  Current source density (CSD) power asymmetry, a measure derived from
electroencephalography (EEG), is a potential biomarker for major depressive
disorder (MDD). Though this measure is functional in nature (defined on the
frequency domain), it is typically reduced to a scalar value prior to analysis,
possibly obscuring the relationship between brain function and MDD. To overcome
this issue, we sought to fit a functional regression model to estimate the
association between CSD power asymmetry and MDD diagnostic status, adjusting
for age, sex, cognitive ability, and handedness using data from a large
clinical study. Unfortunately, nearly 40\% of the observations were missing
either their functional EEG data, their cognitive ability score, or both. In
order to take advantage of all of the available data, we propose an extension
to multiple imputation by chained equations that handles both scalar and
functional data. We also propose an extension to Rubin's Rules for pooling
estimates from the multiply imputed data sets in order to conduct valid
inference. We investigate the performance of the proposed extensions in a
simulation study and apply them to our clinical study data. Our analysis
reveals that the association between CSD power asymmetry and diagnostic status
depends on both age and sex.
