DESIGN OF EXPERIMENTS

Abstract In this article the author reviews and presents the theory involved in the design of experiments for parameter estimation, a process of importance for pharmacokinetics, the study of intermediary metabolism and other sections of biological research. The design of experiments involves both formal and informal aspects. The formal theories of identifiability of parameters and model distinguishability, and the generation of optimal sampling schedules, play major roles. After presenting these theories, both the formal and informal aspects are studied in the examination of a simple but realistic example.

[1]  J A Jacquez,et al.  Parameter estimation: local identifiability of parameters. , 1990, The American journal of physiology.

[2]  K. Popper,et al.  The Logic of Scientific Discovery , 1960 .

[3]  J. Jacquez,et al.  Numerical parameter identifiability and estimability: Integrating identifiability, estimability, and optimal sampling design , 1985 .

[4]  J J DiStefano,et al.  Multiexponential, multicompartmental, and noncompartmental modeling. I. Methodological limitations and physiological interpretations. , 1984, The American journal of physiology.

[5]  Keith Godfrey,et al.  Compartmental Models and Their Application , 1983 .

[6]  Eric Walter,et al.  Qualitative and quantitative experiment design for phenomenological models - A survey , 1990, Autom..

[7]  Eric Walter,et al.  Identifiability of parametric models , 1987 .

[8]  H. Rabitz,et al.  Similarity transformation approach to identifiability analysis of nonlinear compartmental models. , 1989, Mathematical biosciences.

[9]  R. A. Fisher,et al.  Design of Experiments , 1936 .

[10]  Claudio Cobelli,et al.  Optimal Design of Multioutput Sampling Schedules - Software and Applications to Endocrine - Metabolic and Pharmacokinetic Models , 1985, IEEE Transactions on Biomedical Engineering.

[11]  K R Godfrey,et al.  A methodology for compartmental model indistinguishability. , 1989, Mathematical biosciences.

[12]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[13]  Ling Zhang,et al.  Indistinguishability and identifiability analysis of linear compartmental models. , 1991, Mathematical biosciences.

[14]  Yves Lecourtier,et al.  Identifiability and distinguishability testing via computer algebra , 1985 .

[15]  John A. Jacquez,et al.  Qualitative Theory of Compartmental Systems , 1993, SIAM Rev..

[16]  K R Godfrey,et al.  Indistinguishability for a class of nonlinear compartmental models. , 1994, Mathematical biosciences.

[17]  S. G. Rosen,et al.  Norepinephrine metabolism in humans. Kinetic analysis and model. , 1987, The Journal of clinical investigation.

[18]  J. L. Steimer,et al.  Variability in drug therapy : description, estimation, and control : a Sandoz workshop , 1985 .

[19]  M H Nathanson,et al.  Multiple-objective criteria for optimal experimental design: application to ferrokinetics. , 1985, The American journal of physiology.

[20]  DiStefano Jj rd.  Design and optimization of tracer experiments in physiology and medicine. , 1980 .

[21]  E. H. Twizell.  The mathematical modeling of metabolic and endocrine systems: E.R. Carson, C. Cobelli and L. Finkelstein John Wiley and Sons, Chichester, Sussex, UK, 394 pp., £45.15, 1983 , 1984 .

[22]  Joseph J. DiStefano,et al.  Complete parameter bounds and quasiidentifiability conditions for a class of unidentifiable linear systems , 1983 .

[23]  H. Pohjanpalo.  System identifiability based on the power series expansion of the solution , 1978 .

[24]  Maria Pia Saccomani,et al.  Pride: A Program to Test a Priori Global Identifiability of Linear Compartmental Models , 1994 .

[25]  J J DiStefano,et al.  Optimized blood sampling protocols and sequential design of kinetic experiments. , 1981, The American journal of physiology.

[26]  Jacquez Ja.  Identifiability: the first step in parameter estimation. , 1987 .

[27]  J. Platt.  Strong Inference: Certain systematic methods of scientific thinking may produce much more rapid progress than others. , 1964, Science.

[28]  J. Jacquez.  Compartmental analysis in biology and medicine , 1985 .