds for the unstratified model. Crucially, FedRD provides valid confidence intervals and hypothesis testing--capabilities absent in FedAvg-based frameworks. We provide theoretical guarantees by establishing the asymptotic properties of FedRD and prove that FedRD (unstratified) is asymptotically equivalent to pooled individual-level analysis. Simulation studies and real-world clinical applications across different countries demonstrate that FedRD outperforms local and federated baselines in both estimation accuracy and prediction performance, providing an architecturally feasible solution for absolute risk assessment in privacy-restricted, multi-site clinical studies.
Paper Structure (35 sections, 2 theorems, 58 equations, 6 figures, 6 tables, 2 algorithms)

This paper contains 35 sections, 2 theorems, 58 equations, 6 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Background
  2. Related works and limitations
  3. Contributions
  4. Methods
  5. Preliminaries
  6. Federated risk difference estimation via unstratified additive risk model
  7. Federated setting
  8. Federated risk difference estimation via stratified additive risk model
  9. Theoretical Guarantees
  10. Simulation Studies
  11. Simulation setup
  12. Scenario 1: Homogeneous baseline hazards.
  13. Scenario 2: Heterogeneous baseline hazards.
  14. Results
  15. Real Data Application
  16. ...and 20 more sections

Key Result

Theorem 3.1

Under the unstratified additive hazards model and above conditions, let $\hat{\bm{\beta}}_{U}$ be the solution to the estimating equation m4, with above conditions C1--C6, we have: where and with $\mu(t)=E(\bm{X}\mid Y(t)=1)$.

Figures (6)

  • Figure 1: Workflow of FedRD. Each site computes and shares only summary statistics (SS); the exact forms and computations are described in the Methods section. The coordinator performs only aggregation and broadcasting—no iterative optimization—and can be any participating site; no central server is required.
  • Figure 2: Survival risk difference estimates under heterogeneous baseline hazards. Box plots show the distribution of estimated risk differences across 500 replications for five methods: FedRD-U, FedRD-S, Pooled, Meta, and Local. Site sample sizes are $n_1=100$, $n_2=100$, $n_3=500$, $n_4=1000$, and $n_5=1000$ (configuration (ii), imbalanced). Dashed lines indicate true parameter values.
  • Figure 3: Performance of Local, Meta, Pooled, FedRD-S, and ODACH methods evaluated on MIMIC and three SGH sites. Error bars show 95% confidence intervals.
  • Figure 4: Survival risk difference estimates under homogeneous baseline hazards. Box plots show the distribution of estimated risk differences across 500 replications for five methods: FedRD-U, FedRD-S, Pooled, Meta, and Local. Site sample sizes are $n_{1}=n_{2}=n_{3}=n_{4}=n_{5}=100$ (configuration (i), balanced). Dashed lines indicate true parameter values.
  • Figure 5: Survival risk difference estimates under heterogeneous baseline hazards. Box plots show the distribution of estimated risk differences across 500 replications for five methods: FedRD-U, FedRD-S, Pooled, Meta, and Local. Site sample sizes are $n_{1}=n_{2}=n_{3}=n_{4}=n_{5}=100$ (configuration (i), balanced). Dashed lines indicate true parameter values.
  • ...and 1 more figures

Theorems & Definitions (4)

  • Theorem 3.1: Asymptotic Normality of FedRD-U
  • Theorem 3.2: Asymptotic Normality of FedRD-S
  • proof
  • proof