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Statistical Models for Quantitative Bioassay

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Mathematical Modeling in Experimental Nutrition

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 445))

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Abstract

We discuss various statistical approaches useful in the analysis of nutritional dose-response data with a continuous response. The emphasis is on the multivariate case with several predictors. The methods which will be discussed can be classified into parametric models, including change-point models, and nonparametric models, which rely on smoothing methods such as weighted local linear fitting. The methods will be illustrated with the analysis of data generated from a folate depletion-repletion bioassay experiment conducted on rats, where the measured growth rate of the rats is the response variable. We also discuss the biological conclusions that can be drawn from applying various statistical methods to this data set.

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References

  • Bhattacharya P.K. Some aspects of change-point analysis, in: Change-point Problems. Carlstein E; Müller HG; Siegmund D. Eds. Lecture Notes Monograph Series, Vol. 23. Institute of Mathematical Statistics: Hayward, CA. 1994. pp 28–56.

    Chapter  Google Scholar 

  • Bates DM. Nonlinear Regression Analysis and its Applications. John Wiley and Sons: New York. 1988.

    Book  Google Scholar 

  • Carlstein E; Müller HG; Siegmund D; Eds. Change-point Problems. Lecture Notes Monograph Series, Vol. 23. Institute of Mathematical Statistics: Hayward, CA. 1994.

    Google Scholar 

  • Clifford AJ; Bills NA; Peerson JM; Müller HG; Burk GE; Rich KD. A depletion-repletion folate bioassay based on growth and tissue folate concentrations of rats. J Nutr, 1993, 123:926–932.

    CAS  Google Scholar 

  • Fan J; Gijbels I. Local Polynomial Modeling and Its Applications. Chapman and Hall: New York. 1996.

    Google Scholar 

  • Gasser T; Müller HG. Kernel estimation of regression functions. in: Smoothing Techniques for Curve Estimation, Lecture Notes in Mathematics, 757. Springer-Verlag: New York. 1979. pp 23–68.

    Chapter  Google Scholar 

  • Harvard Chart XL Reference Manual. Software Publishing Corporation: Santa Clara, CA. 1995.

    Google Scholar 

  • Hinkley DV. Inference in two-phase regression. J Am Stat Assoc, 1971, 66:736–743.

    Article  Google Scholar 

  • McCullagh P; Neider JA. Generalized Linear Models, 2nd Ed. Chapman and Hall: New York. 1992.

    Google Scholar 

  • Müller HG. Nonparametric Regression Analysis of Longitudinal Data. Lecture Notes in Statistics, Vol. 46. Springer-Verlag: Berlin. 1988.

    Book  Google Scholar 

  • Müller HG; Schmitt T. Choice of number of doses for maximum likelihood estimation for quantal dose-response data. Biometrics, 1990, 46:117–130.

    Article  Google Scholar 

  • Müller HG. Surface and function approximation with nonparametric regression. Rendiconti del Seminario Maternatico e Fisico di Milano, 1993, 63:171–211.

    Article  Google Scholar 

  • Müller HG; Facer MR; Bills NA; Clifford AJ. Statistical interaction model for exchangeability of food folates in a rat growth bioassay. J Nutr, 1996, 126:2585–2592.

    Google Scholar 

  • Neter J; Kutner MH; Nachtsheim CJ; Wasserman W. Applied Linear Statistical Models, 4th Ed. R.D. Irwin: Boston. 1997.

    Google Scholar 

  • Numerical Recipes in FORTRAN, 2nd Ed. Cambridge University Press: New York. 1992.

    Google Scholar 

  • Ruppert D; Wand MP. Multivariate weighted least squares regression. Ann Statist, 1994, 22:1346–1370.

    Article  Google Scholar 

  • S-PLUS Reference Manual. Statistical Sciences, Inc.: Seattle. 1990.

    Google Scholar 

  • Walzern RL; Clifford AJ. Folate deficiency in rats fed diets containing free amino acids or intact proteins. J Nutr, 1988,118:1089–1096.

    Google Scholar 

  • Wand MP; Jones MC. Kernel Smoothing. Chapman and Hall: New York. 1995.

    Google Scholar 

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© 1998 Springer Science+Business Media New York

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Facer, M.R., Müller, HG., Clifford, A.J. (1998). Statistical Models for Quantitative Bioassay. In: Clifford, A.J., Müller, HG. (eds) Mathematical Modeling in Experimental Nutrition. Advances in Experimental Medicine and Biology, vol 445. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1959-5_10

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  • DOI: https://doi.org/10.1007/978-1-4899-1959-5_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1961-8

  • Online ISBN: 978-1-4899-1959-5

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