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
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.