Bayesian Federated Inference for regression models based on non-shared medical center data.

Area of Science:

• Biostatistics
• Statistical Modeling
• Machine Learning

Background:

• Regression models require sufficient sample size for accurate parameter estimation.
• Lack of data leads to overfitting and unreliable predictions in medical settings.
• Pooling data across centers is often infeasible due to privacy and logistical constraints.

Purpose of the Study:

• To introduce Bayesian Federated Inference (BFI) as a method to combine statistical results from decentralized data.
• To enable accurate regression model analysis without pooling sensitive data.
• To provide a practical solution for improving predictive accuracy in data-scarce environments.

Main Methods:

• Bayesian Federated Inference (BFI) methodology is applied to analyze local data separately.
• Statistical inference results from individual centers are combined.
• The approach accounts for both homogeneity and heterogeneity across populations in different centers.

Main Results:

• The proposed BFI methodology demonstrates excellent performance in combining statistical inferences.
• The method effectively computes results as if analysis was performed on combined data.
• An R-package has been developed to facilitate these calculations.

Conclusions:

• Bayesian Federated Inference (BFI) offers a viable solution for regression modeling with distributed and private data.
• This approach enhances predictive reliability for new patients despite data limitations.
• The developed R-package supports the practical implementation of BFI in biostatistics and medical research.