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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
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.
Bates DM. Nonlinear Regression Analysis and its Applications. John Wiley and Sons: New York. 1988.
Carlstein E; Müller HG; Siegmund D; Eds. Change-point Problems. Lecture Notes Monograph Series, Vol. 23. Institute of Mathematical Statistics: Hayward, CA. 1994.
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.
Fan J; Gijbels I. Local Polynomial Modeling and Its Applications. Chapman and Hall: New York. 1996.
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.
Harvard Chart XL Reference Manual. Software Publishing Corporation: Santa Clara, CA. 1995.
Hinkley DV. Inference in two-phase regression. J Am Stat Assoc, 1971, 66:736–743.
McCullagh P; Neider JA. Generalized Linear Models, 2nd Ed. Chapman and Hall: New York. 1992.
Müller HG. Nonparametric Regression Analysis of Longitudinal Data. Lecture Notes in Statistics, Vol. 46. Springer-Verlag: Berlin. 1988.
Müller HG; Schmitt T. Choice of number of doses for maximum likelihood estimation for quantal dose-response data. Biometrics, 1990, 46:117–130.
Müller HG. Surface and function approximation with nonparametric regression. Rendiconti del Seminario Maternatico e Fisico di Milano, 1993, 63:171–211.
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.
Neter J; Kutner MH; Nachtsheim CJ; Wasserman W. Applied Linear Statistical Models, 4th Ed. R.D. Irwin: Boston. 1997.
Numerical Recipes in FORTRAN, 2nd Ed. Cambridge University Press: New York. 1992.
Ruppert D; Wand MP. Multivariate weighted least squares regression. Ann Statist, 1994, 22:1346–1370.
S-PLUS Reference Manual. Statistical Sciences, Inc.: Seattle. 1990.
Walzern RL; Clifford AJ. Folate deficiency in rats fed diets containing free amino acids or intact proteins. J Nutr, 1988,118:1089–1096.
Wand MP; Jones MC. Kernel Smoothing. Chapman and Hall: New York. 1995.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
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
Download citation
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
eBook Packages: Springer Book Archive