Background: ComBat is a promising harmonization method for biomedical imaging data acquired on multiple scanners, but it cannot harmonize by multiple batch effects. In this work, we generalize the ComBat model to incorporate multiple batch effects and modify the estimation algorithm to estimate the corresponding corrections. We evaluate our method, which we refer to as MultiComBat, in simulated data and demonstrate effective harmonization. Methods: In MultiComBat, the standard ComBat model is generalized to incorporate multiple batch variables by taking the sum and product of location and scale parameters across all batch memberships for a sample. The estimation algorithm for MultiComBat frames the method of moments estimation for the hyperparameters of the prior distributions for the location and scale parameters as a system of equations solvable with least squares. The hyperparameters are then used in posterior estimation for the location and scale correction factors needed for final data adjustment. We evaluate the MultiComBat approach by adding simulated batch effects for multiple batch variables to simulated radiomic features. Results: MultiComBat reduced the number of features with significant distribution differences due to multiple batch variables and resulted in more visually similar feature distributions, indicating successful correction of multiple batch effects. Conclusions: Our findings suggest that MultiComBat can be used to harmonize by multiple batch effects and is superior to standard ComBat. Larger studies are warranted to fully validate these findings.
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