Estimation and inference in pharmacokinetic models: The effectiveness of model reformulation and resampling methods for functions of parameters
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It is well known that high parameter estimate correlations and asymptotic variance estimates can cause estimation and inference problems in the analysis of pharmacokinetic models. In this paper we show that analysis of three important functions of pharmacokinetic parameters, the half-life, mean residence time, and the area under the curve, can sometimes be greatly improved by reformulating the model to address collinearity and by using the bootstrap to form confidence intervals. The resultant estimators can be more accurate than the original ones, and resultant confidence intervals can be narrower. Of the three measures, the half-life estimator is much better behaved than the estimators of mean residence time and area under the curve under collinearity, suggesting that it (or measures like it) should be used more often.
- D. M. Bates and D. G. Watts.Nonlinear Regression Analysis and its Applications, Wiley, New York, 1988.
- D. M. Allen. Parameter estimation for nonlinear models with emphasis on compartmental models.Biometrics 39:629–637 (1983).
- W. J. Westlake. Problems associated with analysis of pharmacokinetic models.J. Pharm. Sci. 60:882–885 (1971).
- H. G. Boxenbaum, S. Riegelman, and R. M. Elashoff. Statistical estimations in pharmacokinetics.J. Pharmacokin. Biopharm. 2:123–148 (1974).
- P. M. Laskarzewski, D. L. Weiner, and L. Ott. A simulation study of parameter estimation in the one and two compartment models.J Pharmacokin. Biopharm. 10:317–334 (1982).
- J. G. Reich. On parameter redundancy in curve fitting of kinetic data. In L. Endrenyi (ed.),Kinetic Data Analysis: Design and Analysis of Enzyme and Pharmacokinetic Experiments, Plenum Press, New York, 1981, pp. 39–50.
- C. M. Metzler. Estimation of pharmacokinetic parameters: Statistical considerations.Pharmacol. Ther. 13:543–556 (1981).
- J. S. Simonoff and C.-L. Tsai. The use of guided reformulations when collinearities are present in nonlinear regression.Appl. Statist. 38:115–126 (1989).
- B. Efron.The Jackknife, the Bootstrap and Other Resampling Plans, SIAM, Philadelphia, 1982.
- W. J. Kennedy, Jr. and J. E. Gentle.Statistical Computing, Marcel Dekker, New York, 1980.
- D. A. Belsley, E. Kuh, and R. E. Welsch.Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, Wiley, New York, 1980.
- D. A. Freedman. Bootstrapping regression models.Ann. Statist. 9:1218–1228 (1981).
- D. A. Freedman and S. C. Peters. Bootstrapping a regression equation: Some empirical results.J. Am. Statist. Assoc. 79:97–106 (1984).
- D. V. Hinkley. Bootstrap methods.J. Royal Statist. Soc. Ser. B. 50:321–337 (1988).
- J. S. Simonoff and C.-L. Tsai. Jackknifing and bootstrapping quasi-likelihood estimators.J. Statist. Comput. Simulation 30:213–232 (1988).
- C. F. J. Wu. Jackknife, bootstrap and other resampling methods in regression analysis (with discussion).Ann. Statist. 14:1261–1350 (1986).
- T. J. DiCiccio and J. P. Romano. A review of bootstrap confidence intervals.J. Royal Statist. Soc. Ser. B 50:338–354 (1988).
- A. C. Davison, D. V. Hinkley, and E. Schechtman. Efficient bootstrap simulation.Biometrika 74:555–566 (1987).
- J. R. Gleason. Algorithms for balanced bootstrap simulations.Am. Statist. 42:263–266 (1988).
- E. S. Soofi. Effects of collinearity on information about regression coefficients.J. Economet. 43: in press.
- IMSL.User's Manual: STAT/LIBRARY, IMSL, Houston, TX, 1987.
- T. S. Weng. Comparison of generalized half-life and mean residence time derived from compartment analysis of pharmacokinetic data.Proc. ASA Biopharm. Sec. pp. 135–141 (1988).
- J. S. Simonoff and C.-L. Tsai. Jackknife-based estimators and confidence regions in nonlinear regression.Technometrics 28:103–112 (1986).
- L. B. Sheiner and S. L. Beal. Pharmacokinetic parameter estimates from several least squares procedures: Superiority of extended least squares.J. Pharmacokin. Biopharm. 13:185–201 (1985).
- S. L. Beal and L. B. Sheiner. Heteroscedastic nonlinear regression.Technometrics 30:327–388 (1988).
- Estimation and inference in pharmacokinetic models: The effectiveness of model reformulation and resampling methods for functions of parameters
Journal of Pharmacokinetics and Biopharmaceutics
Volume 18, Issue 4 , pp 361-377
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers-Plenum Publishers
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- pharmacokinetic modeling
- nonlinear estimation
- Industry Sectors
- Author Affiliations
- 1. Division of Biostatistics, Memorial Sloan-Kettering Cancer Center, 1275 York Avenue, 10021, New York, New York
- 2. Department of Statistics and Operations Research, Leonard N. Stern School of Business, New York University, 90 Trinity Place, 10006, New York, New York