Bioequivalence and Bioavailability Forum

dear HS !

on the assumption of a one-compartmental open model (i.e. one compartmental absorption and one-compartmental elimination) I think that the lee method should be able to distinguish between the "mixture phase" (i.e. absorption and elimination) after Tmax and the pure elimination phase. You are right that Tmax is not a good starting point in the case of higher order models after extravascular administration.

I have to admit that I never performed simulations for the lee method in combination with extra-vascular compartmental models (I studied models after intravenous bolus administration). however, this discussion motivated me to set-up a few simulation scenarios and check the behaviour of the lee method to estimate the terminal elimination rate in such cases.

best regards

martin

PS.: I would very be happy if you could provide me some real life examples of one-compartmental open models (just parameter estimates no source data) to simulate log-normally distributed concentrations based on these models and check the performance of the lee method to select the elimination phase.

dear Yung-jin Lee !

thank you for considering the function lee. this method was originally developed for IV bolus administration models. please note that the lee method is able to distinguish between a distributive and an elimination phase (after IV bolus administration) based on an optimisation criteria when there are in fact two transport processes. for the example of Lee et al (1990) and using the ols criteria the best fit to the data is simply a straight line indicating that the transport process over time can be characterized by an elimination process only.

when there is a distributive and an elimination process the lee method is able to select phases appropriately. for testing the function I suggest to use also data that have a distributive and an elimination process which is not the case for the example provided. I suppose that your tested data cover only one-compartmental models. in such cases the lee method returns, of course, only a monophasic decline.

using this dataset for an IV bolus administration (R package stats) illustrates the lee method in more detail:
Indo.1 <- Indometh[Indometh$Subject==1,] print(Indo.1)

   Subject time conc
1        1 0.25 1.50
2        1 0.50 0.94
3        1 0.75 0.78
4        1 1.00 0.48
5        1 1.25 0.37
6        1 2.00 0.19
7        1 3.00 0.12
8        1 4.00 0.11
9        1 5.00 0.08
10       1 6.00 0.07
11       1 8.00 0.05

res <- lee(conc=Indo.1$conc, time=Indo.1$time, method='lad', points=2, lt=TRUE)
print(res)

$parms
             initial    terminal
halflife   0.4952051  3.06712387
slope     -0.6078895 -0.09814732
intercept  0.3280636 -0.56601802

$chgpt
[1] 1.753988

this results indicate that the decline over time can be described by a distributive and an elimation phase where the "best" time points used to calculate lambda_z are time points greater 1.754 hours to the last sampling time point. for technical details you may find this paper of interest: Wolfsegger M. J. (2006). The R Package PK for Basic Pharmacokinetics. Biometrie und Medizin, 5:61-68.

summarizing, the lee method works correctly - you just have to interpret the results carefully.

best regards

martin

PS.: I found a dataset for an one-compartmental open model (R package stats). please find below my idea to select appropriate time points for calculation of lambda_z when a drug is given by an extravascular route of administration:
> data <- Theoph[Theoph$Subject==5,] > print(data)
   Subject   Wt Dose  Time  conc
45       5 54.6 5.86  0.00  0.00
46       5 54.6 5.86  0.30  2.02
47       5 54.6 5.86  0.52  5.63
48       5 54.6 5.86  1.00 11.40
49       5 54.6 5.86  2.02  9.33
50       5 54.6 5.86  3.50  8.74
51       5 54.6 5.86  5.02  7.56
52       5 54.6 5.86  7.02  7.09
53       5 54.6 5.86  9.10  5.90
54       5 54.6 5.86 12.00  4.37
55       5 54.6 5.86 24.35  1.57
> Tmax <- max(subset(data, conc==max(conc), select='Time'))
> data <- subset(data, Time>Tmax)
> print(data)
   Subject   Wt Dose  Time conc
49       5 54.6 5.86  2.02 9.33
50       5 54.6 5.86  3.50 8.74
51       5 54.6 5.86  5.02 7.56
52       5 54.6 5.86  7.02 7.09
53       5 54.6 5.86  9.10 5.90
54       5 54.6 5.86 12.00 4.37
55       5 54.6 5.86 24.35 1.57
> res <- lee(conc=data$conc, time=data$Time, method='ols', points=2, lt=FALSE)
> print(res)
$parms
              initial    terminal
halflife  15.70395059  8.24935257
slope     -0.01916906 -0.03649135
intercept  1.00860315  1.08685775

$chgpt
[1] 4.517567

this results indicate that the "best" time points used to calculate lambda_z are time points greater 4.518 hours to the last sampling time point. note that you have to specify the option lt=FALSE as after Tmax there is an absorption and elimination process after extravascular administration. you get the corresponding plot with plot(res,log='y'). you have also the choice to use more robust methods of estimation by using the option method.