Efficient Experimental Design Strategies in Toxicology and Bioassay
AbstractModelling in bioassay often uses linear or nonlinear logistic regression models, and relative potency is often the focus when two or more compounds are to be compared. Estimation in these settings is typically based on likelihood methods. Here, we focus on the 3-parameter model representation given in Finney (1978) in which the relative potency is a model parameter. Using key matrix results and the general equivalence theorem of Kiefer & Wolfowitz (1960), this paper establishes key design properties of the optimal design for relative potency using this model. We also highlight aspects of subset designs for the relative potency parameter and extend geometric designs to efficient design settings of bioassay. These latter designs are thus useful for both parameter estimation and checking for goodness-of-fit. A typical yet insightful example is provided from the field of toxicology to illustrate our findings.
Atkinson, A.C., Donev, A. N. & Tobias, R.D., 2007, Optimum Experimental Designs, with SAS, Oxford: New York.
Bates, D.M. & Watts, D.G., 2007, Nonlinear Regression Analysis and its Applications, Wiley: New York.
Collett, D., 2003, Modelling Binary Data, 2ndEd., Boca Raton: Chapman & Hall/CRC.
Dobson, A.J. & Barnett, A.G., 2008, An Introduction to Generalized Linear Models, 3rdEd., Boca Raton: CRC Press.
Finney, D.J., 1978, Statistical Method in Biological Assay, 3rdEdition, London: Griffin.
Imrey, P.B., Koch, G.G. & Stokes, M.E., 1982, Categorical Data Analysis: Some Reflections on the Log Linear Model and Logistic Regression. Part II: Data Analysis, Inter. Stat. Rev., 50, 35-63.
Kiefer, J. & Wolfowitz, J., 1960, The Equivalence of Two Extremum Problems, Canad. J. Math., 12, 363-366.
McCullagh, P. & Nelder, J.A., 1989, Generalized Linear Models, 2ndEd., Boca Raton: Chapman & Hall/CRC.
Nemeroff, C.B, Bissette, G., Prange, Jr., A.J., Loosen, P.T., Barlow, T.S. & Lipton, M.A., 1977, Neurotensin: Central Nervous System Effects of a Hypothalamic Peptide, Brain Res., 128, 485-496.
O’Brien, T.E., 2005, Designing for Parameter Subsets in Gaussian Nonlinear Regression Models, J. Data Sci., 3, 179-197.
O’Brien, T.E., Chooprateep, S. & Homkham, N., 2009, Efficient Geometric and Uniform Design Strategies for Sigmoidal Regression Models, S. African Statist. J., 43, 49-83.
O’Brien, T.E. & Funk, G.M., 2003, A Gentle Introduction to Optimal Design for Regression Models, Amer. Statist., 57, 265-267.
SAS Institute Inc., SAS/IML Software Version 9.3.1, Cary, NC.
Seber, G.A.F. & Wild, C.J., 1989, Nonlinear Regression, Wiley: New York.
Silvey, S.D., 1980, Optimal Design, London: Chapman & Hall.
Smith, D.M. & Ridout, M.S., 2003, Optimal Designs for Criteria Involving log(potency) in Comparative Binary Bioassays, J. Stat. Plann. Inf., 113, 617-632.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).