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

Hi Nastia,

» I'd like to understand the correct method to calculate AUC0-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).

• 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 AUC0-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 AUC0-τ in such cases (linear extrapolation for example)?

In PHX not without massive tweaks.
A linear interpolation of t0|C0 and t1|C1 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 t0|C0 and C1|C1. Then the interpolated concentration at t=0 is given by: –t0(C1–C0)/(t1–t0)+C0 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 AUC0-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?

Cheers,
Helmut Schütz

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