## Don’t include tmax [NCA / SHAM]

Hi Raman,

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-method

If you have a tight sampling schedule (in order to ‘catch’

<terminology>

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

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

_{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-method

^{1}(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.

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

<terminology>

* T* is the SI abbreviation of the absolute temperature and

*the one for time. Hence, we should use*

**t****instead of**

*t*_{max}**.**

*T*_{max}- 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.

- Noe DA.
*Performance characteristics of the adjusted r*^{2}*algorithm for determining the start of the terminal disposition phase and comparison with a simple r*^{2}*algorithm and a visual inspection method.*Pharmaceut Stat. 2019; 1–13. doi:10.1002/pst.1979.

—

Helmut Schütz

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Science Quotes

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!_{}Helmut Schütz

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

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### Complete thread:

- Selection of points for Elimination rate constant ryraman2661 2023-12-23 08:41 [NCA / SHAM]
- Don’t include tmaxHelmut 2023-12-23 11:46
- Don’t include tmax ryraman2661 2023-12-26 08:40

- Don’t include tmaxHelmut 2023-12-23 11:46