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

Santiago Silva, Ghiles Reguig, Neil P Oxtoby, Andre Altmann, Marco Lorenzi

TL;DR

Fed-ComBat addresses batch effects in multi-site studies where data cannot be centralized due to privacy constraints. It generalizes ComBat to preserve nonlinear covariate effects via a flexible kernel $\phi(\mathbf{x}; \boldsymbol{\theta}_g)$ and trains in a federated manner using SGD with FedAVG/FedProx, followed by standard Empirical Bayes harmonization. In experiments on synthetic data and seven neuroimaging cohorts, Fed-ComBat achieves harmonization performance comparable to centralized methods, with the MLP variant capturing nonlinear age effects and producing life-span trajectories consistent with literature. The method offers a privacy-preserving, scalable solution for harmonization in collaborative studies and can be extended to imaging data with CNN-based covariate modeling.

Abstract

The use of multi-centric analyses is crucial for obtaining sufficient sample sizes and representative clinical populations in experimental studies. In this setting, data harmonization techniques are typically employed to address systematic biases and ensure the interoperability of the data. State-of-the-art harmonisation approaches are based on the statistical theory of random effect modeling, allowing to account for either linear of non-linear biases and batch effects. However, optimizing these statistical methods generally requires data centralization at some point during the analysis pipeline, therefore introducing the risk of exposing individual patient information while posing significant data governance issues. To overcome this challenge, in this paper we present Fed-ComBat, a federated framework for batch effect harmonization on decentralized data. Fed-ComBat enables the preservation of nonlinear covariate effects without requiring centralization of data and without prior parametric hypothesis on the variables to account for. We demonstrate the effectiveness of Fed-ComBat against a comprehensive panel of existing approaches based on the state-of-the-art ComBat, along with distributed and nonlinear variants. Our experiments are based on extensive simulated data, and on the analysis of multiple cohorts based on 7 neuroimaging studies comprising healthy controls (CI) and subjects with various disorders such as Parkinson's disease (PD), Alzheimer's disease (AD), and autism spectrum disorder (ASD). Our results show that in a federated settings, Fed-ComBat harmonization exhibits comparable results to centralized methods for both linear and nonlinear cases. On real data, harmonized trajectories of the thickness ofthe right hippocampus across lifespan measured on a set of 7 public studies show comparable results between centralized and federated models and are consistent with the literature when using a nonlinear model. The code is publicly available at: https://gitlab.inria.fr/greguig/fedcombat

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

TL;DR

Fed-ComBat addresses batch effects in multi-site studies where data cannot be centralized due to privacy constraints. It generalizes ComBat to preserve nonlinear covariate effects via a flexible kernel and trains in a federated manner using SGD with FedAVG/FedProx, followed by standard Empirical Bayes harmonization. In experiments on synthetic data and seven neuroimaging cohorts, Fed-ComBat achieves harmonization performance comparable to centralized methods, with the MLP variant capturing nonlinear age effects and producing life-span trajectories consistent with literature. The method offers a privacy-preserving, scalable solution for harmonization in collaborative studies and can be extended to imaging data with CNN-based covariate modeling.

Abstract

The use of multi-centric analyses is crucial for obtaining sufficient sample sizes and representative clinical populations in experimental studies. In this setting, data harmonization techniques are typically employed to address systematic biases and ensure the interoperability of the data. State-of-the-art harmonisation approaches are based on the statistical theory of random effect modeling, allowing to account for either linear of non-linear biases and batch effects. However, optimizing these statistical methods generally requires data centralization at some point during the analysis pipeline, therefore introducing the risk of exposing individual patient information while posing significant data governance issues. To overcome this challenge, in this paper we present Fed-ComBat, a federated framework for batch effect harmonization on decentralized data. Fed-ComBat enables the preservation of nonlinear covariate effects without requiring centralization of data and without prior parametric hypothesis on the variables to account for. We demonstrate the effectiveness of Fed-ComBat against a comprehensive panel of existing approaches based on the state-of-the-art ComBat, along with distributed and nonlinear variants. Our experiments are based on extensive simulated data, and on the analysis of multiple cohorts based on 7 neuroimaging studies comprising healthy controls (CI) and subjects with various disorders such as Parkinson's disease (PD), Alzheimer's disease (AD), and autism spectrum disorder (ASD). Our results show that in a federated settings, Fed-ComBat harmonization exhibits comparable results to centralized methods for both linear and nonlinear cases. On real data, harmonized trajectories of the thickness ofthe right hippocampus across lifespan measured on a set of 7 public studies show comparable results between centralized and federated models and are consistent with the literature when using a nonlinear model. The code is publicly available at: https://gitlab.inria.fr/greguig/fedcombat
Paper Structure (21 sections, 9 equations, 7 figures, 2 tables, 1 algorithm)

This paper contains 21 sections, 9 equations, 7 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Methods
  3. Generalized ComBat model
  4. Federated learning
  5. SGD-ComBat: Flexible and General ComBat optimization
  6. From SGD-ComBat to Fed-ComBat
  7. Materials
  8. Synthetic data
  9. Brain MRI-Data
  10. Image processing
  11. Results
  12. Synthetic data
  13. Brain MRI-data
  14. Discussion and Conclusion
  15. Limitations and Future Directions
  16. ...and 6 more sections

Figures (7)

  • Figure 1: Population pyramid representing the demographics of the real data used in this study. The left panel shows the distribution of sex, the middle panel shows the distribution of age, and the right panel shows the sample size distribution. Cohorts were sorted by ascending median age. The demographics for the population are described in \ref{['tab:demographics']}.
  • Figure 2: Boxplot of the means of the residuals over 50 runs of simulation. The left, center and right plots respectively show the results for linear, non-linear and mixed simulated data. We note that federated models achieve the similar results as their centralized counterparts, for both linear and nonlinear data.
  • Figure 3: Bland-Altman plots and root mean square errors (RMSE) contrasting the different centralized and federated harmonization methods against the groundtruth. We note that the linear models all show higher RMSE compared to the nonlinear ones. The nonlinear models also show more homogeneous data distributions.
  • Figure 4: Brain regions where a generalized additive model (GAM) provides a better fit than a linear model, as measured by the difference in Akaike Information Criterion (AIC) between the two models. The parameters for the GAM are set as in combatgam, with age as a smoothing term, B-splines with 10 degrees of freedom or control points uniformly distributed between the minimum and maximum values, and a maximum polynomial of 3rd degree. A negative difference indicates a better fit with the GAM, while a positive difference indicates a better fit with the linear model.
  • Figure 5: Results of regression using a GAM on the top 4 regions with the most discrepant AIC values on the left and residual plots illustrating goodness of fit of a GAM on the right. From the top to the bottom row: 1) Left ventral diencephalon; 2) Right hippocampus; 3) Left caudal middle frontal gyrus; 4) Left precentral gyrus. On the left, we observe nonlinearity of the trajectories with different rates of atrophy across lifespan. On the right, we see the residuals of the fitted GAM which are centered towards 0 across lifespan, showing that a GAM suitably learns the nonlinearity of the trajectories
  • ...and 2 more figures