Empirical assessment of the assumptions of ComBat with diffusion tensor imaging

Diffusion tensor imaging (DTI) is a magnetic resonance imaging technique that provides unique information about white matter microstructure in the brain but is susceptible to confounding effects introduced by scanner or acquisition differences. ComBat is a leading approach for addressing these site biases. However, despite its frequent use for harmonization, ComBat's robustness toward site dissimilarities and overall cohort size have not yet been evaluated in terms of DTI.

As a baseline, we match $N=358$ participants from two sites to create a "silver standard" that simulates a cohort for multi-site harmonization. Across sites, we harmonize mean fractional anisotropy and mean diffusivity, calculated using participant DTI data, for the regions of interest defined by the JHU EVE-Type III atlas. We bootstrap 10 iterations at 19 levels of total sample size, 10 levels of sample size imbalance between sites, and 6 levels of mean age difference between sites to quantify (i) ${\beta }_{\mathrm{AGE}}$, the linear regression coefficient of the relationship between FA and age; (ii) ${\hat{\gamma }}_{sf}^{*}$, the ComBat-estimated site-shift; and (iii) ${\hat{\delta }}_{sf}^{*}$, the ComBat-estimated site-scaling. We characterize the reliability of ComBat by evaluating the root mean squared error in these three metrics and examine if there is a correlation between the reliability of ComBat and a violation of assumptions.

ComBat remains well behaved for ${\beta }_{\mathrm{AGE}}$ when $N>162$ and when the mean age difference is less than 4 years. The assumptions of the ComBat model regarding the normality of residual distributions are not violated as the model becomes unstable.

Prior to harmonization of DTI data with ComBat, the input cohort should be examined for size and covariate distributions of each site. Direct assessment of residual distributions is less informative on stability than bootstrap analysis. We caution use ComBat of in situations that do not conform to the above thresholds.