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Communication-efficient distributed hazard difference estimation for heterogeneous multi-site survival data

This paper introduces DiSAH, a communication-efficient, non-iterative federated algorithm that enables multi-site estimation of hazard differences for survival analysis without sharing patient-level data, demonstrating superior accuracy and statistical power compared to local models and meta-analysis across diverse clinical datasets.

Original authors: Ziwen Wang, Siqi Li, Marcus Eng Hock Ong, Nan Liu

Published 2026-08-11

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CC BY 4.0

Original authors: Ziwen Wang, Siqi Li, Marcus Eng Hock Ong, Nan Liu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a detective trying to solve a mystery: why do some patients get sick and pass away sooner than others? In the world of medicine, this is called "survival analysis." Doctors look at clues like age, blood pressure, or heart history to predict how long a patient might live. Usually, they use a special math tool to figure out if a specific clue makes the risk of dying go up or down.

For a long time, the best way to solve this mystery was to gather every single patient record from every hospital into one giant pile. But there's a huge problem: patient records are locked away in secret vaults because of privacy laws. Hospitals can't just hand over their data to a central computer. So, they tried a different trick called "federated learning," where hospitals talk to each other without sharing the actual files. However, the old tricks required a constant, live phone line between all the hospitals and a central boss computer. If the internet connection dropped or a hospital's firewall blocked the call, the whole system crashed. Plus, the old methods mostly told doctors relative risk (e.g., "this factor doubles your risk"), which is hard to use when you need to know exactly how many extra deaths a factor causes to make real-world decisions.

This is where a new team of researchers steps in with a clever new invention called DiSAH. Think of DiSAH as a game of "telephone" that doesn't require a phone line at all. Instead of sending the actual patient files or keeping a live connection open, each hospital does the math on its own data and sends back only the final "summary notes." These notes are then combined by any willing hospital acting as a temporary leader. The magic of DiSAH is that it calculates the "hazard difference"—which is like counting the exact number of extra days of life lost or gained due to a specific risk factor—without ever needing a central server or moving a single patient's name.

The researchers tested this idea in two ways. First, they ran computer simulations with fake data from five different "hospitals." They found that DiSAH was just as accurate as if they had actually broken the privacy rules and pooled all the data together. It was much better than just averaging the results from each hospital separately (a method called meta-analysis), which often missed important clues because individual hospitals didn't have enough patients to be sure.

Then, they tried it for real using data from 47,778 emergency room patients from the United States and Singapore. They split the Singapore data into three fake "sites" to mimic a distributed network. The results were impressive: DiSAH successfully identified dangerous risk factors for death within 30 days—such as gender, blood pressure, and heart conditions—that the individual hospitals were too small to detect on their own. It performed just as well as a centralized analysis would have, but it did so while respecting privacy and without needing a permanent internet connection to a central server.

The paper argues that the old methods, which rely on constant server connections and only measure relative risk, are often too clunky or imprecise for modern healthcare needs. By using this new "additive" approach, DiSAH proves that hospitals can collaborate to save lives and allocate resources better, even when they can't share their secret patient files. It's a way to turn many small, isolated puzzles into one big, clear picture, all without ever breaking the rules of privacy.

Technical Summary: DiSAH – Distributed Survival via Additive Hazards

Problem Statement
Multi-site survival analysis is hindered by two primary constraints: privacy regulations that prohibit sharing patient-level data across institutions, and technical barriers where clinical data reside in protected environments behind firewalls that block the persistent server connections required by iterative federated learning methods (e.g., FedAvg, FedProx). Existing distributed survival methods, such as ODAC and ODACH, operate within the Cox proportional hazards framework, yielding hazard ratios (relative risk). However, many clinical and public health decisions require hazard differences (absolute risk), which quantify the absolute change in event rates attributable to risk factors. Currently, no federated method exists to estimate hazard differences without centralizing data or requiring continuous server connectivity.

Methodology
The authors propose DiSAH (Distributed Survival via Additive Hazards), a communication-efficient, privacy-preserving algorithm based on the additive hazards model:
$\lambda(t | X) = \lambda_0(t) + \beta^T X$
where $\beta$ represents the hazard difference (absolute change in hazard per unit covariate change). DiSAH avoids iterative optimization and patient-level data sharing by utilizing a closed-form, non-iterative structure that relies solely on the aggregation of summary statistics.

The framework offers two variants:

DiSAH-U (Unstratified): Designed for settings where sites share a common baseline hazard $\lambda_0(t)$ . It requires three rounds of communication. Sites exchange ordered observed event times to construct a global risk set, followed by the aggregation of summary statistics (covariate sums and weighted sums) to compute the estimator $\hat{\beta}_U$ and its covariance matrix.
DiSAH-S (Stratified): Designed for heterogeneous settings where baseline hazards differ across sites ( $\lambda_{0k}(t)$ ), but covariate effects ( $\beta$ ) are shared. It requires only one round of communication. Each site computes local score function components (summary statistics) which are aggregated by a coordinator to form the global estimator $\hat{\beta}_S$ .

In both variants, the coordinator role is server-independent; any participating site can perform the aggregation and broadcasting. The method establishes asymptotic normality for both estimators and proves that DiSAH-U is asymptotically equivalent to the pooled oracle estimator.

Key Contributions

First Federated Hazard Difference Estimator: DiSAH is the first method to enable the estimation of hazard differences (absolute risk) in a federated setting, addressing a critical gap in survival analysis where relative risk (hazard ratios) is insufficient for resource allocation and triage.
Server Independence and Privacy: Unlike iterative federated methods, DiSAH requires no persistent central server or external connections. It operates entirely on summary statistics, ensuring no patient-level data leaves the originating site.
Communication Efficiency: The algorithm minimizes communication overhead, requiring only 1 or 3 rounds of data exchange depending on the heterogeneity of baseline hazards.
Theoretical Guarantees: The paper provides proofs of asymptotic normality and demonstrates that the unstratified variant achieves efficiency comparable to a centralized pooled analysis.

Results
The authors evaluated DiSAH through simulations and a real-world application involving 47,778 emergency department patients from the US (MIMIC-IV-ED) and Singapore (Singapore General Hospital).

Simulations: Across balanced and imbalanced sample configurations, both DiSAH-U and DiSAH-S produced nearly unbiased estimates with coverage probabilities near the nominal 95% level. They achieved estimation efficiency comparable to the pooled oracle and substantially outperformed meta-analysis (which aggregates local estimates) and local site-specific models, particularly in detecting significant risk factors in smaller sites.
Real-World Application: In the multi-site ED study, DiSAH identified mortality risk factors (e.g., gender, systolic blood pressure, pulse, malignancy) that individual sites lacked the statistical power to detect. DiSAH's discrimination performance (C-index) matched the centralized pooled analysis and significantly outperformed local models and the federated Cox method (ODACH). The lower performance of ODACH suggested that the proportional hazards assumption may not hold in these heterogeneous populations, reinforcing the utility of the additive hazards framework.

Significance and Claims
The paper claims that DiSAH provides a practical solution for collaborative survival analysis in healthcare settings where IT infrastructure varies and data governance prohibits centralization. By enabling the estimation of absolute risk without sharing raw data, DiSAH offers an actionable scale for clinical triage, resource allocation, and health-economic evaluation. The authors emphasize that server-independence is not merely a convenience but a precondition for collaboration in environments with strict firewall constraints. The method bridges the gap between the statistical power of pooled data and the privacy constraints of multi-institutional research, offering a robust alternative when proportional hazards assumptions fail.

Technical Summary: DiSAH – Distributed Survival via Additive Hazards

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