Table 1.

Summary of methods introduced in this work.

	Description	Use Case
Optimized Permutation Nested ComBat (OPNested ComBat)	Updated version of Nested ComBat that optimizes harmonization order by selecting the permutation associated with the smallest number of features with statistically significant differences in distribution due to batch effects	Datasets heterogeneous in multiple imaging parameters
OPNested + GMM ComBat	Generalizes OPNested by adding a mixture model grouping to the list of imaging parameters for OPNested ComBat harmonization	Datasets heterogeneous in multiple imaging parameters with bimodality assumed to be associated with an imaging parameter
OPNested − GMM ComBat	Generalizes OPNested by adding a mixture model grouping to the list of clinical covariates protected during OPNested ComBat harmonization	Datasets heterogeneous in multiple imaging parameters with bimodality assumed to be associated with a clinical covariate of interest