Optimal designs for random effect models with correlated errors with applications in population pharmacokinetics

Annals of Applied Statistics

Volumn 4, Issue 3, 2010, Pages 1430-1450

  Dette, Holger ^a   Pepelyshev, Andrey ^b   Holland Letz, Tim ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Asymptotic optimal design density; Compartmental models; Correlated observations; Nonlinear least squares estimate; Random effect models

Indexed keywords

EID: 84865456999     PISSN: 19326157     EISSN: 19417330     Source Type: Journal    
DOI: 10.1214/09-AOAS324     Document Type: Article

References (37)

1. Aarons, L. (1999). Software for population pharmacokinetics and pharmacodynamics. Clinical Pharmacokinetics 36 255-264.
2. Atkinson, A. C. (2008). Examples of the use of an equivalence theorem in constructing optimum experimental designs for random-effects nonlinear regression models. J. Statist. Plann. Inference 138 2595-2606.
3. Atkinson, A. C. and Donev, A. (1992). Optimum Experimental Designs. Clarendon Press, Oxford.
4. Atkinson, A. C., Chaloner, K., Herzberg, A. M. and Juritz, J. (1993). Optimum experimental designs for properties of a compartmental model. Biometrics 49 325-337.
5. Bickel, P. J. and Herzberg, A. M. (1979). Robustness of design against autocorrelation in time I: Asymptotic theory, optimality for location and linear regression. Ann. Statist. 7 77-95.
6. Bickel, P. J., Herzberg, A. M. and Schilling, M. F. (1981). Robustness of design against autocorrelation in time II: Optimality, theoretical and numerical results for the first-order autoregressive process. J. Amer. Statist. Assoc. 76 870-877.
7. Biedermann, S., Dette, H. and Pepelyshev, A. (2004). Maximin optimal designs for a compartmental model. In MODA 7-Advances in Model-Oriented Design and Analysis 41-48. Physica-Verlag, Heidelberg.
8. Box, G. E. P. and Lucas, H. L. (1959). Design of experiments in non-linear situations. Biometrika 46 77-90.
9. Buelga, D. S., del Mar Fernandez de Gatta, M., Herrera, E. V., Dominguez-Gil, A. and Garcia, M. J. (2005). The Bateman function revisited: A critical reevaluation of the quantitative expressions to characterize concentrations in the one compartment body model as a function of time with first-order invasion and first-order elimination. Antimicrobial Agents and Chemotherapy 49 103-128.
10. Chaloner, K. and Verdinelli, I. (1995). Bayesian experimental design: A review. Statist. Sci. 10 237-304.
11. Chernoff, H. (1953). Locally optimal designs for estimating parameters. Ann. Math. Statist. 24 586-602.
12. Colombo, S., Buclin, T., Cavassini, M., Decosterd, L., Telenti, A., Biollaz, J. and Csajka, C. (2006). Population pharmacokinetics of atazanavir in patients with human immunodeficiency virus infection. Antimicrobial Agents and Chemotherapy 50 3801-3808.
13. Dette, H. (1995). Designing of experiments with respect to "standardized" optimality criteria. J. Roy. Statist. Soc. Ser. B 59 97-110.
14. Dette, H. and O'Brien, T. (1999). Optimality criteria for regression models based on predicted variance. Biometrika 86 93-106.
15. Dette, H., Bretz, F., Pepelyshev, A. and Pinheiro, J. C. (2008). Optimal designs for dose finding studies. J. Amer. Statist. Assoc. 103 1225-1237.
16. Fan, S. K. and Chaloner, K. (2003). A geometric method for singular c-optimal designs. J. Statist. Plann. Inference 113 249-257.
17. Fedorov, V. V. (1972). Theory of Optimal Experiments. Academic Press, New York.
18. Fedorov, V. V. and Hackl, P. (1997). Model-Oriented Design of Experiments. Lecture Notes in Statist. 125. Springer, New York.
19. Ford, I., Torsney, B. and Wu, C. F. J. (1992). The use of canonical form in the construction of locally optimum designs for nonlinear problems. J. Roy. Statist. Soc. Ser. B 54 569-583.
20. Gaffke, N. and Krafft, O. (1982). Exact D-optimum designs for quadratic regression. J. Roy. Statist. Soc. Ser. B 44 394-397.
21. Garrett, E. R. (1994). The Bateman function revisited: A critical reevaluation of the quantitative expressions to characterize concentrations in the one compartment body model as a function of time with first-order invasion and first-order elimination. Journal of Pharmacokinetics and Biopharmaceutics 22 103-128.
22. Gibaldi, M. and Perrier, D. (1982). Parmacokinetics, 2nd ed. Dekker, New York.
23. Harville, D. (1976). Extension of the Gauss-Markov theorem to include the estimation of random effects. Ann. Statist. 4 384-395.
24. Mentré, F., Mallet, A. and Baccar, D. (1997). Optimal design in random-effects regression models. Biometrika 84 429-442.
25. Pázman, A. (1986). Foundations of Optimum Experimental Design. D. Reidel, Dordrecht.
26. Pinheiro, J. C. and Bates, D. M. (1995). Approximations to the log-likelihood function in the nonlinear mixed effects model. J. Comput. Graph. Statist. 4 12-35.
27. Pukelsheim, F. (1993). Optimal Design of Experiments. Wiley, New York.
28. Retout, S. and Mentré, F. (2003). Further developments of the Fisher information matrix in nonlinear mixed-effects models with evaluation in population pharmacokinetics. Journal of Biopharmaceutical Statistics 13 209-227.
29. Retout, S., Duffull, S. and Mentre, F. (2001). Development and implementation of the Fisher information matrix for the evaluation of population pharmakokinetic designs. Computer Methods and Programs in Biomedicine 65 141-151.
30. Retout, S., Mentré, F. and Bruno, R. (2002). Fisher information matrix for nonlinear mixed-effects models: Evaluation and application for optimal design of enoxaparin population pharmacokinetics. Stat. Med. 21 2623-2639.
31. Sacks, J. and Ylvisaker, N. D. (1966). Designs for regression problems with correlated errors. Ann. Math. Statist. 37 66-89.
32. Sacks, J. and Ylvisaker, N. D. (1968). Designs for regression problems with correlated errors; many parameters. Ann. Math. Statist. 39 49-69.
33. Schmelter, T. (2007a). Considerations on group-wise identical designs for linear mixed models. J. Statist. Plann. Inference 137 4003-4010.
34. Schmelter, T. (2007b). The optimality of single-group designs for certain mixed models. Metrika 65 183-193.
35. Shargel, L. (1993). Applied Biopharmaceutics and Pharmacokinetics. Chapman & Hall, London.
36. Silvey, S. D. (1980). Optimal Design. Chapman & Hall, London.
37. Thürmann, P., Neff, A. and Fleisch, J. (2004). Interference of Uzara glycosides in assays of digitalis glycosides. International Journal of Clinical Pharmacology and Therapeutics 42 281-284.