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Further Applications

  • Hans-Georg Müller
Part of the Lecture Notes in Statistics book series (LNS, volume 46)

Abstract

The remarks made here concern typical problems in the medical field which can as well be encountered in other fields of application. Longitudinal medical data are not only collected with the aim of description and assessment of the dynamics of some time-dependent physiological or pathological process, but also for purposes of patient monitoring and classification w.r. to prognosis. The data for the prognosis problem usually would consist of a vector of covariates like age, sex and age at diagnosis plus a vector of longitudinal observations per patient. The basic idea is then to extract a few longitudinal parameters from the time course data and to add them to the vector of (stationary) covariates. These vectors are then subjected to discriminant analysis techniques with the aim of selecting the variables that separate best between the groups with good and bad prognosis; one possible method is e.g. CART (Breiman et al, 1982, compare Grossmann, 1985), which has some appealing features in a medical context, like ease of classifying a new case by means of a classification tree. Besides classical longitudinal parameters, also the variability of the observations as measured by \( \hat{\sigma}\) (7.1), (7.2) can be of interest for classification purposes (with prognosis as a special case) as well as more complicated functionals of the curves which would be estimated by evaluating the corresponding functional of the estimated curves. The parameters should be extracted and selected with the ultimate goal of minimizing the misclassification rate which usually is estimated by a cross-validation procedure (see Breiman et al, 1982).

Keywords

Prediction Interval Nonparametric Regression Kernel Estimate Kernel Estimator Epanechnikov Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Hans-Georg Müller
    • 1
    • 2
  1. 1.Institute of Medical StatisticsUniversity of Erlangen-NürnbergErlangenFederal Republic of Germany
  2. 2.Division of StatisticsUniversity of CaliforniaDavisUSA

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