Abstract
We propose a semiparametric method to estimate model-independent pharmacokinetic (PK) measures such as area under concentration–time, peak concentration and time to peak concentration (Tpeak ), for noisy population PK data from a sparsely sampled prospectively designed trial. The method is developed within the mixed-effect model framework, for the single-dose and steady-state case. We describe individual concentration vs. time using a longitudinal spline, consisting of a template spline, common to all individuals, and an individual-specific distortion spline accounting for individual differences. We impose a number of constraints on the longitudinal spline, including (i) it has a decreasing tail, (ii) its typical Tpeak is near the modal Tpeak observed in the population data, and (iii) its value is zero at time zero (single dose), or the same nonzero value at the beginning and end of a dosing interval (steady state). We test our method using simulated data and compare its performance to that of a parametric and a nonparametric method. An actual data example is also shown. The performance of the method is as good or better than that of a standard nonparametric method, and when the analysis model is misspecified, the method is superior to a standard parametric one. Since it is often not apparent that an analysis model is correct, we propose this approach as a general method for analysis.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
A. C. Collier, R. W. Coombs, D. A. Schoenfeld, R. Bassett, J. Timpone, A. Baruch, M. Jones, and the AIDS Clinical Trials Group. Treatment of human immunodeficiency virus infection with saquinavir, zidovudine and zalcitabine. New Engl. J. Med. 334:1011–1017 (1996).
L. B. Sheiner and L. Z. Benet. Premarketing observational studies of population pharmacokinetics of new drugs. Clin. Pharmacol. Ther. 38:481–487 (1985).
B. Whiting, A. W. Kelman, and J. Grevel. Population pharmacokinetics: Theory and clinical application. Clin. Pharmacokin. 11:387–401 (1986).
L. B. Sheiner and T. M. Ludden. Population pharmacokinetics/dynamics. Ann. Rev. Pharmacol. Toxicol. 32:185–209 (1992).
T. J. Hastie and R. J. Tibshirani. Generalized Additive Models, Chapman and Hall, New York, 1990.
C. DeBoor. A Practical Guide to Splines, Springer-Verlag, New York, 1978.
K. C. Yeh and K. C. Kwan. A comparison of numerical integrating algorithms by trapezoidal, Lagrange, and spline approximation. J. Pharmacokin. Biopharm. 6:79–98 (1978).
L. Yuh, S. Beal, M. Davidian, F. Harrison, A. Hester, K. Kowalski, E. Vonesh, and R. Wolfinger. Population pharmacokinetic/pharmacodynamic methodology and applications: A bibliography. Biometrics 50:566–575 (1994).
K. E. Fattinger, L. B. Sheiner, and D. Verotta. A new method to explore the distribution of interindividual random effects in nonlinear mixed effects models. Biometrics 51:1236–1251 (1995).
M. J. Lindstrom. Self-modelling with random shift and scale parameters and a free-knot spline shape function. Statist. Med. 14:2009–2021 (1995).
D. Verotta. Longitudinal splines. Technical report no. 36, Department of Biostatistics, University of California, San Francisco (1993).
D. Verotta. New approaches to self-modeling nonlinear regression. In D. Z. D'Argenio, (ed.), Advanced Methods of Pharmacokinetic and Pharmacodynamic Systems Analysis, Vol. 2, Plenum Press, New York, 1995, pp. 121–143.
K. E. Fattinger and D. Verotta. A nonparametric subject-specific population method for deconvolution: I. Description, internal validation, and real data examples. J. Pharmacokin. Biopharm. 23:581–610 (1995).
K. E. Fattinger and D. Verotta. A nonparametric subject-specific population method for deconvolution: II. External validation. J. Pharmacokin. Biopharm. 23:611–634 (1995).
J. M. Gries, I. F. Troconiz, D. Verotta, M. Jacobson, and L. B. Sheiner. A pooled analysis of CD4 response to zidovudine and zalcitabine treatment in patients with AIDS and AIDS-related complex. Clin. Pharmacol. Ther. 61:70–82 (1997).
S. L. Beal and L. B. Sheiner. NONMEM Users Guides, NONMEM Project Group, University of California at San Francisco, San Francisco, 1991.
S. L. Beal and L. B. Sheiner. Estimating population kinetics. CRC Crit. Rev. Biomed. Eng. 8:195–222 (1982).
M. Davidian and D. M. Giltinan. Nonlinear Models for Repeated Measurement Data, Chapman and Hall, New York, 1995.
B. Efron and R. J. Tibshirani. An Introduction to the Bootstrap, Chapman and Hall, New York, 1993.
G. Wahba. On the minimization of a quadratic functional subject to a continuous family of linear inequality constraints. SIAM J. Control Optimization 11:64–79 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Park, K., Verotta, D., Blaschke, T.F. et al. A Semiparametric Method for Describing Noisy Population Pharmacokinetic Data. J Pharmacokinet Pharmacodyn 25, 615–642 (1997). https://doi.org/10.1023/A:1025769431364
Published:
Issue Date:
DOI: https://doi.org/10.1023/A:1025769431364