## partial AUCs [NCA / SHAM]

Dear all,

since partial AUC are required for some MR-products, I’m facing a increasing number of miscalculations in reports…
For users of Phoenix/WinNonlin: Please RTFM (User’s Guide → Noncompartmental Analysis → Partial areas).
If we split the AUC at certain (≥1) cut-off time(s), the sum of partial AUCs should equal AUC0–t. If not, something went wrong in the calculation.

Let’s explore a recent example. A multiphasic release product, cut-off time 4 h, linear-up / logarithmic-down trapezoidal method (data at the end):

Correct:

AUC0–t = 980.78 ng/mL, pAUC0–4 = 54.05 ng/mL, pAUC4–72 = 926.73 ng/mL; Σ pAUC = AUC0–t✔️

Reported:

AUC0–t = 980.78 ng/mL, pAUC0–4 = 54.05 ng/mL, pAUC4–72 = 966.33 ng/mL; Σ pAUC > AUC0–t

What’s going on here? The CRO split the data set at four hours and performed separate NCAs on the splits. Works fine for the first one but fails for the second because naturally all time points <4 h are missing and the software automatically added t=0 and C=0. Consequently the area of the triangle given by $$\small{t_0|C_0,\,t_4|C_0,\,t_4|C_4}$$ was added: $$\small{AUC_{\textit{i}-\textit{i}+1}=\frac{1}{2}(t_{\textit{i}+1}-t_\textit{i})(C_{\textit{i}+1}+C_\textit{i})=\frac{1}{2}(4-0)(19.80+0)=2\times19.80=39.60}$$.

I asked the CRO for the project-file to check. Of course, the “Core output” contained the information:
   Time       Conc.      AUC       h       ng/mL    h*ng/mL ------------------------------  0.0000 @    0.0000    0.0000  4.000      19.80     39.60  4.500      22.80     50.25 ... @) Note - the concentration at dose time was added for extrapolation purposes.

You can’t avoid that. If you think about adding a concentration 0 at 4 hours, you would be punished by

and
*** ERROR 14062: Duplicate time values on data file. Please ensure you have defined a unique profile

There’s another flaw when splitting the data set in case of missings and/or deviations from scheduled sampling time points. Even when the split is performed on the scheduled ones, one might end up with an apples-and-oranges comparison. Contrary to that, partial AUCs in PHX/WNL are calculated exactly for the specified start- / end-times and inter-/extrapolated according to the selected AUC method.

AFAIK, partial AUCs were introduced in PHX/WNL 6.0 (2009!). In earlier versions one has to work with split data sets. In all but the first one: Generate a new column where e.g., new.time = time – cut-off and map this one to time in NCA.

Data and correct calculation:
 t       C   Δ C  Δ AUC  AUC0–t   pAUC4–t  0      0.00       0.00   0.00  0.5    0.00  ↔    0.00   0.00  1      7.23  ↑    1.81   1.81  1.25  10.10  ↑    2.17   3.97  1.5   12.80  ↑    2.86   6.84  1.75  17.60  ↑    3.80   10.64  2     21.50  ↑    4.89   15.52  2.25  18.60  ↓    5.00   20.53  2.5   20.40  ↑    4.88   25.40  3     18.60  ↓    9.74   35.15  3.5   18.60  ↔    9.30   44.45  4     19.80  ↑    9.60   54.05    0.00  4.5   22.80  ↑   10.65   64.70   10.65  5     27.30  ↑   12.53   77.22   23.18  5.5   34.00  ↑   15.33   92.55   38.50  6     40.00  ↑   18.50  111.05   57.00  6.5   38.00  ↓   19.50  130.54   76.50  7     37.30  ↓   18.82  149.37   95.32  7.5   36.30  ↓   18.40  167.76  113.72  8     34.90  ↓   17.80  185.56  131.52  9     35.30  ↑   35.10  220.66  166.92 12     28.30  ↓   95.01  315.68  261.63 24     18.00  ↓  273.16  588.83  534.79 36     11.10  ↓  171.28  760.11  706.06 48      7.01  ↓  106.79  866.90  812.85 72      3.03  ↓  113.88  980.78  926.73   54.05 + 926.73 = 980.78 ✔️

Wrong after splitting (where the first split with AUC0–4 = 54.05 is correct):
 t       C   Δ C  Δ AUC  AUC0–t  0 @    0.00       0.00    0.00  ← automatically added  4     19.80  ↑   39.60   39.60  4.5   22.80  ↑   10.65   50.25  5     27.30  ↑   12.53   62.78  5.5   34.00  ↑   15.33   78.10  6     40.00  ↑   18.50   96.60  6.5   38.00  ↓   19.50  116.10  7     37.30  ↓   18.82  134.92  7.5   36.30  ↓   18.40  153.32  8     34.90  ↓   17.80  171.12  9     35.30  ↑   35.10  206.22 12     28.30  ↓   95.01  301.23 24     18.00  ↓  273.16  574.39 36     11.10  ↓  171.28  745.66 48      7.01  ↓  106.79  852.45 72      3.03  ↓  113.88  966.33   54.05 + 966.33 = 1020.38 > 980.73 ❌

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Helmut Schütz

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