Fed-ComBat: A Generalized Federated Framework for Batch Effect Harmonization in Collaborative Studies

In neuroimaging research, the utilization of multi-centric analyses is crucial for obtaining sufficient sample sizes and representative clinical populations. Data harmonization techniques are typically part of the pipeline in multi-centric studies to address systematic biases and ensure the comparability of the data. However, most multi-centric studies require centralized data, which may result in exposing individual patient information. This poses a significant challenge in data governance, leading to the implementation of regulations such as the GDPR and the CCPA, which attempt to address these concerns but also hinder data access for researchers. Federated learning offers a privacy-preserving alternative approach in machine learning, enabling models to be collaboratively trained on decentralized data without the need for data centralization or sharing. In this paper, we present Fed-ComBat, a federated framework for batch effect harmonization on decentralized data. Fed-ComBat extends existing centralized linear methods, such as ComBat and distributed as d-ComBat, and nonlinear approaches like ComBat-GAM in accounting for potentially nonlinear and multivariate covariate effects. By doing so, Fed-ComBat enables the preservation of nonlinear covariate effects without requiring centralization of data and without prior knowledge of which variables should be considered nonlinear or their interactions, differentiating it from ComBat-GAM. We assessed Fed-ComBat and existing approaches on simulated data and multiple cohorts comprising healthy controls (CN) and subjects with various disorders such as Parkinson’s disease (PD), Alzheimer’s disease (AD), and autism spectrum disorder (ASD). Results indicate that Fed-ComBat outperforms centralized ComBat in the presence of nonlinear effects and is comparable to centralized methods such as ComBat-GAM. Using synthetic data, Fed-ComBat is able to better reconstruct the target unbiased function by 35% (RMSE = 0.5952) with respect to d-ComBat (RMSE = 0.9162) and 12% with respect to our proposal to federate ComBat-GAM, d-ComBat-GAM (RMSE= 0.6751) and exhibits comparable results on MRI-derived phenotypes to centralized methods as ComBat-GAM without the need of prior knowledge on potential nonlinearities. ### Competing Interest Statement The authors have declared no competing interest.