📊 statistics

Studying Competing Events with Federated Cumulative Incidence Curves

This paper introduces a novel federated learning method that enables privacy-preserving, multi-site post-market safety surveillance of competing risks by constructing non-parametric cumulative incidence curves, which was applied to reveal that cancer patients with pre-existing non-endocrine autoimmune diseases experience significantly greater loss of event-free survival time due to endocrine immune-related adverse events following immune checkpoint inhibitor treatment compared to those without such history.

Original authors: Malcolm Risk (Serena), Shuang Yang (Serena), Jiang Bian (Serena), Yi Guo (Serena), Hyojung Jang (Serena), Jingchuan (Serena), Guo, Xu Shi, Lili Zhao

Published 2026-07-30

📖 4 min read☕ Coffee break read

CC BY 4.0

Original authors: Malcolm Risk (Serena), Shuang Yang (Serena), Jiang Bian (Serena), Yi Guo (Serena), Hyojung Jang (Serena), Jingchuan (Serena), Guo, Xu Shi, Lili Zhao

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, but the suspects are hiding in different, locked rooms. You can't bring them all into one interrogation room because the rules of privacy forbid it. This is the daily challenge for modern medical researchers who want to study how drugs affect patients. They have access to millions of patient records stored in hospitals across the country, but they cannot simply copy and paste that data into a single file to analyze it. To solve this, scientists use a clever trick called "federated learning." Think of it like a group of detectives who each stay in their own room but pass a single, encrypted notebook back and forth. They update the clues in the notebook based on what they see in their own room, then pass the notebook to the next detective. No one ever sees the raw data of the others, but by the end, the notebook contains the solution to the mystery.

The specific mystery this paper tackles involves "competing risks." In the world of survival analysis, imagine you are waiting for a bus (the event you care about, like a side effect from a drug). But, you might get hit by a car (a different event, like death) before the bus ever arrives. If you get hit by the car, you can never catch the bus. Traditional methods often get confused here, treating the car accident as if you just "left the bus stop" rather than acknowledging you were knocked out of the race entirely. This paper introduces a new way to track these bus-and-car scenarios across all those locked rooms without ever sharing the individual stories of the passengers.

The authors of this paper, a team of statisticians from universities like Michigan and Florida, have built a new algorithm that acts as a "federated cumulative incidence curve." In plain English, this is a way to draw a map showing exactly how likely patients are to experience a specific side effect over time, while accounting for the fact that some might die first. They tested their method using computer simulations, creating fake patient data to see if their "notebook-passing" trick worked as well as if they had been allowed to see all the data at once. The simulations showed that their method was just as accurate as the "gold standard" of pooling all data together, but without the privacy risks. They also compared their approach to other existing methods, like "meta-analysis," which tries to combine results from different studies. Their new method proved to be much more efficient and accurate, especially when dealing with messy real-world data where many patients drop out or die.

To prove their method works in the real world, the team applied it to a massive network of hospitals called OneFlorida+. They looked at 10,281 cancer patients who were treated with a type of immunotherapy called immune checkpoint inhibitors (ICIs). These drugs are powerful, but they can sometimes cause the immune system to attack the body, leading to "immune-related adverse events" (irAEs). The researchers wanted to know: Do patients who already have an autoimmune disease (like lupus or rheumatoid arthritis, but not thyroid issues) get these side effects more often than those who don't?

Using their new federated tool, they found a clear difference. After adjusting for factors like age and other health conditions, they discovered that patients with a pre-existing non-endocrine autoimmune disease lost significantly more time without side effects compared to those without such a history. Specifically, in the first 18 months of treatment, patients with the pre-existing condition lost an average of 4.8 months of "side-effect-free" time to endocrine-related irAEs. In contrast, patients without the pre-existing condition only lost 3.2 months. This suggests that having a prior autoimmune condition makes a patient more vulnerable to these specific drug side effects.

The paper doesn't claim to have solved every problem in medical research, nor does it say this method is perfect for every single scenario. For instance, the authors note that their method calculates the "total effect" of the exposure, which combines the direct risk of the side effect with the indirect risk caused by competing events like death. They acknowledge that teasing apart these two effects would require even more complex tools in the future. However, their work provides a crucial new tool for doctors and regulators. It allows them to see the risks of new treatments for vulnerable groups of patients—like those with autoimmune diseases who were often excluded from early clinical trials—without violating patient privacy. By turning complex, scattered data into a clear, shared picture, this method helps ensure that the next generation of cancer treatments is safer for everyone.

Technical Summary: Studying Competing Events with Federated Cumulative Incidence Curves

Problem Statement
Post-market safety surveillance of medical products increasingly relies on combining Electronic Health Record (EHR) data from multiple institutions to achieve sufficient sample sizes and generalizability. However, privacy concerns and regulatory barriers prevent the sharing of individual-level patient data. While Federated Learning (FL) offers a solution for fitting models across sites without data transfer, existing FL methods for competing risks analysis are limited. Current approaches rely on semi-parametric models (e.g., Fine-Gray) which require proportional hazards assumptions that are difficult to verify in multi-center settings, or pseudo-observation methods that require sharing local risk tables, thereby introducing privacy risks by making individual survival times and event indicators identifiable. Furthermore, there is a lack of non-parametric FL tools that allow for intuitive visualization and causal interpretation of competing risks, such as cumulative incidence curves (CIF) and restricted mean time lost (RMTL).

