Non-invasive biomedical imaging
technologies have been widely used in various medical
disciplines for interrogation of the pathophysiology and
pathogenesis of diseases. Functional data are often
generated when diseases features are accessed repeatedly
over time and at multiple spatially interdependent units.
The problem is motivated by a liver cancer study where
patients underwent a dynamic computed tomography (CT)
protocol to enable evaluation of multiple perfusion
characteristics. The study was undertaken with the
objective of determining the effectiveness of using
perfusion characteristics to identify and discriminate
between regions of liver that contain malignant tissues
from normal liver tissue. To reduce model complexity and
simplify the resulting inference, possible spatial
correlation among neighboring units is often neglected. In
this work, we consider a multivariate functional data
model and propose a modified kernel smoothing estimation
to leverage the spatial and temporal correlation. We also
address the companion problem of developing a simultaneous
classification method that that utilizes the inter-unit
correlation information to predict disease state. The
proposed method outperforms conventional functional data
classification approaches in the presence of strong
correlation. The method offers maximal relative
improvement in the presence of temporal sparsity wherein
measurements are obtainable at only a few time points.
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