Federated Survival Analysis in Healthcare: A Multi-Model Evaluation on Cross-Institutional Heterogeneous Breast Cancer Data

Technical Summary: Federated Survival Analysis in Healthcare

Problem Statement
Survival analysis is critical for clinical decision-making in oncology, particularly for breast cancer, where estimating time-to-event outcomes (e.g., death, relapse) informs prognosis and treatment. However, developing robust models requires large, diverse cohorts, which are rarely available at a single institution due to the decentralized nature of healthcare data. Furthermore, privacy regulations (e.g., GDPR, HIPAA) prevent the centralization of patient records. While Federated Learning (FL) offers a privacy-preserving alternative by training shared models without exchanging raw data, its effectiveness for survival modeling under realistic, heterogeneous conditions remains insufficiently understood. Existing literature often focuses on single model families or proposes new algorithms evaluated in isolation, lacking systematic comparisons across different model architectures and training paradigms. Additionally, there is a scarcity of practical, decision-oriented guidance for selecting models and training strategies based on specific data characteristics, privacy constraints, and resource limitations.

Methodology
The study presents a systematic, multi-model evaluation of federated survival analysis using the Fed-TCGA-BRCA dataset from the FLamby benchmark suite. This dataset comprises clinical, pathological, and molecular profiles of 1,088 breast cancer patients across six institutions, exhibiting natural cross-institutional heterogeneity in sample sizes, event rates, and follow-up times.

The evaluation compares three representative survival models:

1. Cox Proportional Hazards (CoxPH): A semi-parametric statistical baseline.
2. DeepSurv: A deep-learning extension of CoxPH using neural networks to model non-linear covariate effects.
3. Random Survival Forest (RSF): A tree-ensemble method that captures non-linear relationships without parametric assumptions.

These models were trained under three paradigms:

• Centralized: All data pooled (best-case reference).
• Local: Independent training on each client's data (lower-bound baseline).
• Federated: Collaborative training via a central server without data sharing.

For gradient-based models (CoxPH and DeepSurv), three federated optimization strategies were assessed: FedAvg (standard averaging), FedProx (adding a proximal term to limit local drift), and FedAdam (adaptive server-side optimization). RSF utilized a tree-aggregation approach (FedSurF++) rather than gradient updates.

Experiments were conducted with varying client configurations (3, 4, and 5 clients) to simulate different levels of data heterogeneity. Performance was evaluated using discrimination metrics (Concordance Index/C-Index, Time-Dependent AUC) and calibration metrics (Integrated Brier Score/IBS).

Key Contributions

1. Unified Empirical Comparison: The paper provides a direct comparison of CoxPH, DeepSurv, and RSF across local, federated, and centralized training on a real, multi-institutional breast cancer cohort with naturally heterogeneous distributions.
2. Heterogeneity Analysis: It analyzes how the number and composition of participating clients affect both discrimination and calibration, revealing that performance depends more on the diversity of data distributions than the sheer number of clients.
3. Optimization Strategy Evaluation: It assesses the robustness of FedAvg, FedProx, and FedAdam for gradient-based survival models under heterogeneous conditions.
4. Decision-Oriented Guidelines: The study derives practical guidelines mapping specific constraints (data heterogeneity, privacy, interpretability, computational resources) to recommended model and training-paradigm choices.

Results

• Federated vs. Local/Centralized: Federated learning consistently outperformed local training and approached, and occasionally exceeded, centralized performance. Notably, DeepSurv in the federated setting achieved higher discrimination (C-Index: 0.727) than centralized training (0.707) in the 5-client configuration, suggesting that the aggregation of heterogeneous updates may act as a regularizer.
• Model Performance:
  • RSF demonstrated the best overall balance of discrimination, calibration, and robustness across heterogeneous clients. It consistently achieved the lowest IBS (best calibration) and stable performance across clients.
  • DeepSurv showed strong predictive capability, often matching or exceeding centralized performance in federated settings, though it exhibited slightly higher variability than RSF.
  • CoxPH performed well in homogeneous settings but showed lower discrimination and higher variability under heterogeneity, likely due to its reliance on proportional hazards assumptions and global risk sets.
• Optimization Strategies: FedAvg and FedProx proved to be stronger and more stable than FedAdam for both CoxPH and DeepSurv. FedAdam consistently yielded lower discrimination performance and higher IBS values. FedProx offered marginal gains over FedAvg in highly heterogeneous scenarios (e.g., 3-client configuration for DeepSurv).
• Impact of Client Composition: Reducing the number of clients did not monotonically degrade performance; rather, the specific data distributions of the excluded clients mattered. Calibration (IBS) was particularly sensitive to the diversity of observed survival times and event patterns, degrading when specific client distributions were excluded.

Significance and Claims
The paper claims that federated survival analysis is a viable and effective approach for healthcare, offering a privacy-preserving alternative that can match or surpass centralized performance without data centralization. The study highlights that RSF is the most robust choice for heterogeneous, real-world federated settings, offering the best trade-off between discrimination and calibration. Conversely, CoxPH remains preferable for scenarios prioritizing interpretability or where data is homogeneous.

The authors emphasize that the choice of model and training strategy should be driven by specific constraints:

• For heterogeneous clients or calibration-critical applications, RSF with federated training is recommended.
• For interpretability-focused studies, CoxPH is preferred despite lower predictive performance in heterogeneous settings.
• For scarce or imbalanced data, federated training with RSF or DeepSurv significantly improves performance over local training.
• For strict privacy constraints, federated approaches are shown to be practical solutions that approximate centralized performance.

The study concludes that while federated learning is effective, its success is governed by the diversity of client distributions rather than just the number of participants, and that simpler aggregation strategies like FedAvg often suffice over more complex adaptive methods like FedAdam in this specific context.