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Kalman Filter zur On-Line-Diskriminanz-Analyse von Verlaufskurven

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Multivariate Modelle

Part of the book series: Medizinische Informatik, Biometrie und Epidemiologie ((MEDINFO,volume 74))

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Zusammenfassung

Bisher vorgeschlagene Methoden für die sequentielle Zuordnung bzw. Prognosestellung (z.B. bei Patienten) unter Verwendung wiederholter Messungen werden skizziert. Zur Beurteilung dieser Methoden wird das Zuordnungsproblem in einem allgemeinen parametrischen Rahmen formuliert. Es zeigt sich, daß ein Bayes’scher Zugang der natürlichste ist und die Diskriminanzfunktion auf einem Filtersystem basiert. Für die Verlaufskurven wird eine Modellklasse zugrundegelegt, welches den von Laird & Ware (1982) beschriebenen Modellen für Repeated Measurements verwandt ist. Es wird ein sequentieller Diskriminanzanalyse - Algorithmus entwickelt, der auf einem nichtlinearen (adaptiven) Filter für das Trainings - Sample und einer Kombination von zwei Kaiman - Filtern für die Diskriminanzfunktion beruht. Schließlich analysieren wir ein biologisches Beispiel.

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Referenzen

  • Afifi, A. A., Sacks, S. T., Liu, V. Y., Weil, M. H. and Shubin, H. (1971). Accumulative prognostic index for patients with barbiturate, glutethimide and meprobamate intoxication. New England Journal of Medicine 285, 1497.

    Article  Google Scholar 

  • Albert, A. (1983). Discriminant analysis based on multivariate response curves: a descriptive approach to dynamic allocation. Statistics in Medicine 2, 95–106.

    Article  Google Scholar 

  • Albert, A., Chapelle, J. P. and Bourguignat, A. (1984). Dynamic outcome prediction from repeated laboratory measurements made on intensive care unit patients. I. Statistical aspects and logistic models. Scand. J. Clin. Lab. Invest. 44, suppl. 171, 259–268.

    Google Scholar 

  • Altham, P. M. E. (1984). Improving the precision of estimation by fitting a model. J. R. Statist. Soc. B, 46, 118–119.

    MathSciNet  Google Scholar 

  • Anderson, B. D. O. and Moore, J. B. (1979). Optimal Filtering. Englewood Cliffs, N. J.: Prentice-Hall.

    MATH  Google Scholar 

  • Azen, S. P. and Afifi, A. A. (1972a). Two models for assessing prognosis on the basis of successive observations. Math. Biosci. 14, 169.

    Article  Google Scholar 

  • Azen, S. P. and Afifi, A. A. (1972b). Asymptotic and small-sample behavior of estimated Bayes rules for classifying time-dependent observations. Biometrics 28, 989–998.

    Article  MathSciNet  Google Scholar 

  • Azen, S. P., Garcia-Pena, J. and Afifi, A. (1975). Classification of time-dependent observations: The exponential model and the robustness of the linear model. Biom. J. 17, 203–212.

    Article  Google Scholar 

  • Browdy, B. L. (1978). A comparison of procedures for the classification of multivariate time-dependent data. Ph. D. Thesis, Univ. of California, Los Angeles.

    Google Scholar 

  • Browdy, B. L. and Chang, P. C. (1982). Bayes procedures for the classification of multiple polynomial trends with dependent residuals. J. Amer. Statist. Assoc. 77, 483–487.

    Article  MATH  Google Scholar 

  • Chi, E. M. and Reinsei, G. C. (1989). Models for longitudinal data with random effects and AR(1) errors. J. Amer. Statist Assoc. 84, 452–459.

    Article  MathSciNet  Google Scholar 

  • Christi, H. L. (1976). Time dependence and Bayesian approach. In de Dombal, F. T. and Gremy, F. (eds.) Decision Making and Medical Care. 467–476. Amsterdam: North-Holland Publishing Company.

    Google Scholar 

  • Crowder, M. J. and Hand, D. J. (1990). Analysis of Repeated Measures. London: Chapman and Hall.

    MATH  Google Scholar 

  • De Jong, P. (1988). The likelihood for a state space model. Biometrika 75, 165–169.

    Article  MathSciNet  MATH  Google Scholar 

  • Dennis, J. E., Gay, D. M. and Welsch, R. E. (1981). An adaptive nonlinear least-squares algorithm. ACM Transactions on Mathematical Software 7, 348–383.

    Article  MATH  Google Scholar 

  • Diggle, P. J. (1988). An approach to the analysis of repeated measurements. Biometrics 44, 959–971.

    Article  MathSciNet  MATH  Google Scholar 

  • Diggle, P. J. (1990). Time series: a bio statistical introduction. Oxford: Oxford Univ. Press.

    Google Scholar 

  • Ferrante, M. and Runggaldier, W. J. (1990). On necessary conditions for the existence of finite-dimensional filters in discrete time. Systems & Control Letters 14, 63–69.

    Article  MathSciNet  MATH  Google Scholar 

  • Geary, D. N. (1989). Modelling the covariance structure of repeated measurements. Biometrics 45, 1183–1195.

    Article  MATH  Google Scholar 

  • Goodrich, R. L. and Caines, P. E. (1979). Linear system identification from nonstatio-nary cross-sectional data. IEEE Trans, on Automatic Control 24, 403–411.

    Article  MathSciNet  MATH  Google Scholar 

  • Grossmann, W. (1985). Diskrimination und Klassifikation von Verlaufskurven. In: Neuere Verfahren der nichtparametrischen Statistik. G. C. Pflug (Ed.) ( Medizin. Inform, und Statistik, Vol. 60 ). Berlin: Springer.

