Identifying predictive factors via multivariable statistical analysis is for
rare diseases often impossible because the data sets available are too small.
Combining data from different medical centers into a single (larger) database
would alleviate this problem, but is in practice challenging due to regulatory
and logistic problems. Federated Learning (FL) is a machine learning approach
that aims to construct from local inferences in separate data centers what
would have been inferred had the data sets been merged. It seeks to harvest the
statistical power of larger data sets without actually creating them. The FL
strategy is not always feasible for small data sets. Therefore, in this paper
we refine and implement an alternative Bayesian Federated Inference (BFI)
framework for multi center data with the same aim as FL. The BFI framework is
designed to cope with small data sets by inferring locally not only the optimal
parameter values, but also additional features of the posterior parameter
distribution, capturing information beyond that is used in FL. BFI has the
additional benefit that a single inference cycle across the centers is
sufficient, whereas FL needs multiple cycles. We quantify the performance of
the proposed methodology on simulated and real life data.Comment: 19 pages, 3 figures, 4 table