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Functional data analytic approach of modeling ECG T-wave shape to measure cardiovascular behavior
The T-wave of an electrocardiogram (ECG) represents the ventricular
repolarization that is critical in restoration of the heart muscle to a
pre-contractile state prior to the next beat. Alterations in the T-wave reflect
various cardiac conditions; and links between abnormal (prolonged) ventricular
repolarization and malignant arrhythmias have been documented. Cardiac safety
testing prior to approval of any new drug currently relies on two points of the
ECG waveform: onset of the Q-wave and termination of the T-wave; and only a few
beats are measured. Using functional data analysis, a statistical approach
extracts a common shape for each subject (reference curve) from a sequence of
beats, and then models the deviation of each curve in the sequence from that
reference curve as a four-dimensional vector. The representation can be used to
distinguish differences between beats or to model shape changes in a subject's
T-wave over time. This model provides physically interpretable parameters
characterizing T-wave shape, and is robust to the determination of the endpoint
of the T-wave. Thus, this dimension reduction methodology offers the strong
potential for definition of more robust and more informative biomarkers of
cardiac abnormalities than the QT (or QT corrected) interval in current use.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS273 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Fast DD-classification of functional data
A fast nonparametric procedure for classifying functional data is introduced.
It consists of a two-step transformation of the original data plus a classifier
operating on a low-dimensional hypercube. The functional data are first mapped
into a finite-dimensional location-slope space and then transformed by a
multivariate depth function into the -plot, which is a subset of the unit
hypercube. This transformation yields a new notion of depth for functional
data. Three alternative depth functions are employed for this, as well as two
rules for the final classification on . The resulting classifier has
to be cross-validated over a small range of parameters only, which is
restricted by a Vapnik-Cervonenkis bound. The entire methodology does not
involve smoothing techniques, is completely nonparametric and allows to achieve
Bayes optimality under standard distributional settings. It is robust,
efficiently computable, and has been implemented in an R environment.
Applicability of the new approach is demonstrated by simulations as well as a
benchmark study
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