  To estimate accurately the parameters of a regression model, the sample size
must be large enough relative to the number of possible predictors for the
model. In practice, sufficient data is often lacking, which can lead to
overfitting of the model and, as a consequence, unreliable predictions of the
outcome of new patients. Pooling data from different data sets collected in
different (medical) centers would alleviate this problem, but is often not
feasible due to privacy regulation or logistic problems. An alternative route
would be to analyze the local data in the centers separately and combine the
statistical inference results with the Bayesian Federated Inference (BFI)
methodology. The aim of this approach is to compute from the inference results
in separate centers what would have been found if the statistical analysis was
performed on the combined data. We explain the methodology under homogeneity
and heterogeneity across the populations in the separate centers, and give real
life examples for better understanding. Excellent performance of the proposed
methodology is shown. An R-package to do all the calculations has been
developed and is illustrated in this paper. The mathematical details are given
in the Appendix.
