  Alzheimer's disease (AD) is a chronic neurodegenerative condition responsible
for most cases of dementia and considered as one of the greatest challenges for
neuroscience in this century. Early Ad signs are usually mistaken for normal
age-related cognitive dysfunctions, thus patients usually start their treatment
in advanced AD stages, when its benefits are severely limited. AD has no known
cure, as such, hope lies on early diagnosis which usually depends on
neuroimaging techniques such as Positron Emission Tomography (PET). PET data is
then analyzed with Statistical Parametric Mapping (SPM) software, which uses
mass univariate statistical analysis, inevitably incurring in errors derived
from this multiple testing approach. Recently, Wang et al. (2020) formulated an
alternative: applying functional data analysis (FDA), a relatively new branch
of statistics, to calculate mean function and simultaneous confidence corridors
(SCCs) for the difference between two groups' PET values. Here we test this
approach with a practical application for AD diagnosis, estimating mean
functions and SCCs for the difference between AD and control group's PET
activity and locating regions where this difference galls outside estimated
SCCs, indicating differences in brain activity attributable to AD-derived
neural loss. Our results are consistent with previous literature on AD
pathology and suggest that this FDA approach is more resilient to reductions in
sample size and less dependent on ad hoc selection of an {\alpha} level than
its counterpart, suggesting that this novel technique is a promising venue for
research in the field of medical imaging.
