## AUC0-τ estimation with time deviations [NCA / SHAM]

❝ I'd like to understand the correct method to calculate AUC_{0-τ} […]

Duno what is

*correct*. Just my opinion.

❝ Aiming to calculate concentration at t=0, Phoenix use the minimum observed during the dose interval (from dose time to dose time+tau) for extravascular and infusion data (while for IV bolus data it performs a log-linear regression).

Ha-ha, you’ve read the manual.

**Inserting initial time points**: If a PK profile does not contain an observation at dose time, Phoenix inserts a value using the following rules. (Note that, if there is no dosing time specified, the dosing time is assumed to be zero.)**Extravascular**and**Infusion**data: For single dose data, a concentration of zero is used; for steady-state, the minimum observed during the dose interval (from dose time to dose time +tau) is used.

**IV Bolus**data: Phoenix performs a log-linear regression of first two data points to backextrapolate C0. If the regression yields a slope ≥0, or at least one of the first two y-values is zero, or if one or both of the points is viewed as an outlier and excluded from the Lambda Z regression, then the first observed y-value is used as an estimate for C0. If a weighting option is selected, it is used in the regression.

❝ That is for extravascular or infusion data in the listed dataset first point (time=0) would be replaced by 20, …

Yep, cause it is the minimum within {0, τ}. The concentration 2 at 24.5 is ignored. What a strange idea!

❝ … so that AUC_{0-τ} equals 1325

By the linear trapezoidal method (dammit!)… With lin-up/log-down I get 1298.

❝ […] I was slightly suprised that a difference in one minute should totally change the input data: in fact we throw pre-dose concentration to the bin. Are there another methdos for handling AUC_{0-τ} in such cases (linear extrapolation for example)?

In PHX not without massive tweaks.

A linear interpolation of t

_{0}|C

_{0}and t

_{1}|C

_{1}would give 1.986. Much better than 20. You could ask for the concentration at τ and get 2.388 – higher than the 2 at 24.5 but the fit is not that good. Note that this value confirms what PHX reports for Ctau.

**✔**

Interesting: If you enter in the field 0 you get again 20. As designed but IMHO, stupid.

What I would do:

- Option 1 (substitute the first concentration by Ctau):

Perform an NCA where you ask only for Ctau. Play around with the Data Wizard to get a table with one row and three columns: id (1), Time (0), Conc (2.3875533). Rank your original dataset by Time and specify a new column id. Join with the results of the DW. Rank: sort by id, source Time, Conc. DW: sort by id, source Conc. You get a new table id 1–14, Time –0.017–24.5, Conc_1 your original ones, and Conc_2 2.3875533 in the first row (all others empty). Another DW with a custom transformation, new column Conc, Formula:`if(IsNull(Conc_2), Conc_1, Conc_2)`

. Then a filter, which replaces all Times <0 with 0. This stuff to NCA. AUCtau 1289, Tmin 0 (!), Cmin 2.388 (!).

- Option 2: Linear interpolation (likely better):

Let’s call the first two datapoints t_{0}|C_{0}and C_{1}|C_{1}. Then the interpolated concentration at t=0 is given by: –t_{0}(C_{1}–C_{0})/(t_{1}–t_{0})+C_{0}or 1.986234. Too stupid to come up with a workflow for it. Maybe Mittyri can help.

- What most people do:

Ignore any negative time of the predose samples and replace it with 0.

❝ There are also some more questions about AUC_{0-τ}:

❝ Interval of dosing (τ, 24 hour) is always a constant for all subjects not depending for the actual dose period, isn't it?

Yes. Otherwise you would open Pandora’s box.

❝ What is the best way to handle with BLQ in the end of the dosing period for steady-state?

Lin-up/log-down as usual. Don’t you have any accumulation or is the method lousy?

*Dif-tor heh smusma*🖖🏼 Довге життя Україна!

_{}

Helmut Schütz

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

Science Quotes

### Complete thread:

- AUC0-tau at steady state BNR 2016-03-31 22:46 [NCA / SHAM]
- AUC0-tau at steady state jag009 2016-03-31 23:05
- AUC0-tau at steady state BNR 2016-03-31 23:43
- RTFM Helmut 2016-04-01 00:59
- RTFM BNR 2016-04-01 02:05
- AUC0-τ estimation with time deviations Astea 2019-02-10 16:38
- AUC0-τ estimation with time deviationsHelmut 2019-02-10 19:32
- Cτ for lin and lin-up/log-down Astea 2019-02-10 20:50
- Cτ by lin-/lin, lin-up/log-down, and λz Helmut 2019-02-11 01:45
- inter- vs extra- Astea 2019-02-11 19:46
- inter- vs extra- Helmut 2019-02-12 02:20
- No rule fits all mittyri 2019-02-14 12:55
- one size fits all vs goal posts Astea 2019-02-16 08:33
- one size fits all vs goal posts ElMaestro 2019-02-16 13:33
- Bias etc. Helmut 2019-02-16 14:26

- software: NCA not validated Helmut 2019-02-16 13:59
- no way out for NCA validation? mittyri 2019-02-20 21:22

- Default rules mittyri 2019-02-20 21:40

- one size fits all vs goal posts ElMaestro 2019-02-16 13:33

- one size fits all vs goal posts Astea 2019-02-16 08:33

- inter- vs extra- Astea 2019-02-11 19:46

- Cτ by lin-/lin, lin-up/log-down, and λz Helmut 2019-02-11 01:45

- Cτ for lin and lin-up/log-down Astea 2019-02-10 20:50

- AUC0-τ estimation with time deviationsHelmut 2019-02-10 19:32

- RTFM Helmut 2016-04-01 00:59

- AUC0-tau at steady state BNR 2016-03-31 23:43

- AUC0-tau at steady state jag009 2016-03-31 23:05