  Federated learning (FL) has received high interest from researchers and
practitioners to train machine learning (ML) models for healthcare. Ensuring
the trustworthiness of these models is essential. Especially bias, defined as a
disparity in the model's predictive performance across different subgroups, may
cause unfairness against specific subgroups, which is an undesired phenomenon
for trustworthy ML models. In this research, we address the question to which
extent bias occurs in medical FL and how to prevent excessive bias through
reward systems. We first evaluate how to measure the contributions of
institutions toward predictive performance and bias in cross-silo medical FL
with a Shapley value approximation method. In a second step, we design
different reward systems incentivizing contributions toward high predictive
performance or low bias. We then propose a combined reward system that
incentivizes contributions toward both. We evaluate our work using multiple
medical chest X-ray datasets focusing on patient subgroups defined by patient
sex and age. Our results show that we can successfully measure contributions
toward bias, and an integrated reward system successfully incentivizes
contributions toward a well-performing model with low bias. While the
partitioning of scans only slightly influences the overall bias, institutions
with data predominantly from one subgroup introduce a favorable bias for this
subgroup. Our results indicate that reward systems, which focus on predictive
performance only, can transfer model bias against patients to an institutional
level. Our work helps researchers and practitioners design reward systems for
FL with well-aligned incentives for trustworthy ML.
