Don’t include tmax [NCA / SHAM]

posted by Helmut Homepage – Vienna, Austria, 2023-12-23 12:46 (203 d 03:27 ago) – Posting: # 23803
Views: 1,424

Hi Raman,

❝ For AUC(0 to inf) for determination of Kel (elimination rate constant), shall we include Tmax point also for lambda _z lower.

In general, no. See this article (scroll down to the section ‘Past and Present’ for some references).

❝ Is there any specific guidance is there to fix lambda z lower or not to take Tmax point

No. However, the earliest time point of the estimation of λz is the one after tmax in the automatic algorithms of standard PK software (Phoe­nix WinNonlin, PKanalix).
Let’s consider a one-compartment model with an absorption half life of 1 h, an elimination half life of 4 h, and last sampling at 24 h. The true \(\small{t_\text{max}=2.67\phantom{0}\text{h}}\). Now we estimate \(\small{\lambda_\text{z}}\) increasing with time.
t_\text{start} & \text{abs}\phantom{0}(\%) & \widehat{\lambda}_\text{z} & \widehat{t}_\text{el} & \text{bias}\phantom{0}(\%)\cr\hline
\hfil t_\text{max} & \sim84.29 & 0.1630 & 4.253 & +6.31\\
2\times t_\text{max} & \sim97.53 & 0.1715 & 4.041 & +1.02\cr
3\times t_\text{max} & \sim99.61 & 0.1727 & 4.013 & +0.32\cr
4\times t_\text{max} & \sim99.94 & 0.1731 & 4.004 & +0.11
\end{matrix}}$$It’s clear that if we would start at \(\small{t_\text{max}}\), the estimate would be biased because absorption is still ongoing. On the other hand, at \(\small{\geq2\times t_\text{max}}\), absorption is practically complete and the bias negligible. That’s the idea of the TTT-method1 (search the forum for details and examples).
If you have a tight sampling schedule (in order to ‘catch’ Cmax), even starting with the one after tmax might still be too early. Say, you sampled every 20 minutes and the automatic algo (in Win­Non­lin’s lingo ‘Best Fit’) suggests to start at 3 h. Then 12.5% are not absorbed yet and the estimate is ‘contaminated’ (bias +5.45%). Hence, visual inspection of fits is mandatory and manual selection of time points necessary. In simulations of two-compartment models visual inspection outperformed automatic methods.2

❝ If Tmax point is included for 20 % subjects, will there be any query from regulators.

No idea.

❝ Both Cmax and AUC(0 to t) are passed.



T is the SI abbreviation of the absolute temperature and t the one for time. Hence, we should use tmax instead of Tmax.


  1. Scheerans C, Derendorf H, Kloft C. Proposal for a Standardised Identification of the Mono-Exponential Ter­mi­nal Phase for Orally Administered Drugs. Biopharm Drug Dispos. 2008; 29(3): 145–57. doi:10.1002/bdd.596.
  2. Noe DA. Performance characteristics of the adjusted r2 algorithm for determining the start of the terminal disposition phase and comparison with a simple r2 algorithm and a visual inspection method. Pharmaceut Stat. 2019; 1–13. doi:10.1002/pst.1979.

Dif-tor heh smusma 🖖🏼 Довге життя Україна! [image]
Helmut Schütz

The quality of responses received is directly proportional to the quality of the question asked. 🚮
Science Quotes

Complete thread:

UA Flag
 Admin contact
23,099 posts in 4,857 threads, 1,646 registered users;
52 visitors (0 registered, 52 guests [including 9 identified bots]).
Forum time: 17:14 CEST (Europe/Vienna)

Imagine if every Thursday your shoes exploded
if you tied them the usual way.
This happens to us all the time with computers,
and nobody thinks of complaining.    Jef Raskin

The Bioequivalence and Bioavailability Forum is hosted by
BEBAC Ing. Helmut Schütz