Project Summary
With a rapidly aging world population, understanding, diagnosing, and treating Alzheimer's disease (AD)
is becoming an international imperative. In recent years, a number of large-scale neuroimaging databases
are emerging, which collect multiple imaging modalities from multiple imaging centers, at both the baseline
and repeatedly over a number of years of follow-up. Such multicenter multimodal longitudinal neuroimag-
ing data are particularly useful to understand neurodegenerative disorders such as AD. However, they
pose numerous challenges, including ultrahigh dimensionality, complex spatial and temporal correlations,
high proportion of missing values, data heterogeneity, and lack of formal inference or theoretical guaran-
tee. These challenges have seriously hindered the application of those large neuroimaging databases to
advance our understanding of AD and normal aging. In this proposal, we aim to develop new statistical
methods to address those challenges, and to answer some fundamental questions in the ¿eld of AD and
aging research. Speci¿cally, (1) we develop a new simultaneous covariance inference procedure that
provides an explicit quanti¿cation of statistical signi¿cance, a much improved detection power, a rigorous
theoretical support, and a rigid false discovery control in association analysis of multiple imaging modal-
ities; (2) we develop an integrative version of linear discriminant analysis for multimodal neuroimaging
based classi¿cation and disease diagnosis, and aim to show the method is guaranteed to asymptotically
improve the classi¿cation error rate when using multimodal data than using unimodal data; (3) we develop
a dynamic tensor response regression model that can simultaneously handle the longitudinally correlated
images and the high proportion of missing scans, through a mixture of sparsity and low-rank structures,
fusion regularization and tensor completion; and (4) we propose a heterogeneity correction strategy and
embed it with tensor response regression, which models the change of brain images or brain connectiv-
ity patterns as the disease status or age changes, meanwhile correcting for potential heterogeneity from
multiple imaging sites. Our proposal is motivated by two in vivo studies of AD and normal aging: the
Berkeley Aging Cohort Study and the Alzheimer's Disease Neuroimaging Initiative, while it is also appli-
cable to studies of other neurological disorders. It addresses a number of overarching challenges facing
longitudinal and multimodal neuroimaging analysis, and offers a timely response to the growing demand
for analysis of large neuroimaging databases. It also contributes to novel statistical methodology, and
advances high-dimensional statistical inference theory. Our proposal is to result in a number of useful
tools, in particular, a new computer software, which will be made freely available to both the end users at
UC Berkeley and the neuroscience community at large.