    Google Scholar 

  • Harville, D. A. (1974). Bayesian inference for variance components using only error contrasts. Biometrika 61, 383–385.

    Article  MathSciNet  MATH  Google Scholar 

  • Harville, D. A. (1976). Extensions of the Gauss-Markov theorem to include the estimation of random effects. Annals of Statistics 4, 384–395.

    Article  MathSciNet  MATH  Google Scholar 

  • Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and to related problems. J. Amer. Statist. Assoc. 72, 320–340.

    Article  MathSciNet  MATH  Google Scholar 

  • Jennrich, R. I. and Schluchter, M. D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics 42, 805–820.

    Article  MathSciNet  MATH  Google Scholar 

  • Jones, R. H. and Ackerson, L. M. (1990). Serial correlation in unequally spaced longitudinal data. Biometrika 77, 721–731.

    Article  MathSciNet  Google Scholar 

  • Jones, R. H. and Boadi-Boateng, F. (1991). Unequally spaced longitudinal data with AR(1) serial correlation. Biometries 47, 161–175.

    Article  Google Scholar 

  • Kaiman, R. E. (1960). A new approach to linear filtering and prediction problems. Trans. ASME, J. Basic Engineering 82, 35–45.

    Article  Google Scholar 

  • Laird, N. M. and Ware, J. H. (1982). Random-effects models for longitudinal data. Biometrics 38, 963–974.

    Article  MATH  Google Scholar 

  • Lee, J. C. (1977). Bayesian classification of data from growth curves. South African Statist J. 11, 155–166.

    MathSciNet  Google Scholar 

  • Lee, J. C. (1982). Classification of growth curves. In: Krishnaiah, P. R. and Kanal, L. N. (eds.) Handbook of Statistics, 2, 121–137. Chichester: Wiley.

    Google Scholar 

  • Mansour, H., Nordheim, E. V., and Rutledge, J. J. (1985). Maximum likelihood estimation of variance components in repeated measures designs assuming autoregressive errors. Biometrics 41, 287–294.

    Article  MathSciNet  MATH  Google Scholar 

  • Maybeck, P. S. ( 1979, 1982). Stochastic Models, Estimation, and Control. Vol. 1, Vol. 2. New York: Academic Press.

    MATH  Google Scholar 

  • Mehra, R. K. (1972). Approaches to adaptive filtering. IEEE Trans, on Autom. Control 17, 693–698.

    Article  MathSciNet  MATH  Google Scholar 

  • Morrison, D. F. (1967). Multivariate statistical methods. New York: McGraw-Hill.

    MATH  Google Scholar 

  • Nagel, P. J. A. and de Waal, D. J. (1979). Bayesian classification, estimation and prediction of growth curves. South African Statist. J. 13, 127–137.

    Google Scholar 

  • Sallas, W. M. and Harville, D. A. (1981). Best linear recursive estimation for mixed linear models. J. Amer. Statist. Assoc. 76, 860–869.

    Article  MathSciNet  MATH  Google Scholar 

  • Sallas, W. M. and Ilarville, D. A. (1988). Noninformative priors and restricted maximum likelihood estimation in the Kaiman filter. In: J. C. Spall (Ed.) Bayesian Analysis of Time Series and Dynamic Models. New York: Marcel Dekker.

    Google Scholar 

  • Schnatter, S. (1988). Dynamische Bayes’sche Modelle und ihre Anwendung zur hydrologischen Kurzfristvorhersage. Dissertation. Technische Universität Wien.

    Google Scholar 

  • Schneider, W. (1986). Der Kaimanfilter als Instrument zur Diagnose und Schätzung variabler Parameter in ökonometrischen Modellen. Heidelberg, Wien: Physica-Verlag.

    Google Scholar 

  • Shumway, R. H. (1982). Discriminant analysis for time series. In: Krishnaiah, P. R. and Kanal, L. N. (eds.) Handbook of Statistics, 2, 1–46. Chichester: Wiley.

    Google Scholar 

  • Ulm, K. (1984). Classification on the basis of successive observations. Biometrics 40, 1131–1136.

    Article  Google Scholar 

  • van Schuppen, J. H. (1979). Stochastic filtering theory: a discussion of concepts, methods, and results. In M. Kohlmann and W. Vogel, (eds.), Stochastic Control Theory and Stochastic Differential Systems, Lect. Notes in Control and Inform. Sei. No. 16, 209–226. Berlin: Springer.

    Chapter  Google Scholar 

  • Welch, M. E. (1987). Classification methods for linear dynamic models. Unpublished Ph. D. Thesis, Univ. of California, Los Angeles.

    Google Scholar 

  • Wilson, P. D. (1988). Autoregressive growth curve and Kaiman filtering. Statistics in Medicine 7, 73–86.

    Article  Google Scholar 

  • Wilson, P. D., Hebel, J. R., and Sherwin, R. (1981). Screening and diagnosis when within-individual observations are Markov-dependent. Biometrics 37, 553–565.

    Article  MATH  Google Scholar 

  • Zeger, S. L., Liang, K. -Y. and Albert, P. S. (1988). Models for longitudinal data: a generalized estimating equation approach. Biometrics 44, 1049–1060.

    Article  MathSciNet  MATH  Google Scholar 

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© 1991 Springer-Verlag Berlin Heidelberg

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Stronegger, WJ. (1991). Kalman Filter zur On-Line-Diskriminanz-Analyse von Verlaufskurven. In: Seeber, G.U.H., Minder, C.E. (eds) Multivariate Modelle. Medizinische Informatik, Biometrie und Epidemiologie, vol 74. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95669-0_6

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  • DOI: https://doi.org/10.1007/978-3-642-95669-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54511-8

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