An alternative method for the estimation of the terminal slope when a few data points are available

Citation
A. Dokoumetzidis et al., An alternative method for the estimation of the terminal slope when a few data points are available, J PHARM SCI, 88(5), 1999, pp. 557-560
Citations number
15
Categorie Soggetti
Pharmacology & Toxicology
Journal title
JOURNAL OF PHARMACEUTICAL SCIENCES
ISSN journal
00223549 → ACNP
Volume
88
Issue
5
Year of publication
1999
Pages
557 - 560
Database
ISI
SICI code
0022-3549(199905)88:5<557:AAMFTE>2.0.ZU;2-Y
Abstract
Phase plane plots are graphical expressions for differential equations plot ing the state derivative dc/dt versus the state c. Using these plots, we de veloped a novel method for the estimation of the terminal slope from time-c oncentration data. The values of the derivatives used for the construction of the phase plane plots were calculated by two different methods of numeri cal differentiation. The first method (D1) is based on the classical calcul ation of slope of the line connecting two successive data points. The alter native method (D2) relies on an initial second-order polynomial interpolati on utilizing three successive data points followed by the calculation of th e derivative at each one of the concentration values. A forced-through-zero linear regression of the phase plane plot data is used to derive an estima te for the slope. For comparative purposes, the standard approach based on the semilogarithmic plot was also applied. For a hypothetical drug absorbed by first-order process into a one-compartment model, simulated time-concen tration data disturbed by a Gaussian zero mean random error with various co efficients of variation were generated. Various sampling schedules, with tw o, three, four, or five data points, were utilized for the estimation of th e terminal slope. Performances of the proposed methods on simulated data we re expressed by means of root-mean-squared error, bias, and standard deviat ion. In all cases, D2 was superior to D1. The D2 method outperforms the sta ndard method in that it furnishes estimates closer to the real values in al l cases when two data points and in most cases when three data points were used. All methods behave similarly when four or five data points were used.