Longitudinal ComBat (LongComBat)

Longitudinal ComBat (LongComBat)#

LongComBat extends ComBat to longitudinal neuroimaging data with multiple timepoints per subject [1].

Standard ComBat assumes independent observations, violating the within-subject correlation structure of longitudinal studies. LongComBat preserves these correlations while removing site/scanner effects.

Method#

LongComBat uses a mixed-effects model:

\[Y_{ijsf} = \alpha_f + X_{ijs}\beta_f + \gamma_{sf} + \delta_{sf}\epsilon_{ijs} + \omega_{if}\]

where:

  • \(i\) = subject, \(j\) = timepoint, \(s\) = site, \(f\) = feature

  • \(\omega_{if}\) = random intercept per subject (captures within-subject correlation)

  • \(\gamma_{sf}\), \(\delta_{sf}\) = site-specific location and scale effects (empirical Bayes shrunk)

Key points#

Aspect

Detail

Advantage

Preserves longitudinal within-subject correlations

Requirement

Subject IDs linking multiple timepoints

Limitation

Assumes linear trajectories (use LongComBat-GAM for non-linear)

Use when

Harmonizing multi-scanner longitudinal data (e.g., baseline + follow-up)

Reference#