Bioequivalence and Bioavailability Forum

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 λ_z is the one after t_max 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.
$$\small{\begin{matrix}
t_\text{start} & \text{abs}\phantom{0}(\%) & \widehat{\lambda}_\text{z} & \widehat{t}_\text{el} & \text{bias}\phantom{0}(\%)\cr\hline
\hfil t_\text{max} & \sim84.29 & 0.1630 & 4.253 & +6.31\\
2\times t_\text{max} & \sim97.53 & 0.1715 & 4.041 & +1.02\cr
3\times t_\text{max} & \sim99.61 & 0.1727 & 4.013 & +0.32\cr
4\times t_\text{max} & \sim99.94 & 0.1731 & 4.004 & +0.11
\end{matrix}}$$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’ C_max), even starting with the one after t_max 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.

Fine.

<terminology>

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

</terminology>

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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.