Abstract
In pharmacokinetic (PK) studies, blood samples are taken over time on subjects after the administration of a drug to measure the time-course of the plasma drug concentration. In bioequivalence studies, the trapezoidal rule on the sampled time points is often used to estimate the area under the plasma concentration-time curve, a quantity of principal interest. This article investigates the choice of sampling time points to estimate the area under the curve. In particular, we explore the relative merits of several objective functions, those functions which are minimized with respect to the sampling times to obtain an optimal study design. Consequently, we propose an objective function which overcomes some of the deficits of existing choices. We also present a simulated annealing algorithm to perform the minimization. The main benefits of the simulated annealing algorithm are the ease in which it can handle constraints on the sampling schedules and its ability to accommodate a variety of models and objective functions. The manuscript presents optimal sampling times for some key examples of true underlying models.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Atkinson, A.C., Chaloner, K., Herzberg, A.M., Juritz, J.: Optimum experimental designs for properties of a compartmental model. Biometrics 49, 325–337 (1993)
Bailer, A.J., Piegorsch, W.W.: Estimating integrals using quadrature methods with an application in pharmacokinetics. Biometrics 46, 1201–1211 (1990)
Beatty, D., Piegorsch, W.W.: Optimal statistical design for toxicokinetic studies. Stat. Methods Med. Res. 6, 359–376 (1997)
Bohachevsky, I.O., Johnson, M.E., Stein, M.L.: Generalized simulated annealing for function optimization. Technometrics 28, 209–217 (1986)
Chiou, W.L.: Critical evaluation of the potential error in pharmacokinetic studies of using the linear trapezoidal rule method for the calculation of the area under the plasma level-time curve. J. Pharmacokinet. Biopharm. 6, 539–546 (1978)
Duffull, S.B., Retout, S., Mentré, F.: The use of simulated annealing for finding optimal population designs. Comput. Methods Programs Biomed. 69, 25–35 (2002)
FDA guidance. Bioavailability and Bioequivalence Studies for Orally Administered Drug Products—General Considerations (2003)
Gibaldi, M., Perrier, D.: Pharmacokinetics, 2nd edn. Marcel Dekker, New York (1982)
Goffe, W.L., Ferrier, G.D., Rogers, J.: Global optimization of statistical functions with simulated annealing. J. Econom. 60, 65–99 (1994)
Jones, B., Wang, J.: Constructing optimal designs for fitting pharmacokinetic models. Stat. Comput. 9, 209–218 (1999)
Katz, D.: Optimal quadrature points for approximating integrals when function values are observed with error. Math. Mag. 59, 284–290 (1984)
Katz, D., D’Argenio, D.Z.: Experimental design for estimating integrals by numerical quadrature, with applications to pharmacokinetic studies. Biometrics 39, 621–628 (1983)
Kong, F.H., Gonin, R.: Optimal sampling times in bioequivalence tests. J. Biopharm. Stat. 10, 31–44 (2000)
Mentré, F., Mallet, A., Baccar, D.: Optimal design in random-effects regression models. Biometrika 84, 429–442 (1997)
Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A.: Equation of state calculation by fast computing machines. J. Chem. Phys. 21, 1087–1092 (1953)
Retout, S., Duffull, S., Mentré, F.: Development and implementation of the population Fisher information matrix for the evaluation of population pharmacokinetic designs. Comput. Methods Programs Biomed. 65, 141–151 (2001)
Tod, M., Mentré, F., Mallet, A.: Robust optimal design for the estimation of hyperparameters in population pharmacokinetics. J. Pharmacokinet. Biopharm. 26, 689–716 (1998)
Wang, J.: Optimal design for linear interpolation of curves. Stat. Med. 20, 2467–2477 (2001)
Wang, J., Endrenyi, L.: A computationally efficient approach for the design of population pharmacokinetic studies. J. Pharmacokinet. Biopharm. 20, 279–294 (1992)
Westlake, W.J.: Statistical aspects of comparative bioavailability trials. Biometrics 35, 273–280 (1979)
Yeh, K., Kwan, K.: A comparison of numerical integrating algorithms by trapezoidal, Lagrange, and spline approximation. J. Pharmacokinet. Biopharm. 6, 79–98 (1978)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Choi, L., Caffo, B. & Rohde, C. Optimal sampling times in bioequivalence studies using a simulated annealing algorithm. Stat Comput 17, 337–347 (2007). https://doi.org/10.1007/s11222-007-9023-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11222-007-9023-1