Methodology
The authors propose a novel non-parametric federated algorithm for estimating cause-specific cumulative incidence functions (CIF) and restricted mean time lost (RMTL) under competing risks, incorporating covariate adjustment via inverse propensity weighting (IPW).

Data Structure: The method handles observational data where patients are followed until an event (e.g., immune-related adverse event [irAE] or death) or censoring. It addresses two competing event types ( $\Omega=1$ for the event of interest, $\Omega=2$ for death) and a binary exposure (e.g., pre-existing autoimmune disease).
Covariate Adjustment: To address confounding in observational data, the method employs IPW. Propensity scores are estimated using a federated Generalized Linear Model (GLM) approach (e.g., renewable estimation or ODAL). These scores are broadcast to all sites to calculate individual weights.
Federated Estimation Process: The algorithm operates in three sequential rounds of communication between sites, ordered by sample size (largest to smallest):
1. Propensity Score Estimation: Federated estimation of GLM coefficients to derive weights.
2. Survival Function Estimation: Using a previously published federated weighted Kaplan-Meier (KM) method to estimate counterfactual survival functions ( $\hat{S}^a(t)$ ) and at-risk functions ( $\hat{Y}^a(t)$ ). To protect privacy, these are transmitted as continuous monotonic polynomial spline functions rather than step functions.
3. CIF Estimation: This is the core innovation. Instead of sharing raw data or risk tables, sites iteratively update the CIF estimate using the empirical influence function.
  - The first site calculates an initial CIF based on local data and converts it to a spline representation.
  - Subsequent sites receive the current spline parameters and update them using their local data. The update rule is derived from the estimating equation $\sum \psi(\hat{F}; o_i) = 0$ , where $\psi$ is the empirical influence function.
  - The update step utilizes a Newton-like method: $\hat{F}^{(r+1)} = \hat{F}^{(r)} + \frac{\text{Residual} + \sum \psi}{\text{Denominator}}$ .
  - This process continues sequentially until all sites are incorporated, yielding a global counterfactual CIF without ever sharing individual patient records.
Inference and RMTL: Variance estimation is performed by summing the squared influence functions across sites. The Restricted Mean Time Lost (RMTL) is calculated as the area under the CIF curve up to a time $\tau$ . Its variance is estimated by integrating the influence function of the CIF, avoiding the need for bootstrapping which is computationally prohibitive in federated settings.

Key Contributions

First Non-Parametric Federated CIF: This is the first method to extend non-parametric competing risks tools (CIF and RMTL) to the federated context, eliminating the need for proportional hazards assumptions required by semi-parametric federated models like ODACoR.
Enhanced Privacy: Unlike pseudo-observation methods that require sharing local risk tables (which can leak individual survival times), this method shares only summary spline parameters and influence function statistics, significantly reducing privacy risks.
Interpretability: The method provides intuitive, clinically meaningful outputs (cumulative incidence curves and time lost) that are easier to communicate to clinicians and regulators than black-box machine learning predictions or complex hazard ratios.
Robustness to Small Sites: The algorithm can accommodate sites with very small sample sizes (even as few as one observation), whereas meta-analysis approaches often require stable site-specific estimates that small sites cannot provide.

Results

Simulations: The method was evaluated across three simulation scenarios with varying event distributions (Exponential and Weibull) and censoring rates. Compared to a pooled "gold standard" analysis, the federated method demonstrated negligible bias and equivalent statistical efficiency. In contrast, meta-analysis approaches showed inferior efficiency (especially under high censoring) and suffered from inflated Type I error rates or reduced power.
Real-World Application: The method was applied to the OneFlorida+ network ( $N=10,281$ $N = 10, 281$ patients, $K=10$ $K = 10$ sites) to study endocrine irAEs following immune checkpoint inhibitor (ICI) treatment in patients with pre-existing non-endocrine autoimmune diseases (AID).
- After covariate adjustment, patients with pre-existing AID lost a mean of 4.8 months (95% CI: 4.3, 5.2) of event-free survival time to endocrine irAEs within the first 18 months.
- This was significantly higher than the 3.2 months (95% CI: 3.1, 3.3) lost by patients without prior AID.
- The study confirmed that pre-existing AID is associated with a higher incidence of endocrine irAEs, providing evidence for a population initially excluded from clinical trials.

Significance and Claims
The authors claim that this work provides a crucial alternative for post-market safety surveillance where data sharing is restricted. By avoiding the proportional hazards assumption, the method offers a more flexible and robust approach for multi-center studies where time-varying effects are common. The ability to generate adjusted cumulative incidence curves and RMTL estimates without sharing patient-level data addresses a critical gap in federated analytics. The authors position this as a tool that enables "informative causal comparison" and "intuitive visualization," facilitating better decision-making for clinicians and regulators regarding adverse event risks in specific patient subgroups. The paper acknowledges that while the method estimates the total effect of exposure (combining direct and indirect effects via competing events), it does not currently separate these effects, suggesting that extending the method to include inverse probability of censoring weighting (IPCW) for direct effect estimation is a direction for future work.

Technical Summary: Studying Competing Events with Federated Cumulative Incidence Curves

More like this