Bayesian Federated Inference for Survival Models

TL;DR

This paper extends Bayesian Federated Inference to survival models, enabling accurate analysis of medical data across centers without data sharing, demonstrated through simulations and real data with an available R package.

Contribution

It generalizes the BFI methodology from generalized linear models to survival models, maintaining high accuracy without data merging.

Findings

BFI results closely match merged data analysis.

Simulation studies confirm the method's effectiveness.

Real data analysis validates practical applicability.

Abstract

In cancer research, overall survival and progression free survival are often analyzed with the Cox model. To estimate accurately the parameters in the model, sufficient data and, more importantly, sufficient events need to be observed. In practice, this is often a problem. Merging data sets from different medical centers may help, but this is not always possible due to strict privacy legislation and logistic difficulties. Recently, the Bayesian Federated Inference (BFI) strategy for generalized linear models was proposed. With this strategy the statistical analyses are performed in the local centers where the data were collected (or stored) and only the inference results are combined to a single estimated model; merging data is not necessary. The BFI methodology aims to compute from the separate inference results in the local centers what would have been obtained if the analysis had been based on the merged data sets. In this paper we generalize the BFI methodology as initially developed for generalized linear models to survival models. Simulation studies and real data analyses show excellent performance; i.e., the results obtained with the BFI methodology are very similar to the results obtained by analyzing the merged data. An R package for doing the analyses is available.